Scilab Textbook Companion for
Engineering Thermodynamics: A Computer
Approach (SI Units Version)
by R. K. Rajput1
Created by
Tanay Bobde
B.Tech
Chemical Engineering
Indian Institute of Technology, BHU
College Teacher
R S Singh
Cross-Checked by
July 31, 2019
1 Funded
by a grant from the National Mission on Education through ICT,
http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab
codes written in it can be downloaded from the ”Textbook Companion Project”
section at the website http://scilab.in
Book Description
Title: Engineering Thermodynamics: A Computer Approach (SI Units Version)
Author: R. K. Rajput
Publisher: Laxmi Pulications (P) Ltd., New Delhi
Edition: 3
Year: 2007
ISBN: 9780763782726
1
Scilab numbering policy used in this document and the relation to the
above book.
Exa Example (Solved example)
Eqn Equation (Particular equation of the above book)
AP Appendix to Example(Scilab Code that is an Appednix to a particular
Example of the above book)
For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means
a scilab code whose theory is explained in Section 2.3 of the book.
2
Contents
List of Scilab Codes
4
2 Basic Concepts Of Thermodynamics
7
3 Properties Of Pure Substances
18
4 First Law of Thermodynamics
40
5 Second Law of Thermodynamics and Entropy
89
6 Availability and Irreversibility
129
7 Thermodynamic Relations
149
8 Ideal and Real Gases
152
9 Gases and Vapour Mixtures
168
10 Psychrometrics
200
11 Chemical Thermodynamics
221
12 Vapour Power Cycles
259
13 Gas Power Cycles
296
3
14 Refrigeration Cycles
350
15 Heat Transfer
379
16 Compressible Flow
405
4
List of Scilab Codes
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
3.1
3.2
3.3
3.4
3.5
3.6
3.7
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
15
16
17
18
19
20
21
22
1 .
2 .
3 .
4 .
5 .
6 .
7 .
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7
8
8
9
9
10
10
11
11
12
12
12
13
14
14
14
15
15
16
16
17
18
18
19
21
21
22
23
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
4.1
4.2
4.3
4.4
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
8 .
9 .
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
1 .
2 .
3 .
4 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
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24
24
26
27
28
28
29
30
30
31
32
33
33
34
35
35
36
37
37
38
38
40
40
41
41
41
42
42
43
44
45
45
46
47
47
48
49
50
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
4.19
4.20
4.21
4.23
4.25
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
19
20
21
23
25
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
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.
51
51
52
53
54
55
56
57
58
58
60
60
62
63
64
65
66
66
67
67
68
68
69
70
70
71
71
72
72
73
74
75
76
78
78
79
80
81
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
4.60
4.61
4.62
4.63
4.64
4.65
4.66
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.30
5.31
5.32
60
61
62
63
64
65
66
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
20
21
23
24
25
26
27
28
29
30
31
32
.
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8
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.
81
82
82
83
85
85
86
89
89
90
90
91
91
92
92
93
93
94
95
96
97
97
98
99
99
100
100
101
102
103
105
105
106
106
107
108
109
110
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
5.33
5.34
5.35
5.36
5.37
5.39
5.40
5.41
5.42
5.44
5.45
5.46
5.47
5.49
5.50
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
6.17
6.18
6.19
6.20
6.21
6.22
7.17
33
34
35
36
37
39
40
41
42
44
45
46
47
49
50
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
20
21
22
17
.
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9
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.
111
112
113
115
117
119
119
120
121
122
123
124
124
125
126
129
130
130
132
132
133
134
134
135
136
137
138
139
139
140
141
142
143
144
145
146
147
149
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
7.18
7.19
7.20
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
18
19
20
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
.
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10
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.
150
150
151
152
153
153
154
156
158
159
160
161
162
163
164
164
165
165
166
168
169
170
172
174
175
176
177
179
181
184
186
188
188
189
190
191
192
194
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
9.20
9.21
9.22
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
10.13
10.14
10.15
10.17
10.18
10.19
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
20
21
22
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
17
18
19
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
11
12
13
14
15
16
17
18
.
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11
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.
196
197
198
200
201
201
202
204
205
207
208
210
211
212
213
214
215
216
217
218
219
221
222
223
223
225
226
227
229
231
233
234
235
236
237
237
238
239
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
11.19
11.20
11.21
11.22
11.23
11.24
11.25
11.26
11.27
11.28
11.29
11.30
11.31
11.32
11.33
11.34
11.35
11.36
11.37
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
12.13
12.14
12.15
12.16
12.17
12.18
12.19
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
.
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12
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240
241
243
245
247
248
249
250
251
252
253
253
254
254
255
255
256
256
257
259
261
262
263
264
265
267
267
268
269
271
272
273
275
276
277
279
281
282
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
12.20
12.21
12.22
12.23
12.24
12.25
12.26
12.27
13.1
13.2
13.3
13.4
13.5
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
13.17
13.18
13.19
13.20
13.21
13.22
13.23
13.24
13.25
13.26
13.27
13.28
13.29
13.30
13.31
13.32
20
21
22
23
24
25
26
27
1 .
2 .
3 .
4 .
5 .
7 .
8 .
9 .
10
11
12
13
14
15
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
.
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13
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282
283
285
288
289
290
292
294
296
297
298
300
301
301
302
302
304
305
306
307
309
311
312
312
313
313
314
316
317
318
319
320
322
323
325
327
330
330
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
13.33
13.34
13.35
13.36
13.37
13.38
13.39
13.40
13.41
13.42
13.43
13.44
13.45
13.46
13.47
13.48
13.49
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
14.15
14.16
14.17
14.18
14.19
14.20
14.21
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
20
21
.
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14
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.
331
332
333
334
335
336
337
338
339
340
340
341
342
344
345
346
348
350
351
351
352
352
353
354
355
355
356
358
359
360
361
362
363
367
368
369
370
371
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
14.22
14.23
14.24
14.25
14.26
14.27
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
15.10
15.11
15.12
15.13
15.14
15.15
15.16
15.17
15.18
15.19
15.20
15.21
15.22
15.23
15.24
15.25
15.26
15.27
15.28
15.29
15.30
15.31
15.32
22
23
24
25
26
27
1 .
2 .
3 .
4 .
5 .
6 .
7 .
8 .
9 .
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
.
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372
373
373
374
376
377
379
379
380
381
382
383
383
384
386
386
387
388
388
389
389
390
390
391
392
393
394
395
396
397
397
399
399
400
401
402
402
403
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
Exa
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
16.15
16.16
16.17
16.18
16.19
1 .
2 .
3 .
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405
405
406
407
407
408
408
409
410
411
411
412
413
413
414
414
415
418
419
Chapter 2
Basic Concepts Of
Thermodynamics
Scilab code Exa 2.1 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
clc
rho_Hg =13596; // kg /mˆ3
g =9.806; //m/ s ˆ2
h =0.76; //m
P = rho_Hg * g * h /1000; // kPa
disp ( ” ( i ) P r e s s u r e o f 80 cm o f Hg” )
h1 =0.80; //m
P1 = h1 / h * P ;
disp ( P1 )
disp ( ” kPa ” )
disp ( ” ( i i ) 30 cm Hg vacuum ” )
H2 =0.30; //cm Hg vacuum
h2 =h - H2 ; //cm o f Hg a b s o l u t e
disp ( ” P r e s s u r e due t o 46 cm o f Hg” )
P2 = h2 / h * P ;
disp ( P2 )
17
20 disp ( ” kPa ” )
21
22 disp ( ” ( i i i ) P r e s s u r e due t o 1 . 3 5 m H2O g a u g e ” )
23 rho_H2O =1000; // kg /mˆ3
24 h3 =1.35; //m
25 P3 = rho_H2O * g * h3 /1000;
26 disp ( P3 )
27 disp ( ” kPa ” )
28
29 disp ( ” ( i v ) 4 . 2 b a r ” )
30 P4 =4.2*10^2;
31 disp ( P4 )
32 disp ( ” kPa ” )
Scilab code Exa 2.2 2
1
2
3
4
5
6
7
8
clc
d =0.1; //m
F =1000; //N
A = %pi /4* d ^2; //mˆ2
P = F / A /10^3;
disp ( ” P r e s s u r e on t h e p i s t o n=” )
disp ( P )
disp ( ”kN/mˆ2 ” )
Scilab code Exa 2.3 3
1
2
3
4
5
6
clc
SG =0.9;
h =1.2; //m
g =9.81; //m/ s ˆ2
rho_w =1000; // kg /mˆ3
rho = SG * rho_w ; // kg /mˆ3
18
7 P = rho * g * h /10^3;
8 disp ( ” Gauge p r e s s u r e P=” )
9 disp ( P )
10 disp ( ”kN/mˆ2 ” )
Scilab code Exa 2.4 4
1 clc
2 Vacuum_recorded =740; //mm o f Hg
3 Barometric_reading =760; //mm o f Hg
4
5 Absolute_pressure =( Barometric_reading -
Vacuum_recorded ) *133.4;
6 disp ( ” A b s o l u t e p r e s s u r e i n t h e c o n d e n s e r=” )
7 disp ( Absolute_pressure )
8 disp ( ”Pa” )
Scilab code Exa 2.5 5
1
2
3
4
5
6
7
8
9
10
clc
d =0.5; //m
h =0.75; //m
m =4; // kg
Manometer_reading =620; //mm o f Hg a b o v e a t m o s p h e r e
Barometer_reading =760; //mm o f Hg
V = %pi /4* d ^2* h ; //mˆ3
disp ( ” ( i ) T o t a l p r e s s u r e i n t h e v e s s e l ” )
P =( Barometer_reading + Manometer_reading ) *133.4/10^5;
// b a r
11 disp ( ”P=” )
12 disp ( P )
13 disp ( ” b a r ” )
19
14 disp ( ” ( i i ) S p e c i f i c volume and d e n s i t y ” )
15 SV = V / m ;
16 disp ( ” S p e c i f i c volume=” )
17 disp ( SV )
18 disp ( ”mˆ3/ kg ” )
19 D = m / V ;
20 disp ( ” D e n s i t y=” )
21 disp ( D )
22 disp ( ” kg /mˆ3 ” )
Scilab code Exa 2.6 6
1
2
3
4
5
6
7
8
9
clc
h0 =.761; //m
h =.55; //m
g =9.79; //m/ s ˆ2
rho =13640; // kg /mˆ3
P = rho * g *( h0 + h ) ; //N/mˆ2
disp ( ” Gas p r e s s u r e=” )
disp ( P /10^5)
disp ( ” b a r ” )
Scilab code Exa 2.7 7
1 clc
2 h_H2O =34; //mm o f Hg
3 g =9.81; //m/ s ˆ2
4 rho =13600; // kg /mˆ3
5 P_Hg =97.5; //mm o f Hg
6 P_atm =760; //mm o f Hg
7 P_H2O = h_H2O /13.6; //mm o f Hg
8 Pabs = rho * g *( P_Hg + P_atm - P_H2O ) /10^8; // b a r
9 disp ( ” a b s o l u t e p r e s s u r e =” )
20
10
11
disp ( Pabs )
disp ( ” b a r ” )
Scilab code Exa 2.8 8
1
2
3
4
5
6
7
8
9
10
11
12
clc
SG =0.8;
rho_H2O =1000; // kg /mˆ3
g =9.81; //msˆ2
h =0.17; //m
Patm =1.01325; // b a r
rho = SG * rho_H2O ; // kg /mˆ3
P_liq = rho * g * h /10^5; // b a r
P_gas = Patm - P_liq ;
disp ( ” g a s p r e s s u r e= ” )
disp ( P_gas )
disp ( ” b a r ” )
Scilab code Exa 2.9 9
1
2
3
4
5
6
7
8
9
10
clc
d =0.2; //m
g =9.81; //m/ s ˆ2
h =0.117; //m
rho =13600; // kg /mˆ3
p = rho * g * h ;
m =( p * %pi /4* d ^2) / g ;
disp ( ” mass=” )
disp ( m )
disp ( ” kg ” )
21
Scilab code Exa 2.10 10
1
2
3
4
5
6
7
8
9
clc
v =800; //m/ s
g =9; //m/ s ˆ2
F =3600; //N
m=F/g;
KE =1/2* m * v ^2/10^6;
disp ( ” K i n e t i c Energy=” )
disp ( KE )
disp ( ”MJ” )
Scilab code Exa 2.11 11
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
clc
m =6; // kg
T1 =25; // 0C
T2 =125; // 0C
disp ( ” ( i ) Heat t r a n s f e r r e d ” )
Q = integrate ( ’m∗ ( 0 . 4 + 0 . 0 0 4 ∗T) ’ , ’T ’ ,T1 , T2 ) ;
disp ( ” h e a t t r a n f e r r e d =” )
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( i i ) Mean s p e c i f i c h e a t o f t h e g a s ” )
c_n = Q / m /( T2 - T1 ) ;
disp ( ”Mean s p e c i f i c h e a t=” )
disp ( c_n )
disp ( ” kJ / kg . 0 C” )
Scilab code Exa 2.12 12
22
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
clc
Ice_point =0;
Steam_point =100;
// t=a ∗ l o g ( p )+b
// from g i v e n c o n d i t i o n s e q u a t i o n s f o r m e d a r e
// a ∗ l o g ( 1 . 5 ) +b=0
// a ∗ l o g ( 7 . 5 ) +b=100
// s o l v i n g e q u a t i o n s
P =[ log (1.5) ,1; log (7.5) ,1];
Q =[0;100];
X = inv ( P ) * Q ;
a = X (1 ,1) ;
b = X (2 ,1) ;
p =3.5;
t = a * log ( p ) + b ;
disp ( ” The v a l u e o f t e m p e r a t u r e i s g i v e n by ” )
disp ( t )
disp ( ” C ” )
Scilab code Exa 2.13 13
1
2
3
4
5
6
7
8
9
10
11
12
clc
deff ( ” [ e ]= f u n c ( t ) ” ,” e =0. 20 ∗ t −5∗10ˆ( −4) ∗ t ˆ2 ” )
t1 =0; // 0C
e1 = func ( t1 ) ;
t2 =100; // 0C
e2 = func ( t2 ) ;
t3 =70; // 0C
e3 = func ( t3 ) ;
t = e3 *( t2 - t1 ) / e2 - e1 ;
disp ( ” t h e r m o c o u p l e w i l l r e a d ” )
disp ( t )
disp ( ” C ” )
23
Scilab code Exa 2.15 15
1
2
3
4
5
6
7
8
clc
p =101.325; // kPa
V2 =0.6; //mˆ3
V1 =0; //mˆ3
W = p *( V2 - V1 ) ;
disp ( ” work done by a t m o s p h e r e=” )
disp ( - W )
disp ( ” kJ ” )
Scilab code Exa 2.16 16
1
2
3
4
5
6
7
8
clc
p =1.013*10^5; //N/mˆ2
V1 =1.5; //mˆ3
V2 =0; //mˆ3
W = p *( V2 - V1 ) ;
disp ( ”W=” )
disp ( W /10^3)
disp ( ” kJ ” )
Scilab code Exa 2.17 17
1
2
3
4
5
clc
T =1.25; //N .m
N =9500;
W1 =2* %pi * N * T /1000; // kJ
p =101.3; // kPa
24
6
7
8
9
10
11
12
13
d =0.65; //m
A = %pi /4* d ^2; //mˆ2
L =0.6; //m
W2 = p * A * L ; // kJ
Wnet =( - W1 ) + W2 ;
disp ( ” The n e t work t r a n s f e r f o r t h e s y s t e m=” )
disp ( Wnet )
disp ( ” kJ ” )
Scilab code Exa 2.18 18
1
2
3
4
5
6
7
8
9
10
clc
A =45*10^( -4) ; //mˆ2
P =0.9*10^5; //N/mˆ2
Patm =1.013*10^5; //N/mˆ2
L =0.05; //m
dV =300*10^( -6) ; //mˆ3
W = P * A *L - Patm * dV ;
disp ( ” n e t work done =” )
disp ( W )
disp ( ” J ” )
Scilab code Exa 2.19 19
1
2
3
4
5
6
7
8
9
clc
p1 =1.5; // b a r
p2 =7.5; // b a r
V1 =3/ p1 ;
V2 =3/ p2 ;
W = integrate ( ’ 3/V∗ 1 0 ˆ 2 ’ , ’V ’ , V1 , V2 ) ;
disp ( ”Work done=” )
disp ( W )
disp ( ” kJ ” )
25
Scilab code Exa 2.20 20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
clc
W =150; // kJ
V1 =0.6; //mˆ3
// p=8−4∗V
// W= i n t e g r a t i o n o f p∗dV from V1 t o V2
// S o l v i n g a b o v e e q u a t i o n we g e t
V2 =0.354; //mˆ3
disp ( ” F i n a l volume =” )
disp ( V2 )
disp ( ”mˆ3 ” )
p2 =8 -4* V2 ;
disp ( ” F i n a l p r e s s u r e =” )
disp ( p2 )
disp ( ” b a r ” )
Scilab code Exa 2.21 21
1
2
3
4
5
6
7
8
9
10
clc
p1 =3*10^5; // Pa
v1 =0.18; //mˆ3/ kg
C = p1 * v1 ^2;
p2 =0.6*10^5; // Pa
v2 = sqrt ( C / p2 ) ;
W = integrate ( ’C/ v ˆ2 ’ , ’ v ’ , v1 , v2 ) ;
disp ( ”Work done=” )
disp ( W )
disp ( ”Nm/ kg ” )
26
Scilab code Exa 2.22 22
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
clc
m =1; // kg
p1 =20*10^5; // Pa
V1 =0.05; //mˆ3
V2 =2* V1 ;
p2 = p1 *( V1 / V2 ) ^2;
C = p1 * V1 ^2;
V3 = V1 ;
W_12 = integrate ( ’C/Vˆ2 ’ , ’V ’ , V1 , V2 ) ;
W_23 = p2 *( V2 - V3 ) ;
W_net = W_12 - W_23 ;
disp ( ” Net work done = ” )
disp ( W_net )
disp ( ”Nm” )
27
Chapter 3
Properties Of Pure Substances
Scilab code Exa 3.1 1
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clc
m_s =50; // kg
m_w =1.5; // kg
x = m_s /( m_s + m_w ) ;
disp ( ” d r y n e s s f r a c t i o n =” )
disp ( x )
Scilab code Exa 3.2 2
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V =0.6; //mˆ3
m =3.0; // kg
p =5; // b a r
v=V/m;
// At 5 b a r : From steam t a b l e s
v_g =0.375; //mˆ3/ kg
v_f =0.00109; //mˆ3/ kg
v_fg = v_g - v_f ;
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10 x =1 -(( v_g - v ) / v_fg ) ;
11
12 disp ( ” ( i ) Mass and volume o f l i q u i d ” )
13 m_liq = m *(1 - x ) ;
14 disp ( ” mass o f l i q u i d =” )
15 disp ( m_liq )
16 disp ( ” kg ” )
17 V_liq = m_liq * v_f ;
18 disp ( ” volume o f l i q u i d =” )
19 disp ( V_liq )
20 disp ( ”mˆ3 ” )
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22 disp ( ” ( i i ) Mass and volume o f v a p o u r ” )
23 m_vap = m * x ;
24 disp ( ” mass o f v a p o u r=” )
25 disp ( m_vap )
26 disp ( ” kg ” )
27 V_vap = m_vap * v_g ;
28 disp ( ” volume o f v a p o u r=” )
29 disp ( V_vap )
30 disp ( ”mˆ3 ” )
Scilab code Exa 3.3 3
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V =0.05; //mˆ3
m_f =10; // kg
// From steam t a b l e s c o r r e s p o n d i n g t o 245 0C
p_sat =36.5; // b a r
v_f =0.001239; //mˆ3/ kg
v_g =0.0546; //mˆ3/ kg
h_f =1061.4; // kJ / kg
h_fg =1740.2; // kJ / kg
s_f =2.7474; // kJ / kg . K
s_fg =3.3585; // kJ / kg . K
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disp ( ” ( i ) The p r e s s u r e=” )
disp ( p_sat )
disp ( ” b a r ” )
disp ( ” ( i i ) The mass ” )
V_f = m_f * v_f ;
V_g = V - V_f ;
m_g = V_g / v_g ;
m = m_f + m_g ;
disp ( ” The t o t a l mass o f m i x t u r e=” )
disp ( m )
disp ( ” kg ” )
disp ( ” ( i i i ) The s p e c i f i c volume ” )
v_fg = v_g - v_f ;
x = m_g /( m_g + m_f ) ;
v = v_f + x * v_fg ;
disp ( ” s p e c i f i c volume=” )
disp ( v )
disp ( ”mˆ3/ kg ” )
disp ( ” ( i v ) The s p e c i f i c e n t h a l p y ” )
h = h_f + x * h_fg ;
disp ( ” s p e c i f i c e n t h a l p y=” )
disp ( h )
disp ( ” kJ / kg ” )
disp ( ” ( v ) The s p e c i f i c e n t r o p y ” )
s = s_f + x * s_fg ;
disp ( ” s p e c i f i c e n t r o p y =” )
disp ( s )
disp ( ” kJ / kg . K” )
disp ( ” ( v i ) The s p e c i f i c i n t e r n a l e n e g y ” )
u =h -( p_sat * v *10^2) ; // kJ / kg
disp ( ” s p e c i f i c i n t e r n a l e n e r g y=” )
disp ( u )
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50
disp ( ” kJ / kg ” )
Scilab code Exa 3.4 4
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m_w =2; // kg
t_w =25; // 0C
p =5; // b a r
x =0.9;
c_pw =4.18;
// a t 5 b a r ; from steam t a b l e s
h_f =640.1; // kJ / kg
h_fg =2107.4; // kJ / kg
h = h_f + x * h_fg ;
disp ( ” S e n s i b l e h e a t a s s o c i a t e d w i t h 1 kg o f water , Qw
=” )
Qw = c_pw *( t_w -0) ;
disp ( Qw )
disp ( ” kJ ” )
disp ( ” Net q u a n t i t y o f h e a t t o be s u p p l i e s p e r kg o f
water , Q=” )
Q =h - Qw ;
disp ( Q )
disp ( ” kJ ” )
disp ( ” T o t a l amount o f h e a t s u p p l i e d , Q t o t a l=” )
Q_total = m_w * Q ;
disp ( Q_total )
disp ( ” kJ ” )
Scilab code Exa 3.5 5
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m =4.4; // kg
p =6; // b a r
t_sup =250; // 0C
t_w = 30; // 0C
c_ps =2.2; // kJ / kg
c_pw =4.18;
// At 6 bar , 250 0C ; From steam t a b l e s
t_s =158.8; // 0C
h_f =670.4; // kJ / kg
h_fg =2085; // kJ / kg
h_sup = h_f + h_fg + c_ps *( t_sup - t_s ) ;
disp ( ”Amount o f h e a t added p e r kg o f water , Qw=” )
Qw = c_pw *( t_w -0) ;
disp ( Qw )
disp ( ” Net amount o f h e a t r e q u i r e d t o be s u p p l i e d p e r
kg , Q=” )
19 Q = h_sup - Qw ;
20 disp ( Q )
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disp ( ” T o t a l amount o f h e a t r e q u i r e d , Q t o t a l=” )
Q_total = m * Q ;
disp ( Q_total )
disp ( ” kJ ” )
Scilab code Exa 3.6 6
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v =0.15; //mˆ3
p =4; // b a r
x =0.8;
// At 4 b a r : From steam t a b l e s
v_g =0.462; //mˆ3/ kg
h_f = 604.7; // kJ / kg
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8 h_fg =2133; // kJ / kg
9 density =1/ x / v_g ;
10 disp ( ” mass o f 0 . 1 5 mˆ3 steam , m=” )
11 m = v * density ;
12 disp ( m )
13 disp ( ” kg ” )
14
15 disp ( ” T o t a l h e a t o f 1 m3 o f steam which h a s a mass
o f 2 . 7 0 5 6 kg , Q=” )
16 Q = density *( h_f + x * h_fg ) ;
17 disp ( Q )
18 disp ( ” kJ ” )
Scilab code Exa 3.7 7
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m =1000; // kJ / kg . K
p =16; // b a r
x =0.9;
T_sup =653; //K
T_w =30; // 0C
c_ps =2.2; // kJ / kg
c_pw =4.18;
// At 16 b a r : From steam t a b l e s
T_s =474.4; //K
h_f =858.6; // kJ / kg
h_fg =1933.2; // kJ / kg
disp ( ” ( i ) Heat s u p p l i e d t o f e e d w a t e r p e r h o u r t o
p r o d u c e wet steam i s g i v e n by ” )
15 H = m *[( h_f + x * h_fg ) - c_pw *( T_w -0) ];
16 disp ( H )
17 disp ( ” kJ ” )
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disp ( ” ( i i ) Heat a b s o r b e d by s u p e r h e a t e r p e r hour , Q=
33
”)
20 Q = m *[(1 - x ) * h_fg + c_ps *( T_sup - T_s ) ];
21 disp ( Q )
22 disp ( ” kJ ” )
Scilab code Exa 3.8 8
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disp ( ” ( i ) a t 0 . 7 5 bar , b e t w e e n 100 C
// At 100 C
T1 =100; // C
h_sup1 =2679.4; // kJ / kg
// At 150 C
T2 =150; // C
h_sup2 =2778.2; // kJ / kg
and 150 C ” )
c_ps =( h_sup2 - h_sup1 ) /( T2 - T1 ) ;
disp ( ” mean s p e c i f i c h e a t=” )
disp ( c_ps )
disp ( ” ( i i ) a t 0 . 5 bar , b e t w e e n 300 C
T1 =300; // C
h_sup1 =3075.5; // kJ / kg
T2 =400; // C
h_sup2 =3278.9; // kJ / kg
c_ps =( h_sup2 - h_sup1 ) /( T2 - T1 ) ;
disp ( ” mean s p e c i f i c h e a t c p s=” )
disp ( c_ps )
Scilab code Exa 3.9 9
34
and 400 C ” )
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m =1.5; // kg
p =5; // b a r
x1 =1;
x2 =0.6;
p1 =5*10^5; //N/m
// At 5 b a r : From steam t a b l e s
t_s =151.8; // 0C
h_f =640.1; // kJ / kg
h_fg =2107.4; // kJ / kg
v_g =0.375; //mˆ3/ kg
v_g1 =0.375*10^( -3) ;
h1 = h_f + h_fg ;
V = m * v_g ;
u1 = h1 - p1 * v_g1 ;
v_g2 = V / m / x2 ; //mˆ3/ kg
// From steam t a b l e c o r r e s p o n d i n g t o 0 . 6 2 5 mˆ3/ kg
p2 =2.9; // b a r
disp ( ” P r e s s u r e a t new s t a t e =” )
disp ( p2 )
disp ( ” b a r ” )
t_s =132.4; // 0C
disp ( ” T e m p e r a t u r e a t new s t a t e =” )
disp ( t_s )
disp ( ” C ” )
h_f2 =556.5; // kJ / kg
h_fg2 =2166.6; // kJ / kg
u2 =( h_f2 + x2 * h_fg2 ) - p2 * x2 * v_g2 *10^2;
Q = u2 - u1 ; // h e a t t r a n s f e r r e d a t c o n s t a n t volume p e r
kg
disp ( ” T o t a l h e a t t r a n s f e r e d , Q t o t a l=” )
Q_total = m * Q ;
disp ( Q_total )
disp ( ” kJ ” )
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Scilab code Exa 3.10 10
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V =0.9; //mˆ3
p1 =8; // b a r
x1 =0.9;
p2 =4; // b a r
p3 =3; // b a r
v_g1 =0.24; //mˆ3/ kg
disp ( ” ( i ) The mass o f steam blown o f f : ” )
m1 = V / x1 / v_g1 ;
h_f1 =720.9; // kJ / kg
h_fg1 =2046.5; // kJ / kg
h_f2 =604.7; // kJ / kg
h_fg2 =2133; // kJ / kg
v_g2 =0.462; //mˆ3/ kg
h1 = h_f1 + x1 * h_fg1 ; // The e n t h a l p y o f steam b e f o r e
blowing o f f
h2 = h1 ;
x2 =( h1 - h_f2 ) / h_fg2 ;
m2 = x1 /( x2 * v_g2 ) ;
disp ( ” Mass o f steam blown o f f =” )
m = m1 - m2 ;
disp ( m )
disp ( ” kg ” )
disp ( ” ( i i ) D r y n e s s f r a c t i o n o f steam i n t h e v e s s e l
a f t e r c o o l i n g ”)
29 v_g3 =0.606; //mˆ3/ kg
30 x3 = x2 * v_g2 / v_g3 ;
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disp ( ” d r y n e s s f r a c t i o n =” )
disp ( x3 )
disp ( ” ( i i i ) Heat l o s t d u r i n g c o o l i n g ” )
h_f3 =561.4; // kJ / kg
h_fg3 =2163.2; // kJ / kg
h3 = h_f3 + x3 * h_fg3 ;
u2 = h2 - p2 * x2 * v_g2 *10^2; // kJ / kg
u3 = h3 - p3 * x3 * v_g3 *10^2; // kJ / kg
Q = m *( u3 - u2 ) ;
disp ( ” Heat l o s t d u r i n g c o o l i n g=” )
disp ( - Q )
disp ( ” kJ ” )
Scilab code Exa 3.11 11
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p =8*10^5; // Pa
x =0.8;
v_g =0.240; //mˆ3/ kg
h_fg =2046.5; // kJ / kg
disp ( ” ( i ) E x t e r n a l work done d u r i n g e v a p o r a t i o n ” )
W = p * x * v_g /10^3; // kJ
disp ( ”W=” )
disp ( W )
disp ( ” kJ ” )
disp ( ” ( i i ) I n t e r n a l l a t e n t h e a t ” )
Q = x * h_fg - W ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
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Scilab code Exa 3.12 12
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p1 =10; // b a r
p2 =10; // b a r
x1 =0.85;
V1 =0.15; //mˆ3
t_sup2 =300; // 0C
t_sup1 =179.9; // 0C
c_ps =2.2; // kJ / kg . K
v_g1 =0.194; //mˆ3/ kg
m = V1 /( x1 * v_g1 ) ;
h_fg1 =2013.6; // kJ / kg
Q =(1 - x1 ) * h_fg1 + c_ps *( t_sup2 - t_sup1 ) ;
Q_total = m * Q ;
disp ( ” T o t a l h e a t s u p p l i e d=” )
disp ( Q_total )
disp ( ” kJ ” )
v_sup2 = v_g1 *( t_sup2 +273) /( t_sup1 +273)
W = p1 *( v_sup2 - ( x1 * v_g1 ) ) *10^2;
Percentage = W / Q *100;
disp ( ” P e r c e n t a g e o f t o t a l h e a t s u p p l i e d=” )
disp ( Percentage )
disp ( ”%” )
Scilab code Exa 3.13 13
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p =18; // b a r
x =0.85;
h_f =884.6; // kJ / kg
h_fg =1910.3; // kJ / kg
v_g =0.110; //mˆ3/ kg
u_f =883; // kJ / kg
u_g =2598; // kJ / kg
v = x * v_g ;
disp ( ” S p e c i f i c volume o f wet steam=” )
disp ( v )
disp ( ”mˆ3/ kg ” )
h = h_f + x * h_fg ;
disp ( ” S p e c i f i c e n t h a l p y o f wet steam=” )
disp ( h )
disp ( ” kJ / kg ” )
u =(1 - x ) * u_f + x * u_g ;
disp ( ” S p e c i f i c i n t e r n a l e n e r g y o f wet steam =” )
disp ( u )
disp ( ” kJ / kg ” )
Scilab code Exa 3.14 14
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p =7; // b a r
h =2550; // kJ / kg
h_f =697.1; // kJ / kg
h_fg =2064.9; // kJ / kg
v_g =0.273; //mˆ3/ kg
u_f =696; // kJ / kg
u_g =2573; // kJ / kg
x =( h - h_f ) / h_fg ;
disp ( ” ( i ) D r y n e s s f r a c t i o n =” )
disp ( x )
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13 v = x * v_g ;
14 disp ( ” ( i i ) S p e c i f i c volume o f wet steam =” )
15 disp ( v )
16 disp ( ”mˆ3/ kg ” )
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18 u =(1 - x ) * u_f + x * u_g ;
19 disp ( ” ( i i i ) S p e c i f i c i n t e r n a l e n e r g y o f wet steam=” )
20 disp ( u )
21 disp ( ” kJ / kg ” )
Scilab code Exa 3.15 15
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p =120; // b a r
v =0.01721; //mˆ3/ kg
T =350; // C
disp ( ” T e m p e r a t u r e=” )
disp ( T )
disp ( ” C ” )
h =2847.7; // kJ / kg
disp ( ” s p e c i f i c e n t h a l p y=” )
disp ( h )
disp ( ” kJ / kg ” )
u =h - p * v *10^2; // kJ / kg
disp ( ” I n t e r n a l e n e r g y=” )
disp ( u )
disp ( ” kJ / kg ” )
Scilab code Exa 3.16 16
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p =140; // b a r
h =3001.9; // kJ / kg
T =400; // 0C
disp ( ” T e m p e r a t u r e=” )
disp ( T )
disp ( ” C ” )
v =0.01722; //mˆ3/ kg
disp ( ” The s p e c i f i c volume ” )
disp ( v )
disp ( ”mˆ3/ kg ” )
u =h - p * v *10^2;
disp ( ” s p e c i f i c
disp ( u )
disp ( ” kJ / kg ” )
i n t e r n a l e n e r g y=” )
Scilab code Exa 3.17 17
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// At 10 b a r : From steam t a b l e f o r s u p e r h e a t e d steam
h_sup =3051.2; // kJ / kg
T_sup =573; //K
T_s =452.9; //K
v_g =0.194; //mˆ3/ kg
v_sup = v_g * T_sup / T_s ;
p =10; // b a r
u1 = h_sup - p * v_sup *10^2; // kJ / kg
disp ( ” I n t e r n a l e n e r g y o f s u p e r h e a t e d steam a t 10 b a r
= ”)
12 disp ( u1 )
13 disp ( ” kJ / kg ” )
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// At 1 . 4 b a r : From steam t a b l e s
p =1.4; // b a r
h_f =458.4; // kJ / kg
h_fg =2231.9; // kJ / kg
v_g =1.236; //mˆ3/ kg
x =0.8;
h = h_f + x * h_fg ;
u2 =h - p * x * v_g *10^2; // kJ
du = u2 - u1 ;
disp ( ” Change i n i n t e r n a l e n e r g y=” )
disp ( du )
disp ( ” kJ ” )
Scilab code Exa 3.18 18
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m =1; // kg
p =20; // b a r
T_sup =400; // 0C
x =0.9;
c_ps =2.3; // kJ / kg . K
disp ( ” ( i ) I n t e r n a l e n e r g y o f 1 kg o f s u p e r h e a t e d
steam ” )
// At 20 b a r : From steam t a b l e s
T_s =212.4; // 0C
h_f =908.6; // kJ / kg
h_fg =1888.6; // kJ / kg
v_g =0.0995; //mˆ3/ kg
h_sup = h_f + h_fg + c_ps *( T_sup - T_s ) ;
v_sup = v_g *( T_sup +273) /( T_s +273) ;
u = h_sup - p * v_sup *10^2;
disp ( ” I n t e r n a l e n e r g y=” )
disp ( u )
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19 disp ( ” kJ / kg ” )
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21 disp ( ” ( i i ) I n t e r n a l e n e r g y o f 1 kg o f wet steam ” )
22 h = h_f + x * h_fg ;
23 u =h - p * x * v_g *10^2;
24 disp ( ” I n t e r n a l e n e r g y=” )
25 disp ( u )
26 disp ( ” kJ / kg ” )
Scilab code Exa 3.19 19
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h_g1 =2797.2; // kJ / kg
c_ps = 2.25;
T_sup =350; // 0C
T_s =212.4; // 0C
h1 = h_g1 + c_ps *( T_sup - T_s ) ;
h_f2 =908.6; // kJ / kg
h_fg2 =1888.6; // kJ / kg
// Main : 2 0 bar , 250 0C
T_sup =250; // 0C
Q =2*[ h_g1 + c_ps *( T_sup - T_s ) ];
x2 =( Q - h1 - h_f2 ) / h_fg2 ;
disp ( ” Q u a l i t y o f steam ” )
disp ( x2 )
Scilab code Exa 3.20 20
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m =1; // kg
p =6; // b a r
x =0.8;
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6 h_fg =2085; // kJ / kg
7 c_pw =4.18;
8 s_wet = c_pw * log ( T_s /273) + x * h_fg / T_s ;
9 disp ( ” Entropy o f wet steam=” )
10 disp ( s_wet )
11 disp ( ” kJ / kg . K” )
Scilab code Exa 3.21 21
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p1 =10; // b a r
t_sup =400; // 0C
p2 =0.2; // b a r
x2 =0.9;
h_sup =3263.9; // kJ / kg
s_sup =7.465; // kJ / kg
h1 =3263.9; // kJ / kg
s1 = s_sup ;
h_f2 =251.5; // kJ / kg
h_fg2 =2358.4; // kJ / kg
s_f2 =0.8321; // kJ / kg . K
s_g2 =7.9094; // kJ / kg . K
s_fg2 = s_g2 - s_f2 ;
h2 = h_f2 + x2 * h_fg2 ;
s2 = s_f2 + x2 * s_fg2 ;
disp ( ” ( i ) Drop i n e n t h a l p y ” )
dh = h1 - h2 ;
disp ( ” Drop i n e n t h a l p y = ” )
disp ( dh )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Change i n e n t r o p y ” )
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26 ds = s1 - s2 ;
27 disp ( ” Change i n e n t r o p y = ” )
28 disp ( ds )
29 disp ( ” kJ / kg . K” )
Scilab code Exa 3.22 22
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m =1; // kg
p =12; // b a r
T_sup =523; //K
c_ps =2.1; // kJ / kg . K
T_s =461; //K
h_fg =1984.3; // kJ / kg
c_pw =4.18;
s_sup = c_pw * log ( T_s /273) + h_fg / T_s + c_ps * log ( T_sup / T_s )
;
10 disp ( ” Entropy =” )
11 disp ( s_sup )
12 disp ( ” kJ / kg . K” )
Scilab code Exa 3.23 23
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m =3; // kg
v1 =0.75; //mˆ3/ kg
v2 =1.2363; //mˆ3/ kg
x = v1 / v2 ;
h_f =458.4; // kJ / kg
h_fg =2231.9; // kJ / kg
h_s = m *[ h_f + x * h_fg ]; // kJ
v_sup =1.55; //mˆ3/ kg
p =2; // b a r
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t_s =120.2; // 0C
t_sup =400; // 0C
h =3276.6; // kJ / kg
U =1708; // kJ / kg
Degree = t_sup - t_s ;
h_sup = m * h ;
Q_added = h_sup - h_s ;
disp ( ” Heat added =” )
disp ( Q_added )
disp ( ” kJ ” )
U_s = m * U ;
U_sup = m *( h - p * v_sup *10^2) ;
dU = U_sup - U_s ;
W = Q_added - dU ;
disp ( ” work done = ” )
disp ( W )
disp ( ” kJ ” )
Scilab code Exa 3.24 24
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p =5; // b a r
m =50; // kg
T1 =20; // 0C
m_s =3; // kg
T2 =40; // 0C
m_eq =1.5; // kg
h_f =640.1; // kJ / kg
h_fg =2107.4; // kJ / kg
c_pw =4.18;
m_w = m + m_eq ;
x =[( m_w * c_pw *( T2 - T1 ) ) / m_s + c_pw * T2 - h_f ]/ h_fg ;
disp ( ” D r y n e s s f r a c t i o n o f steam ” )
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disp ( x )
Scilab code Exa 3.25 25
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p =1.1; // b a r
x =0.95;
c_pw =4.18;
m1 =90; // kg
m2 =5.25; // kg
T1 =25; // 0C
T2 =40; // 0C
m = m1 + m2 ;
h_f =428.8; // kJ / kg
h_fg = 2250.8; // kJ / kg
m_s = [ m * c_pw *( T2 - T1 ) ]/[( h_f + x * h_fg ) - c_pw * T2 ];
disp ( ” Mass o f steam c o n d e n s e d=” )
disp ( m_s )
disp ( ” kg ” )
Scilab code Exa 3.26 26
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p1 =8; // b a r
p2 =1; // b a r
T_sup2 =115; // 0C
T_s2 =99.6; // 0C
h_f1 =720.9; // kJ / kg
h_fg1 =2046.5; // kJ / kg
h_f2 =417.5; // kJ / kg
h_fg2 =2257.9; // kJ / kg
c_ps =2.1;
x1 =[ h_f2 + h_fg2 + c_ps *( T_sup2 - T_s2 ) - h_f1 ]/ h_fg1 ;
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disp ( ” D r y n e s s f r a c t i o n o f t h e steam i n t h e main = ” )
disp ( x1 )
Scilab code Exa 3.27 27
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m_w =2; // kg
m_s =20.5; // kg
t_sup =110; // 0C
p1 =12; // b a r
p3 =1; // b a r
p2 = p1 ;
h_f2 =798.4; // kJ / kg
h_fg2 =1984.3; // kJ / kg
T_s =99.6; // 0C
h_f3 =417.5; // kJ / kg
h_fg3 =2257.9; // kJ / kg
T_sup =110; // 0C
c_ps =2; // kJ / kg . K
x2 =[ h_f3 + h_fg3 + c_ps *( T_sup - T_s ) - h_f2 ]/ h_fg2 ;
x1 = x2 * m_s /( m_w + m_s ) ;
disp ( ” Q u a l i t y o f steam s u p p l i e d = ” )
disp ( x1 )
Scilab code Exa 3.28 28
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p1 =15; // b a r
p2 = p1 ;
p3 =1; // b a r
t_sup3 =150; // 0C
m_w =0.5; // kg / min
m_s =10; // kg / min
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8 h_f2 =844.7; // kJ / kg
9 h_fg2 =1945.2; // kJ / kg
10 h_sup3 =2776.4; // kJ / kg
11 x2 =( h_sup3 - h_f2 ) / h_fg2 ;
12 x1 = x2 * m_s /( m_s + m_w ) ;
13 disp ( ” Q u a l i t y o f steam s u p p l i e d = ” )
14 disp ( x1 )
49
Chapter 4
First Law of Thermodynamics
Scilab code Exa 4.1 1
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Q = -50; // kJ / kg
W = -100; // kJ / kg
dU =Q - W ;
disp ( ” g a i n i n i n t e r n a l e n e r g y = ” )
disp ( dU )
disp ( ” kJ / kg ” )
Scilab code Exa 4.2 2
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u1 =450; // kJ / kg
u2 =220; // kJ / kg
W =120; // kJ / kg
Q =( u2 - u1 ) + W ;
disp ( ” Heat r e j e c t e d by a i r =” )
disp ( - Q )
disp ( ” kJ / kg ” )
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Scilab code Exa 4.3 3
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m =0.3; // kg
cv =0.75; // kJ / kg . K
T1 =313; //K
T2 =433; //K
W = -30; // kJ
dU = m * cv *( T2 - T1 ) ;
Q = dU + W ;
disp ( ” Heat r e j e c t e d d u r i n g t h e p r o c e s s=” )
disp ( - Q )
disp ( ” kJ ” )
Scilab code Exa 4.4 4
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p1 =105; // kPa
V1 =0.4; //mˆ3
p2 = p1 ;
V2 =0.20; //mˆ3
Q = -42.5; // kJ
W = p1 *( V2 - V1 ) ;
dU =Q - W ;
disp ( ” c h a n g e i n i n t e r n a l e n e r g y = ” )
disp ( dU )
disp ( ” kJ ” )
Scilab code Exa 4.6 6
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p =1.1; // b a r
x =0.95;
c_pw =4.18;
m1 =90; // kg
m2 =5.25; // kg
T1 =25; // 0C
T2 =40; // 0C
m = m1 + m2 ;
h_f =428.8; // kJ / kg
h_fg = 2250.8; // kJ / kg
m_s = [ m * c_pw *( T2 - T1 ) ]/[( h_f + x * h_fg ) - c_pw * T2 ];
disp ( ” Mass o f steam c o n d e n s e d=” )
disp ( m_s )
disp ( ” kg ” )
Scilab code Exa 4.7 7
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2 W_12 = -82; // kJ
3 Q_12 = -45; // kJ
4 dU_12 = Q_12 - W_12 ;
5 W_21 =100; // kJ
6 dU_21 = - dU_12 ;
7 Q_21 = dU_21 + W_21 ;
8 disp ( ” Heat added t o t h e s y s t e m = ” )
9 disp ( Q_21 )
10 disp ( ” kJ ” )
Scilab code Exa 4.8 8
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2 Q2 =9000; // kJ
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Q1 =3000; // kJ
Q = Q1 - Q2 ;
W =0;
dU =W - Q ;
disp ( ”Work done = ” )
disp ( W )
disp ( ” Change i n i n t e r n a l e n e r g y = ” )
disp ( dU )
disp ( ” kJ ” )
Scilab code Exa 4.9 9
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m =20; // kg
g =9.81; //m/ s ˆ2
z2 =0;
z1 =15;
disp ( ” ( i ) When t h e s t o n e i s a b o u t t o e n t e r t h e w a t e r
”)
Q =0
W =0
dU =0
PE = m * g *( z2 - z1 )
KE = - PE
disp ( ” ( i i ) When t h e s t o n e d i p s i n t o t h e t a n k and
comes t o r e s t ” )
Q =0
W =0
KE =0
PE = m * g *( z2 - z1 )
dU = - PE
disp ( ” ( i i i ) When t h e w a t e r and s t o n e come t o t h e i r
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i n i t i a l temperature ”)
21 W =0
22 KE =0
23 Q = - dU
Scilab code Exa 4.10 10
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2 Q_lqm =168; // kJ
3 W_lqm =64; // kJ
4 dU_lm = Q_lqm - W_lqm ;
5 W_lnm =21; // kJ
6 W_ml = -42; // kJ
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8 Q_lnm = dU_lm + W_lnm ;
9 disp ( ” ( i ) Q lnm=” )
10 disp ( Q_lnm )
11 disp ( ” kJ ” )
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14 Q_ml = W_ml - dU_lm ;
15 disp ( ” ( i i ) Q ml = ” )
16 disp ( Q_ml )
17 disp ( ” kJ ” )
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20 W_ln =21; // kJ
21 dU_ln =84; // kJ
22 Q_ln = dU_ln + W_ln ;
23 Q_nm = Q_lnm - Q_ln ;
24 disp ( ”Q nm = ” )
25 disp ( Q_nm )
26 disp ( ” kJ ” )
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Scilab code Exa 4.11 11
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T1 =55; // 0C
T2 =95; // 0C
W = integrate ( ’ 200 ’ , ’T ’ , T1 , T2 ) ;
Q = integrate ( ’ 160 ’ , ’T ’ , T1 , T2 ) ;
dU =Q - W ;
disp ( ” c h a n g e i n i n t e r n a l e n e r g y=” )
disp ( dU /10^3)
disp ( ” kJ ” )
Scilab code Exa 4.12 12
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2 Q = -340; // kJ
3 n =200; // c y c l e s / min
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5 // For P r o c e s s 1−2
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7 W_12 =4340; // kJ / min
8 Q_12 =0;
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10 dE_12 = Q_12 - W_12 ;
11 disp ( ” dE 12 =” )
12 disp ( dE_12 )
13 disp ( ” kJ / min ” )
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15 // For p r o c e s s 2−3
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17 Q_23 =42000; // kJ / min
18 W_23 =0;
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dE_23 = Q_23 - W_23 ;
disp ( ” dE 23 =” )
disp ( dE_23 )
disp ( ” kJ / min ” )
// For p r o c e s s 3−4
Q_34 = -4200; // kJ / min
dE_34 = -73200; // kJ / min
W_34 = Q_34 - dE_34 ;
disp ( ”W 34 =” )
disp ( W_34 )
disp ( ” kJ / min ” )
// For p r o c e s s 4−1
Q_41 = Q *n - Q_12 - Q_23 - Q_34 ;
disp ( ” Q 41 =” )
disp ( Q_41 )
disp ( ” kJ / min ” )
dE_41 =0 - dE_12 - dE_23 - dE_34 ;
disp ( ” dE 41 =” )
disp ( dE_41 )
disp ( ” kJ / min ” )
W_41 = Q_41 - dE_41 ;
disp ( ”W 41 =” )
disp ( W_41 )
disp ( ” kJ / min ” )
Scilab code Exa 4.13 13
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P =1200; //kW
Qin =3360; // kJ / kg
Qout =2520; // kJ / kg
F =6; //kW
dQ = Qin - Qout ;
dW =P - F ; // kJ / s
m = dW / dQ ;
disp ( ” Steam f l o w round t h e c y c l e ” )
disp ( m )
disp ( ” kg / s ” )
Scilab code Exa 4.14 14
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dT =25; // 0C
Q =30; // kJ
cv =1.2; // kJ / kg . 0 C
m =2.5; // kg
dU = m * cv * dT ;
disp ( ” c h a n g e i n i n t e r n a l e n e r g y = ” )
disp ( dU )
disp ( ” kJ ” )
W = Q - dU ;
disp ( ”Work done = ” )
disp ( W )
disp ( ” kJ ” )
Scilab code Exa 4.15 15
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Q =50; // kJ
dV =0.14; //mˆ3
p =1.2*10^5; //N/mˆ2
m =90; // kg
d =5.5; //m
g =9.8; //m/ s ˆ2
W_adb = -110; // kJ
Wnet = m * g * d /1000; // kJ
disp ( ” ( i ) Change i n i n t e r n a l e n e r g y ” )
W = p * dV /1000 + Wnet ; // kJ
dE =Q - W ;
disp ( ”dE=” )
disp ( dE )
disp ( ” kJ ” )
disp ( ” ( i i ) A d i a b a t i c p r o c e s s ” )
Q =0;
dE = - W_adb ;
disp ( ”dE=” )
disp ( dE )
disp ( ” kJ ” )
disp ( ” ( i i i ) Change i n i n t e r n a l e n e r g y ” )
Q =50; // kJ
dE = Q - [ W_adb + W ];
disp ( ”dE=” )
disp ( dE )
disp ( ” kJ ” )
Scilab code Exa 4.16 16
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2 V1 =0.15; //mˆ3
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V2 =0.05; //mˆ3
Q = -45; // kJ
p1 =(5/ V1 +1.5) *10^5; //N/mˆ2
p2 =(5/ V2 +1.5) *10^5; //N/mˆ2
W = integrate ( ’ ( 5 /V+ 1 . 5 ) ∗ 1 0 ˆ 2 ’ , ’V ’ , V1 , V2 ) ;
disp ( ” ( i ) Change i n i n t e r n a l e n e r g y = ” )
dU =Q - W ;
disp ( ”dU=” )
disp ( dU )
disp ( ” kJ ” )
disp ( ” ( i i ) Change i n e n t h a l p y ” )
dH =( dU *10^3+( p2 * V2 - p1 * V1 ) ) /10^3;
disp ( ”dH=” )
disp ( dH )
disp ( ” kJ ” )
Scilab code Exa 4.17 17
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V1 =0.25; //mˆ3
p1 =500; // kPa
p2 =100; // kPa
V2 = V1 *( p1 / p2 ) ^(1/1.25)
n =1.25
dU =3.64*( p2 * V2 - p1 * V1 )
disp ( ” ( i ) I f t h e e x p a n s i o n i s q u a s i − s t a t i c ” )
W =( p1 * V1 - p2 * V2 ) /( n -1) ;
Q = dU + W
disp ( ” Heat t r a n s f e r e d =” )
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14 disp ( Q )
15 disp ( ” kJ ” )
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19 Q =32; // kJ
20 W =Q - dU ;
21 disp ( ”Work done=” )
22 disp ( W )
23 disp ( ” kJ ” )
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26 disp ( ” ( i i i ) The d i f f e r e n c e ” )
27 disp ( ” ( i i i ) The work i n ( i i ) i s n o t e q u a l t o
dV s i n c e t h e p r o c e s s i s n o t q u a s i − s t a t i c . ” )
Scilab code Exa 4.18 18
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v1 =0.3; //mˆ3/ kg
T1 =20; // 0C
v2 =0.55; //mˆ3/ kg
T2 =260; // 0C
p =1.6*10^5; // Pa
disp ( ” ( i ) Heat added p e r kg = ” )
Q = integrate ( ’ 1 . 5 + 7 5 / (T+45) ’ , ’T ’ , T1 , T2 ) ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) The work done p e r kg o f f l u i d ” )
W = p *( v2 - v1 ) /1000; // kJ / kg
disp ( ”W=” )
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19 disp ( ” kJ / kg ” )
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22 disp ( ” ( i i i ) Change i n i n t e r n a l e n e r g y ” )
23 dU =Q - W ;
24 disp ( ”dU=” )
25 disp ( dU )
26 disp ( ” kJ / kg ” )
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29 disp ( ” ( i v ) Change i n e n t h a l p y ” )
30 dH = Q ;
31 disp ( ”dH=” )
32 disp ( dH )
33 disp ( ” kJ / kg ” )
Scilab code Exa 4.19 19
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m =1; // kg
du = -42000; // J
cp =840; // J / kg . 0 C
cv =600; // J / kg . 0 C
dT = du / m / cv ;
Q = m * cp * dT ;
W =( Q - du ) /10^3;
disp ( ”Work done=” )
disp ( W )
disp ( ” kJ ” )
Scilab code Exa 4.20 20
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p1 =190; // kPa
V1 =0.035; //mˆ3
p2 =420; // kPa
V2 =0.07; //mˆ3
dU =3.6*( p2 * V2 - p1 * V1 ) ;
// p=a+b∗ v
// a + 0 . 0 3 5 ∗ b=190
// a + 0.0 7 ∗ b=420
// s o l v i n g t h e two e q u a t i o n s
p =[1 ,0.035;1 ,0.07];
q =[190;420];
X = inv ( p ) * q ;
a = X (1 ,1) ;
b = X (2 ,1) ;
W = integrate ( ’ a+b∗V ’ , ’V ’ , V1 , V2 ) ;
disp ( ”Work done by t h e s y s t e m = ” )
disp ( W )
disp ( ” kJ ” )
Q = dU + W ;
disp ( ” Heat t r a n s f e r i n t o t h e s y s t e m = ” )
disp ( Q )
disp ( ” kJ ” )
Scilab code Exa 4.21 21
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Qv =90; // kJ
Qp = -95; // kJ
W = -18; // kJ
U_l =105; // kJ
W_lm =0;
Q_lm =90;
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U_m = U_l +90;
dU_mn = Qp - W ;
U_n = U_m + dU_mn ;
dQ = Qv + Qp ;
dW = dQ ;
W_nl = dW - W ;
disp ( ” W nl ( i n kJ )=” )
disp ( W_nl )
disp ( ” U l i n kJ =” )
disp ( U_l )
disp ( ”U m i n kJ =” )
disp ( U_m )
disp ( ” U n i n kJ ” )
disp ( U_n )
Scilab code Exa 4.23 23
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V1 =0.2; //mˆ3
p1 =4*10^5; //N/mˆ2
T1 =403; //K
p2 =1.02*10^5; //N/mˆ2
dH =72.5; // kJ
Q_23 = dH ;
cp =1; // kJ / kg
cv =0.714; // kJ / kg
y =1.4;
V2 = V1 *( p1 / p2 ) ^(1/ y ) ;
T2 = T1 *(( p2 / p1 ) ^(( y -1) / y ) ) ;
R =( cp - cv ) *1000; // J / kg . K
m = p1 * V1 / R / T1 ;
T3 = Q_23 /( m * cp ) + T2 ;
V3 = V2 * T3 / T2 ;
W_12 =( p1 * V1 - p2 * V2 ) /( y -1) ;
W_23 = p2 *( V3 - V2 ) ;
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19 W_123 = W_12 + W_23 ;
20 disp ( ” T o t a l work done = ” )
21 disp ( W_123 )
22 disp ( ” J ” )
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25 disp ( ” ( i i ) I n d e x o f e x p a n s i o n , n ” )
26 p3 = p2 ;
27 n =( p1 * V1 - p3 * V3 ) / W_123 + 1;
28 disp ( ” v a l u e o f i n d e x = ” )
29 disp ( n )
Scilab code Exa 4.25 25
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d =0.15; //m
T =303; //K
p =3*10^5; //N/mˆ2
l =0.085; //m
Q = -4000; // J
disp ( ” ( i ) Workdone by t h e s y s t e m ” )
dv = %pi /4* d ^2* l ;
W = p * dv ;
disp ( ”W=” )
disp ( W /10^3)
disp ( ” kJ ” )
disp ( ” ( i i ) D e c r e a s e i n i n t e r n a l e n e r g y o f t h e s y s t e m
”)
dU =( Q - W ) /10^3;
disp ( ” D e c r e a s e i n i n t e r n a l e n e r g y = ” )
disp ( - dU )
disp ( ” kJ ” )
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Scilab code Exa 4.27 27
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y =1.4
R =294.2; // J / kg . 0 C
p1 =1*10^5; //N/mˆ2
T1 =353; //K
V1 =0.45; //mˆ3
V2 =0.13; //mˆ3
p2 =5*10^5; //N/mˆ2
cv = R /( y -1) ;
disp ( ” ( i ) The mass o f g a s ” )
m = p1 * V1 / R / T1 ;
disp ( ”m=” )
disp ( m )
disp ( ” kg ” )
disp ( ” ( i i ) The v a l u e o f i n d e x
compression ”)
19 n = log ( p2 / p1 ) / log ( V1 / V2 ) ;
20 disp ( ” n=” )
21 disp ( n )
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n
for
disp ( ” ( i i i ) The i n c r e a s e i n i n t e r n a l e n e r g y o f t h e
gas ”)
T2 = T1 *( V1 / V2 ) ^( n -1) ;
dU = m * cv *( T2 - T1 ) /10^3;
disp ( ”dU=” )
disp ( dU )
disp ( ” kJ ” )
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disp ( ” ( i v ) The h e a t r e c e i v e d o r r e j e c t e d by t h e g a s
during compression . ”)
W = m * R *( T1 - T2 ) /( n -1) /10^3;
Q = dU + W ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
Scilab code Exa 4.28 28
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p1 =1.02*10^5; // Pa
T1 =295; //K
V1 =0.015; //mˆ3
p2 =6.8*10^5; // Pa
y =1.4;
disp ( ” ( i ) F i n a l t e m p e r a t u r e ” )
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
t2 = T2 -273;
disp ( ” t 2=” )
disp ( t2 )
disp ( ” C ” )
disp ( ” ( i i ) F i n a l volume : ” )
V2 = V1 *( p1 / p2 ) ^(1/ y ) ;
disp ( ”V2=” )
disp ( V2 )
disp ( ”mˆ3 ” )
disp ( ” ( i i i ) Work done ” )
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25 R =287;
26 m = p1 * V1 / R / T1 ;
27 W = m * R *( T1 - T2 ) /( y -1) /10^3;
28 disp ( ”W=” )
29 disp ( W )
30 disp ( ” kJ ” )
Scilab code Exa 4.29 29
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m =0.44; // kg
T1 =453; //K
ratio =3; // r a t i o =V2/V1
T2 =288; //K
W_12 =52.5; // kJ
y = log ( T2 / T1 ) / log (1/ ratio ) + 1;
R = W_12 *( y -1) / m /( T1 - T2 ) ;
// We have g o t two e q u a t i o n s
// cp−cv=R
// cp−y ∗ cv=0
M =[1 , -1;1 , - y ];
N =[ R ;0];
X = inv ( M ) * N ;
cp = X (1 ,1) ;
cv = X (2 ,1) ;
disp ( ” cp=” )
disp ( cp )
disp ( ” kJ / kg . K” )
disp ( ” cv=” )
disp ( cv )
disp ( ” kJ / kg . K” )
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Scilab code Exa 4.30 30
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n =1.3;
m =1; // kg
p1 =1.1; // b a r
T1 =300; //K
p2 =6.6; // b a r
R0 =8314;
M =30;
cp =1.75; // kJ / kg . K
R = R0 / M /1000; // kJ / kg . K
cv = cp - R ;
y = cp / cv ;
T2 = T1 *( p2 / p1 ) ^(( n -1) / n ) ;
W = R *( T1 - T2 ) /( n -1) ;
Q =(( y - n ) /( y -1) ) * W ;
disp ( ” Heat s u p p l i e d = ” )
disp ( Q )
disp ( ” kJ / kg ” )
Scilab code Exa 4.31 31
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cp =14.3; // kJ / kg . K
cv =10.2; // kJ / kg . K
V1 =0.1; //mˆ3
T1 =300; //K
p1 =1; // b a r
p2 =8; // b a r
y = cp / cv ;
R = cp - cv ;
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V2 = V1 *( p1 / p2 ) ^(1/ y ) ;
V3 = V2 ;
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
p3 = p1 * V1 / V3 ;
T3 =300; //K
disp ( ” ( i ) P r e s s u r e a t t h e end o f c o n s t a n t volume
c o o l i n g = ”)
18 disp ( p3 )
19 disp ( ” b a r ” )
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disp ( ” ( i i ) Change i n i n t e r n a l e n e r g y d u r i n g c o n s t a n t
volume p r o c e s s ” )
23 m = p1 * V1 / R / T1 *10^2; // kg
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dU_23 = m * cv *( T3 - T2 ) ;
disp ( ” dU 23 = ” )
disp ( dU_23 )
disp ( ” kJ ” )
disp ( ” ( i i i ) Net work done and h e a t t r a n s f e r r e d
during the c y c l e ”)
W_12 = m * R *( T1 - T2 ) /( y -1) ;
W_23 =0;
W_31 = p3 * V3 * log ( V1 / V3 ) *10^2; // kJ
disp ( ” Net work done=” )
Wnet = W_12 + W_23 + W_31 ;
disp ( Wnet )
disp ( ” kJ ” )
Qnet = Wnet ;
disp ( ” Heat t r a n s f e r r e d d u r i n g t h e c o m p l e t e c y c l e = ”
)
disp ( Qnet )
disp ( ” kJ ” )
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Scilab code Exa 4.32 32
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V1 =0.15; //mˆ3
p1 =15; // b a r
T1 =550; //K
T2 = T1 ;
r =4; // r=V2/V1
V2 = r * V1 ;
T3 =290; //K
p2 = p1 * V1 / V2 ;
W_12 = p1 * V1 * log ( V2 / V1 ) *10^2; // kJ
V3 = V2 ;
p3 = p2 * T3 / T2 ;
W_23 =0;
n = log ( p1 / p3 ) / log ( V3 / V1 ) ;
W_31 =( p3 * V3 - p1 * V1 ) /( n -1) *10^2; // kJ
disp ( ” n e t work done = ” )
Wnet = W_12 + W_23 + W_31
disp ( ” kJ ” )
Qnet = Wnet ;
disp ( ” Heat t r a n s f e r r e d d u r i n g t h e c y c l e = ” )
disp ( Qnet )
disp ( ” kJ ” )
Scilab code Exa 4.33 33
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2 m =1; // kg
3 p1 =5; // b a r
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V1 =0.02; //mˆ3
V2 =0.08; //mˆ3
p2 =1.5; // b a r
function p = f ( V )
p=a+b*V;
endfunction
// 5=a +0 .0 2∗ b
// 1.5= a +0. 08 ∗ b
// S o l v i n g a b o v e two e q u a t i o n s
A =[1 ,0.02;1 ,0.08];
B =[5;1.5];
X = inv ( A ) * B ;
a = X (1 ,1) ;
b = X (2 ,1) ;
disp ( ” ( i ) p−V d i a g r a m ” )
V =0.02:0.001:0.08;
p=a+b*V;
plot (V ,p , ’ b ’ )
V =[0.0667 0.08];
p =[1.5 1.5];
plot (V ,p , ’ g ’ )
V =0.02:0.001:0.0667;
function p = fa ( V )
p =0.1/ V ;
endfunction
plot (V , fa , ’ r ’ )
V =[0.0667 0.0667];
p =[1.5 0];
plot (V ,p , ’−− ’ )
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43 xtitle ( ”p−V d i a g r a m ” , ”V(mˆ 3 ) ” , ” p ( b a r ) ” ) ;
44 legend ( ” p=a+b∗V” ,” p=c o n s t a n t ” ,” pv=c o n s t a n t ” )
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47 disp ( ” ( i i ) Work done and h e a t t r a n s f e r ” )
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49 W_12 = integrate ( ’ ( a+b∗V) ∗ 1 0 ˆ 2 ’ , ’V ’ ,V1 , V2 ) ;
50 disp ( ”Work done by t h e s y s t e m =” )
51 disp ( W_12 )
52 disp ( ” kJ ” )
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54 p3 = p2 ;
55 V3 = p1 * V1 / p3 ;
56 W_23 = p2 *( V3 - V2 ) *10^2; // kJ
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58 W_31 = p3 * V3 * log ( V1 / V3 ) *10^2; // kJ
59 disp ( ”Work done on t h e s y s t e m =” )
60 disp ( W_31 )
61 disp ( ” kJ ” )
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63 W_net = W_12 + W_23 + W_31 ;
64 disp ( ” Net work done =” )
65 disp ( W_net )
66 disp ( ” kJ ” )
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68 Q_net = W_net ;
69 disp ( ” Heat t r a n s f e r r e d d u r i n g t h e c o m p l e t e c y c l e =” )
70 disp ( Q_net )
71 disp ( ” kJ ” )
Scilab code Exa 4.34 34
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2 cv =0.71; // kJ / kg . K
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R =0.287; // kJ / kg . K
d =8; //cm
l =3.5; //cm
S =150; //N/cm
p1 =30; //N/cm
V1 =45; //cmˆ3
T1 =293; //K
cv =0.71; // kJ / kg . K
R =0.287; // kJ / kg . K
A = %pi /4* d ^2;
C = p1 - S / A ^2* V1 ;
dV = l * A ;
V2 = V1 + dV ;
p2 = S / A ^2* V2 + C ;
W = integrate ( ’Aˆ2/ S∗p / 1 0 0 ’ , ’ p ’ , p1 , p2 ) ;
T2 = p2 * V2 * T1 / p1 / V1 ;
m = p1 * V1 / R / T1 /10^5; // kg
dU = m * cv *( T2 - T1 ) ;
Q_12 = dU + W *10^( -3) ;
disp ( ”Amount o f h e a t added t o t h e s y s t e m = ” )
disp ( Q_12 )
disp ( ” kJ ” )
Scilab code Exa 4.35 35
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r =10; // kg / min
p1 =1.5*10^5; //N/mˆ2
rho1 =26; // kg /mˆ3
C1 =110; //m/ s
u1 =910; // kJ / kg
p2 =5.5*10^5; //N/mˆ2
rho2 =5.5; // kg /mˆ3
C2 =190; //m/ s
u2 =710; // kJ / kg
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Q =55; // kJ / s
h =55; //m
g =9.81; //m/ s ˆ2
v2 =1/ rho2 ;
v1 =1/ rho1 ;
disp ( ” ( i ) Change i n e n t h a l p y ” )
dh = u2 - u1 + ( p2 * v2 - p1 * v1 ) /10^3;
disp ( dh )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Work done d u r i n g t h e p r o c e s s (W) . ” )
Q =330; // kJ / kg
KE =( C2 ^2 - C1 ^2) /2/10^3; // kJ
PE = g * h /10^3; // kJ
W = -Q - KE - PE - dh ;
disp ( ”Work done = ” )
disp ( W )
disp ( ” kJ ” )
disp ( ”Work done p e r s e c o n d = ” )
P = W *10/60;
disp ( P )
disp ( ”kW” )
Scilab code Exa 4.36 36
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m =15; // kg / s
v =0.45; //mˆ3/ kg
P =12000; //kW
W = P / m ; // kJ / kg
h1 =1260; // kJ / kg
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h2 =400; // kJ / kg
C1 =50; //m/ s
C2 =110; //m/ s
disp ( ” ( i ) Heat r e j e c t e d = ” )
Q = h2 - h1 +( C2 ^2 - C1 ^2) /2/10^3 + W ;
Qnet = m * Q ;
disp ( ” Qnet=” )
disp ( - Qnet )
disp ( ”kW” )
disp ( ” ( i i ) I n l e t a r e a ” )
A = v * m / C1 ;
disp ( ”A=” )
disp ( A )
disp ( ”mˆ2 ” )
Scilab code Exa 4.37 37
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m =0.5; // kg / s
C1 =6; //m/ s
C2 =5; //m/ s
p1 =1; // b a r
p2 =7; // b a r
v1 =0.85; //mˆ3/ kg
v2 =0.16; //mˆ3/ kg
du =90; // kJ / kg
Q = -120; // kJ / kg
disp ( ” ( i ) Power r e q u i r e d t o d r i v e t h e c o m p r e s s o r ” )
W = - du +( C1 ^2 - C2 ^2) /2/1000 + ( p1 * v1 - p2 * v2 ) *10^2 + Q ;
Power = m * W ;
disp ( ” Power=” )
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disp ( - Power )
disp ( ”kW” )
disp ( ” ( i i ) I n l e t and o u t l e t p i p e c r o s s − s e c t i o n a l
a r e a s ”)
A1 = m * v1 / C1 ;
A2 = m * v2 / C2 ;
disp ( ” I n l e t c r o s s s e c t i o n a l a r e a = ” )
disp ( A1 )
disp ( ”mˆ2 ” )
disp ( ” O u t l e t c r o s s e c t i o n a l a r e a=” )
disp ( A2 )
disp ( ”mˆ2 ” )
Scilab code Exa 4.38 38
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h1 =800; // kJ / kg
C1 =5; //m/ s
h2 =2520; // kJ / kg
C2 =50; //m/ s
dZ =4; //m
g =9.81; //m/ s ˆ2
Q =2180; // kJ / kg
W = h1 - h2 +( C1 ^2 - C2 ^2) /2/1000 + dZ * g /1000+ Q ;
disp ( ” Power d e v e l o p e d = ” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 4.39 39
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g =9.8; //m/ s ˆ2
m =4500/3600; // kg / s
C1 =2800/60; //m/ s
Z1 =5.5; //m
h1 =2800; // kJ / g
C2 =5600/60; //m/ s
Z2 =1.5; //m
h2 =2300; // kJ / kg
Q = -16000/3600; // kJ / s
W =Q - m *[( h1 - h2 ) + ( C2 ^2 - C1 ^2) /2/1000 + ( Z2 - Z1 ) * g
/1000];
12 disp ( ” Power o u t p u t o f t h e t u r b i n e = ” )
13 disp ( - W )
14 disp ( ”kW” )
Scilab code Exa 4.40 40
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p1 =6.87; // b a r
C1 =50; //m/ s
p2 =1.37; // b a r
C2 =500; //m/ s
disp ( ”From steam t a b l e c o r r e s p o n d i n g t o p1 ” )
h1 =2850; // kJ / kg
h2 = h1 - ( C2 ^2 - C1 ^2) /2/1000;
disp ( ” F i n a l e n t h a l p y o f steam = ” )
disp ( h2 )
disp ( ” kJ ” )
Scilab code Exa 4.41 41
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m =220/60; // kg / s
C1 =320; //m/ s
p1 =6*10^5; //N/mˆ2
u1 =2000*10^3; // J / kg
v1 =0.36; //mˆ3/ kg
C2 =140; //m/ s
p2 =1.2*10^5; //N/mˆ2
u2 =1400*10^3; // J / kg
v2 =1.3; //mˆ3/ kg
Q =100*10^3; // J / s
W =( m *[( u1 - u2 ) + ( p1 * v1 - p2 * v2 ) + ( C1 ^2 - C2 ^2) /2] -Q )
/10^6;
13 disp ( ” power c a p a c i t y o f t h e s y s t e m = ” )
14 disp ( W )
15 disp ( ”MW” )
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Scilab code Exa 4.42 42
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p1 =7.5*10^5; //N/mˆ2
C1 =140; //m/ s
h1 =950*10^3; // J / kg
p2 =2*10^5; //N/mˆ2
C2 =280; //m/ s
h2 =650*10^3; // J / kg
m =5; // kg / s
W =( h1 - h2 ) +( C1 ^2 - C2 ^2) /2
Power = m * W /1000;
disp ( ” Power c a p a c i t y o f t u r b i n e = ” )
disp ( Power )
disp ( ”kW” )
Scilab code Exa 4.43 43
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C1 =12; //m/ s
p1 =1*10^5; //N/mˆ2
v1 =0.5; //mˆ3/ kg
C2 =90; //m/ s
p2 =8*10^5; //N/mˆ2
v2 =0.14; //mˆ3/ kg
dh =150; // kJ / kg
Q = -11.67; // kJ / s
m =0.2; // kg / s
disp ( ” ( i ) Motor power r e q u i r e d t o d r i v e t h e
compressor ”)
W = m *[ - dh + ( C1 ^2 - C2 ^2) /2/1000] + Q ;
disp ( ” Power=” )
disp ( - W )
disp ( ”kW” )
disp ( ” ( i i ) R a t i o o f i n l e t t o o u t l e t p i p i d i a m e t e r ” )
ratio = sqrt ( C2 / C1 * v1 / v2 ) ;
disp ( ” r a t i o =” )
disp ( ratio )
Scilab code Exa 4.44 44
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W = -175; // kJ / kg
dh =70; // kJ / kg
Q_water = -92; // kJ / kg
Q = dh + W ;
Q_atm =Q - Q_water ;
disp ( ” Heat t r a n s f e r r e d t o t h e a t m o s p h e r e = ” )
disp ( - Q_atm )
disp ( ” kJ / kg ” )
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Scilab code Exa 4.45 45
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h1 =2800*10^3; // J / kg
C1 =50; //m/ s
A1 =900*10^( -4) ; //mˆ2
v1 =0.187; //mˆ3/ kg
h2 =2600*10^3; // J / kg
v2 =0.498; //mˆ3/ kJ
disp ( ” ( i ) V e l o c i t y a t e x i t o f t h e n o z z l e ” )
C2 = sqrt (2*[( h1 - h2 ) + C1 ^2/2]) ;
disp ( ”C2=” )
disp ( C2 )
disp ( ”m/ s ” )
disp ( ” ( i i ) Mass f l o w r a t e ” )
m = A1 * C1 / v1 ;
disp ( ”m=” )
disp ( m )
disp ( ” kg / s ” )
disp ( ” ( i i i ) Area a t t h e e x i t ” )
A2 = m * v2 / C2 *10^4;
disp ( ”A2=” )
disp ( A2 )
disp ( ”cmˆ2 ” )
Scilab code Exa 4.46 46
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h1 =240; // kJ / kg
h2 =192; // kJ / kg
dZ =20; //m
g =9.81; //m/ s ˆ2
Q =( h2 - h1 ) + dZ * g /1000;
disp ( ” h e a t t r a n s f e r = ” )
disp ( - Q )
disp ( ” kJ / kg ” )
Scilab code Exa 4.47 47
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p1 =2; // b a r
C1 =300; //m/ s
Q =0;
h1 =915*10^3; // J / kg
h2 =800*10^3; // J / kg
C2 = sqrt (2*[ h1 - h2 + C1 ^2/2]) ;
disp ( ” R e l a t i v e v e l o c i t y o f g a s l e a v i n g t h e p i p e=” )
disp ( C2 )
disp ( ”m/ s ” )
Scilab code Exa 4.48 48
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mw =50; // kg / s
p1 =10^5; //N/mˆ2
p2 =4.2*10^5; //N/mˆ2
h =10.7; //m
d1 =0.2; //m
d2 =0.1; //m
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v1 =1/1000;
v2 =1/1000;
g =9.81; //m/ s ˆ2
C1 = mw *4/ %pi / d1 ^2* v1 ;
C2 = mw *4/ %pi / d2 ^2* v2 ;
W = mw *[( p1 * v1 - p2 * v2 ) + ( g *(0 - h ) ) +( C1 ^2 - C2 ^2) /2]/10^3;
disp ( ” C a p a c i t y o f e l e c t r i c motor ” )
disp ( - W )
disp ( ”kW” )
Scilab code Exa 4.49 49
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Ca =250; //m/ s
t = -14; // 0C
ha =250; // kJ / kg
hg =900; // kJ / kg
ratio =0.0180;
Ef =45*10^3; // kJ / kg
Q = -21; // kJ / kg
ma =1; // kg
mg =1.018; // kg
mf =0.018; // kg
Eg =0.06* mf / mg * Ef ;
Cg = sqrt (2000*([ ma *( ha + Ca ^2/2/1000) + mf * Ef + Q ]/ mg hg - Eg ) ) ;
14 disp ( ” v e l o c i t y o f e x h a u s t g a s j e t = ” )
15 disp ( Cg )
16 disp ( ”m/ s ” )
Scilab code Exa 4.50 50
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t1 =20; // 0C
C1 =40; //m/ s
t2 =820; // 0C
C2 =40; //m/ s
t3 =620; // 0C
C3 =55; //m/ s
t4 =510; // 0C
m =2.5; // kg / s
cp =1.005; // kJ / kg . 0 C
disp ( ” ( i ) Heat e x c h a n g e r ” )
Q_12 = m * cp *( t2 - t1 ) ;
disp ( ” r a t e o f h e a t t r a n s f e r =” )
disp ( Q_12 )
disp ( ” kJ / s ” )
disp ( ” ( i i ) T u r b i n e ” )
W_23 = m *[( cp *( t2 - t3 ) ) +( C2 ^2 - C3 ^2) /2/1000];
disp ( ” Power o u t p u t o f t u r b i n e=” )
disp ( W_23 )
disp ( ”kW” )
disp ( ” ( i i i ) N o z z l e ” )
C4 = sqrt (2*1000*( cp *( t3 - t4 ) + C3 ^2/2/1000) ) ;
disp ( ” V e l o c i t y a t e x i t from t h e n o z z l e= ” )
disp ( C4 )
disp ( ”m/ s ” )
Scilab code Exa 4.51 51
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V =0.028; //mˆ3
p1 =80; // b a r
t =350; // 0C
p2 =50; // b a r
v1 =0.02995; //mˆ3/ kg
h1 =2987.3; // kJ / kg
v2 =0.02995; //mˆ3/ kg
vg2 =0.0394; //mˆ3/ kg
uf2 =1149; // kJ / kg
ug2 =2597; // kJ / kg
m = V / v1 ;
u1 = h1 - ( p1 * v1 *10^2) ; // kJ / kg
disp ( ” ( i ) S t a t e o f steam a f t e r c o o l i n g ” )
x2 = v2 / vg2 ;
disp ( ” d r y n e s s f r a c t i o n = ” )
disp ( x2 )
disp ( ” ( i i ) Heat r e j e c t e d by t h e steam ” )
u2 =(1 - x2 ) * uf2 + x2 * ug2 ;
Q = m *( u2 - u1 ) ;
disp ( ” Heat r e j e c t e d = ” )
disp ( - Q )
disp ( ” kJ ” )
Scilab code Exa 4.52 52
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m =0.08; // kg
p =2*10^5; // Pa
V =0.10528; //mˆ3
h1 =2706.3; // kJ / kg
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h2 =3071.8; // kJ / kg
v1 =0.885; //mˆ3/ kg
v2 = V / m ; //mˆ3/ kg
disp ( ” ( i ) Heat s u p p l i e d ” )
Q = m *( h2 - h1 ) ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( i i ) Work done ” )
W = p *( v2 - v1 ) ;
W_total = m * W /10^3;
disp ( ” T o t a l work done = ” )
disp ( W_total )
disp ( ” kJ ” )
Scilab code Exa 4.53 53
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m =1; // kg
p =8; // b a r
s1 =6.55; // kJ / kg . K
T =200; // 0C
s_f1 =2.0457; // kJ / kg . K
s_fg1 =4.6139; // kJ / kg . K
h_f1 =720.9; // kJ / kg
h_fg1 =2046.5; // kJ / kg
h2 =2839.3; // kJ / kg
x1 =( s1 - s_f1 ) / s_fg1 ;
h1 = h_f1 + x1 * h_fg1 ;
Q = h2 - h1 ;
disp ( ” Heat s u p p l i e d=” )
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disp ( Q )
disp ( ” kJ / kg ” )
// For T−s d i a g r a m
s =0:0.01:10;
T =( -( s -5) ^2+298) ;
plot (s , T )
T =[295.44 295.44];
s =[6.6 3.45];
plot (s ,T , ’ g ’ )
s =[6.6 7];
T =[295.44 300];
plot (s ,T , ’ g ’ )
s =[6.55 6.55];
T =[270 295.44];
plot (s ,T , ’ r ’ )
s =[6.6 6.6];
T =[270 295.44];
plot (s ,T , ’−−r ’ )
s =[6.66 6.66];
T =[270 295.44];
plot (s ,T , ’ r ’ )
xtitle ( ”T−s d i a g r a m ” , ” s ( kJ / kg K) ” , ”T(K) ” )
// The a r e a i n r e d r e p r e s e n t s t h e h e a t f l o w and i t
g o e s u p t o x−a x i s
Scilab code Exa 4.54 54
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p1 =7*10^5; // Pa
p2 =1.5*10^5; // Pa
Q =420; // kJ / kg
uf =696; // kJ / kg
x =0.95;
ug =2573; // kJ / kg
u_f2 =2580; // kJ / kg
u_g2 =2856; // kJ / kg
x2 =15/50;
h_f1 =697.1; // kJ / kg
h_fg1 =2064.9; // kJ . kg
h_f2 =2772.6; // kJ / kg
h_g2 =2872.9; // kJ / kg
disp ( ” ( i ) Change o f i n t e r n a l e n e r g y ” )
u1 =(1 - x ) * uf + x * ug ;
u2 =2602.8; // kJ / kg
du = u2 - u1 ;
disp ( ” du=” )
disp ( du )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Change i n e n t h a l p y ” )
h1 = h_f1 + x * h_fg1 ;
h2 = h_f2 + x2 *( h_g2 - h_f2 ) ;
dh = h2 - h1 ;
disp ( ” dh=” )
disp ( dh )
disp ( ” kJ / kg ” )
disp ( ” ( i i i ) Work done = ” )
W =Q - du ;
disp ( ”W=” )
disp ( W )
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disp ( ” kJ / kg ” )
Scilab code Exa 4.55 55
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p1 =5.5*10^5; // Pa
x1 =1;
p2 =0.75*10^5; // Pa
v1 =0.3427; //mˆ3/ kg
v2 = p1 * v1 / p2 ;
// S i n c e v2 > vg ( a t 0 . 7 5 b a r ) , t h e r e f o r e , t h e steam
i s superheated at s t a t e 2 .
u2 =2567.25; // kJ / kg
u1 =2565; // kJ / kg
du = u2 - u1 ; // kJ / kg
C = p1 * v1 ;
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13 disp ( ”Work done = ” )
14 W = integrate ( ’C/ v ’ , ’ v ’ , v1 , v2 )
15 disp ( ”N−m/ kg ” )
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18 disp ( ” Heat s u p p l i e d = ” )
19 Q = du + W /10^3;
20 disp ( Q )
21 disp ( ” kJ / kg ” )
Scilab code Exa 4.56 56
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p1 =100; // b a r
p2 =10; // b a r
s1 =5.619; // kJ / kg . K
T =584; //K
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s2 =7.163; // kJ / kg . K
u1 =2545; // kJ / kg
u2 =2811.8; // kJ / kg
disp ( ” ( i ) Heat s u p p l i e d ” )
Q = T *( s2 - s1 ) ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Work done ” )
W =Q -( u2 - u1 ) ;
disp ( ”W=” )
disp ( W )
disp ( ” kJ / kg ” )
Scilab code Exa 4.57 57
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m =1; // kg
p1 =120*10^5; //N/mˆ2
t1 =400; // 0C
p2 =38; // b a r
h1 =3051.3; // kJ / kg
v1 =0.02108; //mˆ3/ kg
u1 = h1 - p1 * v1 /10^3; // kJ / kg
u2 =2602; // kJ / kg
disp ( ”WOrk done = ” )
W = u1 - u2 ;
disp ( W )
disp ( ” kJ / kg ” )
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Scilab code Exa 4.58 58
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p1 =7*10^5; //N/mˆ2
x1 =0.98;
p2 =0.34*10^5; //N/mˆ2
vg =0.273; //mˆ3/ kg
n =1.1;
v_g2 =4.65; //mˆ3/ kg
u_f1 =696; // kJ / kg
u_g1 =2573; // kJ / kg
u_f2 =302; // kJ / kg
u_g2 =2472; // kJ / kg
v1 = x1 * vg ;
v2 = v1 *( p1 / p2 ) ^(1/ n ) ;
x2 = v2 / v_g2 ;
disp ( ” ( i ) Work done by t h e steam d u r i n g t h e p r o c e s s ”
)
W =( p1 * v1 - p2 * v2 ) /( n -1) /10^3; // kJ / kg
disp ( ”W=” )
disp ( W )
disp ( ” kJ / kg ” )
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27 u1 =(1 - x1 ) * u_f1 + x1 * u_g1 ;
28 u2 =(1 - x2 ) * u_f2 + x2 * u_g2 ;
29 Q = u2 - u1 + W ;
30 disp ( ”Q=” )
31 disp ( Q )
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disp ( ” kJ / kg ” )
Scilab code Exa 4.59 59
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p1 =15; // b a r
t1 =350; // 0C
C1 =60; //m/ s
p2 =1.2; // b a r
C2 =180; //m/ s
s1 =7.102; // kJ / kg
s_f2 =1.3609; // kJ / kg
s_g2 =7.2884; // kJ / kg
h_f2 =439.4; // kJ / kg
h_fg2 =2241.1; // kJ / kg
h1 =3147.5; // kJ / kg
x2 =( s1 - s_f2 ) /( s_g2 - s_f2 ) ;
h2 = h_f2 + x2 * h_fg2 ;
W =( h1 - h2 ) + ( C1 ^2 - C2 ^2) /2/1000;
disp ( ”Work done = ” )
disp ( W )
disp ( ” kJ / kg ” )
Scilab code Exa 4.60 60
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p1 =10; // b a r
t1 =200; // 0C
C1 =60; //m/ s ˆ2
c2 =650; //m/ s
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p2 =1.5; // b a r
h1 =2827.9; // kJ / kg
h_f2 =467.1; // kJ / kg
h2 =2618.45; // kJ / kg
h_g2 =2693.4; // kJ / kg
x2 =( h2 - h_f2 ) /( h_g2 - h_f2 ) ;
disp ( ” q u a l i t y o f steam l e a v i n g t h e n o z z l e=” )
disp ( x2 )
Scilab code Exa 4.61 61
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h1 =2776.4; // kJ / kg
h2 = h1 ;
h_f1 =884.6; // kJ / kg
h_fg1 =1910.3; // kJ / kg
x1 =( h1 - h_f1 ) / h_fg1 ;
disp ( ” I n i t i a l d r y n e s s f r a c t i o n = ” )
disp ( x1 )
Scilab code Exa 4.62 62
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p1 =10; // b a r
x1 =0.9; // b a r
p2 =2; // b a r
// U s i n g M o l l i e r c h a r t , we g e t
x2 =0.94;
disp ( ” x2 =” )
disp ( x2 )
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Scilab code Exa 4.63 63
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disp ( ” ( a ) From steam t a b l e s ” )
p1 =15*10^5; // Pa
p2 =7.5*10^5; // Pa
h_f1 =844.7; // kJ / kg
ts1 =198.3; // 0C
s_f1 =2.3145; // kJ / kg . K
s_g1 =6.4406; // kJ / kg . K
v_g1 =0.132; //mˆ3/ kg
h_fg1 =1945.2; // kJ / kg
x1 =0.95;
h_f2 =709.3; // kJ / kg
h_fg2 =2055.55; // kJ / kg
s_f2 =2.0195; // kJ / kg
s_g2 =6.6816; // kJ / kg . K
v_g2 =0.255; //mˆ3/ kg
x2 =0.9;
x3 =1;
s_f3 =0.521; // kJ / kg K
s_g3 =8.330; // kJ / kg K
h2 = h_f2 + x2 * h_fg2 ;
h1 = h_f1 + x1 * h_fg1 ;
s1 = s_f1 + x1 *( s_g1 - s_f1 ) ;
s2 = s1 ;
ds_12 = s2 - s1 ;
s3 = s_f3 + x3 *( s_g3 - s_f3 ) ;
ds_23 = s3 - s2 ;
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ds = ds_12 + ds_23 ;
disp ( ” ( i ) Change i n e n t r o p y =” )
disp ( ds )
disp ( ” kJ / kg K” )
h3 = h2 ;
disp ( ” ( i i ) Change i n e n t h a l p y ” )
dh = h2 - h1 ;
disp ( dh )
disp ( ” kJ / kg ” )
disp ( ” ( i i i ) Change i n i n t e r n a l e n e r g y ” )
u1 = h1 - p1 * x1 * v_g1 /10^3;
u2 = h2 - p2 * x2 * v_g2 /10^3;
du = u2 - u1 ;
disp ( ” du=” )
disp ( du )
disp ( ” kJ / kg ” )
// Only t h e e x p a n s i o n o f steam from p o i n t 1 t o 2 ( i .
e . , i s e n t r o p i c expansion ) i s r e v e r s i b l e because
o f u n r e s i s t e d f l o w w h e r e a s t h e e x p a n s i o n from
point 2 to point 3 ( i . e . , t h r o t t l i n g expansion )
i s i r r e v e r s i b l e because of f r i c t i o n a l r e s i s t a n c e
t o f l o w . I n c r e a s e o f e n t r o p y a l s o shows t h a t
e x p a n s i o n from p o i n t 2 t o p o i n t 3 i s i r r e v e r s i b l e
.
disp ( ” ( b ) U s i n g M o l l i e r c h a r t ” )
h1 =2692; // kJ / kg
h2 =2560; // kJ / kg
s1 =6.23; // kJ / kg K
s2 = s1 ;
s3 =8.3; // kJ / kg K
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66 ds = s3 - s1 ;
67 disp ( ds )
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72 dh = h2 - h1 ;
73 disp ( dh )
74 disp ( ” kJ / kg ” )
Scilab code Exa 4.64 64
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V1 =5.5; //mˆ3
p1 =16*10^5; // Pa
T1 =315; //K
V2 = V1 ;
p2 =12*10^5; // Pa
R =0.287*10^3;
y =1.4;
m1 = p1 * V1 / R / T1 ;
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
m2 = p2 * V2 / R / T2 ;
disp ( ” Mass o f a i r which l e f t t h e r e c e i v e r =” )
m = m1 - m2 ;
disp ( m )
disp ( ” kg ” )
Scilab code Exa 4.65 65
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cp =1; // kJ / kg . K
cv =0.711; // kJ / kg . K
V1 =1.6; //mˆ3
V2 = V1 ;
p1 =5*10^5; // Pa
T1 =373; //K
p2 =1*10^5; // Pa
R =287;
y =1.4;
m1 = p1 * V1 / R / T1 ;
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
m2 = p2 * V2 / R / T2 ;
KE =( m1 * cv * T1 ) -( m2 * cv * T2 ) -( m1 - m2 ) * cp * T2 ;
disp ( ” K i n e t i c e n e r g y o f d i s c h a r g e a i r =” )
disp ( KE )
disp ( ” kJ ” )
disp ( ” T h i s i s t h e e x a c t a n s w e r when u s i n g p r o p e r
v a l u e o f cv ” )
Scilab code Exa 4.66 66
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// For o x y g e n
cpa =0.88; // kJ / kg K
Ra =0.24; // kJ / kg K
V1a =0.035; //mˆ3
p1a =4.5; // b a r
T1a =333; //K
V2a =0.07; //mˆ3
// For methane
V1b =0.07; //mˆ3
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V2b =0.035; //mˆ3
p1b =4.5; // b a r
T1b =261; //K
cpb =1.92; // kJ / kg K
Rb =0.496; // kJ / kg K
yb = cpb /( cpb - Rb ) ; // f o r methane
cva = cpa - Ra ; // f o r o x y g e n
disp ( ” ( i ) F i n a l s t a t e c o n d i t i o n ” )
p2b = p1b *( V1b / V2b ) ^ yb ;
disp ( ” p2 f o r methane =” )
disp ( p2b )
disp ( ” b a r ” )
T2b = p2b * V2b * T1b / p1b / V1b ;
disp ( ”T2 f o r methane =” )
disp ( T2b )
disp ( ”K” )
p2a = p2b ;
T2a = p2a * V2a / p1a / V1a * T1a ;
disp ( ”T2 f o r o x y g e n =” )
disp ( T2a )
disp ( ”K” )
Wb =( p1b * V1b - p2b * V2b ) /( yb -1) *100; // kJ
disp ( ” ( i i ) Work done by t h e p i s t o n ” )
disp ( ” The p i s t o n w i l l be i n v i r t u a l e q u i l i b r i u m and
h e n c e z e r o work i s e f f e c t e d by t h e p i s t o n . ” )
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50 disp ( ” ( i i i ) Heat t r a n s f e r r e d
51 disp ( Q )
52 disp ( ” kJ ” )
98
t o o x y g e n =” )
Chapter 5
Second Law of
Thermodynamics and Entropy
Scilab code Exa 5.1 1
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Q1 =1500/60; // kJ / s
W =8.2; //kW
disp ( ” ( i ) Thermal e f f i c i e n c y ” )
n = W / Q1 ;
disp ( ” n=” )
disp ( n )
disp ( ” ( i i ) Rate o f h e a t r e j e c t i o n ” )
Q2 = Q1 - W ;
disp ( ”Q2=” )
disp ( Q2 )
disp ( ”kW” )
99
Scilab code Exa 5.2 2
1 clc
2 Q_12 =30; // kJ
3 W_12 =60; // kJ
4 dU_12 = Q_12 - W_12 ;
5 Q_21 =0;
6 W_21 = Q_21 + dU_12 ;
7 disp ( ”W 21 =” )
8 disp ( W_21 )
9 disp ( ” Thus 30 kJ work h a s t o be done on t h e s y s t e m
t o r e s t o r e i t t o o r i g i n a l s t a t e , by a d i a b a t i c
p r o c e s s . ”)
Scilab code Exa 5.3 3
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clc
Q2 =12000; // kJ /h
W =0.75*60*60; // kJ /h
COP = Q2 / W ;
disp ( ” C o e f f i c i e n t o f p e r f o r m a n c e ” )
disp ( COP )
Q1 = Q2 + W ;
disp ( ” h e a t t r a n s f e r r a t e=” )
disp ( Q1 )
disp ( ” kJ / h ” )
Scilab code Exa 5.4 4
1 clc
2 T2 =261; //K
3 T1 =308; //K
100
4 Q2 =2; // kJ / s
5 Q1 = Q2 *( T1 / T2 ) ;
6 W = Q1 - Q2 ;
7
8 disp ( ” L e a s t power r e q u i r e d t o pump t h e h e a t
c o n t i n u o s l y ”)
9 disp ( W )
10 disp ( ”kW” )
Scilab code Exa 5.5 5
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disp ( ” ( i ) Heat a b s t r a c t e d from o u t s i d e=” )
Q1 =2*10^5; // kJ /h
W =3*10^4; // kJ /h
Q2 = Q1 - W ;
disp ( ” Heat a b s t r a c t e d from o u t s i d e=” )
disp ( Q2 )
disp ( ” kJ / h ” )
disp ( ” ( i i ) Co− e f f i c i e n t o f p e r f o r m a n c e ” )
COP_hp = Q1 /( Q1 - Q2 ) ;
disp ( ”Co− e f f i c i e n t o f p e r f o r m a n c e=” )
disp ( COP_hp )
Scilab code Exa 5.6 6
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2 T1 =2373; //K
3 T2 =288; //K
4 n_max =1 - T2 / T1 ;
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disp ( ” H i g h e s t p o s s i b l e
disp ( n_max *100)
disp ( ”%” )
theoritical
e f f i c i e n c y =” )
Scilab code Exa 5.7 7
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T1 =523; //K
T2 =258; //K
Q1 =90; // kJ
n =1 - T2 / T1 ;
disp ( ” ( i ) E f f i c i e n c y o f t h e s y s t e m ” )
disp ( n *100)
disp ( ”%” )
disp ( ” ( i i ) The n e t work t r a n s f e r ” )
W = n * Q1 ;
disp ( ”W=” )
disp ( W )
disp ( ” kJ ” )
disp ( ” ( i i i ) Heat r e j e c t e d t o t h e s i n k ” )
Q2 = Q1 - W ;
disp ( ”Q2=” )
disp ( Q2 )
disp ( ” kJ ” )
Scilab code Exa 5.8 8
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T1 =1023; //K
T2 =298; //K
n_carnot =1 - T2 / T1 ;
W =75*1000*60*60;
Q =3.9*74500*1000;
n_thermal = W / Q ;
disp ( ” n c a r n o t =” )
disp ( n_carnot )
disp ( ” n t h e r m a l =” )
disp ( n_thermal )
disp ( ” S i n c e
thermal
>
carnot , t h e r e f o r e c l a i m o f
the i n v e n t o r i s not v a l i d ( or p o s s i b l e ”)
Scilab code Exa 5.9 9
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T1 =1273; //K
T2 =313; //K
n_max =1 - T2 / T1 ;
Wnet =1;
Q1 = Wnet / n_max ;
Q2 = Q1 - Wnet ;
disp ( ” t h e l e a s t r a t e o f h e a t r e j e c t i o n = ” )
disp ( Q2 )
disp ( ”kW” )
Scilab code Exa 5.10 10
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2 one_ton_of_refrigeration =210; // kJ / min
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Cooling_required =40*( one_ton_of_refrigeration ) ; // kJ
/ min
T1 =303; //K
T2 =238; //K
COP_refrigerator = T2 /( T1 - T2 ) ;
COP_actual =0.20* COP_refrigerator ;
W = Cooling_required / COP_actual /60;
disp ( ” power r e q u i r e d = ” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 5.11 11
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E =12000; // kJ / min
T2 =308; //K
// S o u r c e 1
T1 =593; //K
n1 =1 - T2 / T1 ;
// S o u r c e 2
T1 =343; //K
n2 =1 - T2 / T1 ;
W1 = E * n1 ;
disp ( ”W1 =” )
disp ( W1 )
W2 = E * n2 ;
disp ( ”W2 =” )
disp ( W2 )
disp ( ” Thus , c h o o s e s o u r c e 2 . ” )
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23
disp ( ” The s o u r c e 2 i s s e l e c t e d e v e n t h o u g h
e f f i c i e n c y in t h i s case i s lower , because the
c r i t e r i o n f o r s e l e c t i o n i s the l a r g e r output . ”)
Scilab code Exa 5.12 12
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T1 =973; //K
T2 =323; //K
T3 =248; //K
Q1 =2500; // kJ
W =400; // kJ
disp ( ” ( i ) Heat r e j e c t i o n t o t h e 50 C r e s e r v o i r ” )
n_max =1 - T2 / T1 ;
W1 = n_max * Q1 ;
COP_max = T3 /( T2 - T3 ) ;
W2 = W1 - W ;
Q4 = COP_max * W2 ;
COP1 = Q4 / W2 ;
Q3 = Q4 + W2 ;
Q2 = Q1 - W1 ;
disp ( ” Heat r e j e c t i o n t o t h e 50 C r e s e r v o i r =” )
disp ( Q2 + Q3 )
disp ( ” kJ ” )
disp ( ” ( i i ) Heat r e j e c t e d t o 50 C
n =0.45* n_max ;
W1 = n * Q1 ;
W2 = W1 - W ;
COP2 =0.45* COP1 ;
Q4 = W2 * COP2 ;
Q3 = Q4 + W2 ;
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r e s e r v o i r ”)
30 Q2 = Q1 - W1 ;
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32 disp ( ” Heat r e j e c t e d
33 disp ( Q2 + Q3 )
34 disp ( ” kJ ” )
t o 50 C
r e s e r v o i r =” )
Scilab code Exa 5.13 13
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T1 =298; //K
T2 =273; //K
Q1 =24; // kJ / s
T3 =653; //K
COP = T1 /( T1 - T2 ) ;
disp ( ” ( i ) d e t e r m i n e COP and work i n p u t r e q u i r e d ” )
disp ( ” C o e f f i c i e n t o f p e r f o r m a n c e = ” )
disp ( COP )
COP_ref = T2 /( T1 - T2 ) ;
W = Q1 / COP_ref ;
disp ( ”Work i n p u t r e q u i r e d = ” )
disp ( W )
disp ( ”kW” )
disp ( ” ( i i ) D e t e r m i n e o v e r a l l COP o f t h e s y s t e m ” )
Q4 = T1 * W /( T3 - T1 ) ;
Q3 = Q4 + W ;
Q2 = Q1 + W ;
COP = Q1 / Q3 ;
disp ( ”COP=” )
disp ( COP )
COP_overall =( Q2 + Q4 ) / Q3 ;
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disp ( ” O v e r a l l COP=” )
disp ( COP_overall )
Scilab code Exa 5.14 14
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T_e1 =493; //K
T_e2 =298; //K
T_p1 =298; //K
T_p2 =273; //K
Amt =15; // t o n n e s p r o d u c e d p e r day
h =334.5; // kJ / kg
Q_abs =44500; // kJ / kg
Q_p2 = Amt *10^3* h /24/60;
COP_hp = T_p2 /( T_p1 - T_p2 ) ;
W = Q_p2 / COP_hp /60;
disp ( ” ( i ) Power d e v e l o p e d by t h e e n g i n e = ” )
disp ( W )
disp ( ”kW” )
disp ( ” ( i i ) F u e l consumed p e r h o u r ” )
n_carnot =1 -( T_e2 / T_e1 ) ;
Q_e1 = W / n_carnot *3600; // kJ /h
fuel_consumed = Q_e1 / Q_abs ;
disp ( ” Q u a n t i t y o f f u e l consumed / h o u r = ” )
disp ( fuel_consumed )
disp ( ” kg /h ” )
Scilab code Exa 5.15 15
1 clc
2 T1 =550; //K
107
3 T3 =350; //K
4 // W=Q2 ∗ ( ( T1−T2 ) /T2 )
5 // W=Q2 ( ( T2−T3 ) /T2 )
6 // From t h i s we g e t f o l l o w i n g e x p r e s s i o n
7 T2 =( T1 + T3 ) /2;
8 disp ( ” I n t e r m e d i a t e t e m p e r a t u r e =” )
9 disp ( T2 )
10 disp ( ”K” )
Scilab code Exa 5.16 16
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clc
T1 =600; //K
T2 =300; //K
disp ( ” ( i ) When Q1=Q2” )
T3 =2* T1 /( T1 / T2 +1) ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
disp ( ” ( i i ) E f f i c i e n c y o f C a r n o t e n g i n e and COP o f
carnot r e f r i g e r a t o r ”)
14 n =( T1 - T3 ) / T1 ; // c a r n o t e n g i n e
15 COP = T2 /( T3 - T2 ) ; // r e f r i g e r a t o r
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disp ( ” E f f i c i e n c y o f c a r n o t e n g i n e = ” )
disp ( n )
disp ( ”COP o f c a r n o t r e f r i g e r a t o r = ” )
disp ( COP )
108
Scilab code Exa 5.17 17
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T3 =278; //K
T2 =350; //K
T4 = T2 ;
T1 =1350; //K
Q1 =100/[(( T4 / T1 ) *( T1 - T2 ) /( T4 - T3 ) ) + T2 / T1 ]; //Q4+Q2
=100; Q4=Q1 ∗ ( ( T4/T1 ) ∗ ( T1−T2 ) / ( T4−T3 ) ) ; Q2=T2/T1∗
Q1 ;
disp ( ”Q1=” )
disp ( Q1 )
disp ( ” kJ ” )
Scilab code Exa 5.18 18
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Q1 =300; // kJ / s
T1 =290; // 0C
T2 =8.5; // 0C
disp ( ” l e t dQ /T = A” )
disp ( ” ( i ) 215 kJ / s a r e r e j e c t e d ” )
Q2 =215; // kJ / s
A = Q1 /( T1 +273) - Q2 /( T2 +273)
disp ( ” S i n c e , A<0 , C y c l e i s i r r e v e r s i b l e . ” )
disp ( ” ( i i ) 150 kJ / s a r e r e j e c t e d ” )
Q2 =150; // kJ / s
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15 A = Q1 /( T1 +273) - Q2 /( T2 +273)
16 disp ( ” S i n c e A=0 , c y c l e i s r e v e r s i b l e ” )
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19 disp ( ” ( i i i ) 75 kJ / s a r e r e j e c t e d . ” )
20 Q2 =75; // kJ / s
21 A = Q1 /( T1 +273) - Q2 /( T2 +273)
22 disp ( ” S i n c e A>0 , c y c l e i s i m p o s s i b l e ” )
Scilab code Exa 5.19 19
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P1 =0.124*10^5; //N/mˆ2
T1 =433; //K
T2 =323; //K
h_f1 =687; // kJ / kg
h2 =2760; // kJ / kg
h3 =2160; // kJ / kg
h_f4 =209; // kJ / kg
Q1 = h2 - h_f1 ;
Q2 = h_f4 - h3 ;
disp ( ” L e t A= dQ /T” )
A = Q1 / T1 + Q2 / T2 ;
disp ( A )
disp ( ”A<0. Hence c l a s s i u s i n e q u a l i t y i s
Scilab code Exa 5.20 20
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T1 =437; //K
T2 =324; //K
h2 =2760; // kJ / kg
h1 =690; // kJ / kg
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v e r i f i e d ”)
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h3 =2360; // kJ / kg
h4 =450; // kJkg
Q1 = h2 - h1 ;
Q2 = h4 - h3 ;
disp ( ” L e t A= dQ /T” )
A = Q1 / T1 + Q2 / T2 ;
disp ( A )
disp ( ” S i n c e A<0 , C l a s s i u s i n e q u a l i t y i s
v e r i f i e d ”)
Scilab code Exa 5.21 21
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T0 =273; //K
T1 =673; //K
T2 =298; //K
m_w =10; // kg
T3 =323; //K
c_pw =4186; // kJ / kg . K
disp ( ” L e t C=mi ∗ c p i ” )
C = m_w * c_pw *( T3 - T2 ) /( T1 - T3 ) ;
S_iT1 = C * log ( T1 / T0 ) ; // Entropy o f i r o n a t 673 K
S_wT2 = m_w * c_pw * log ( T2 / T0 ) ; // Entropy o f w a t e r a t 298
K
13 S_iT3 = C * log ( T3 / T0 ) ; // Entropy o f i r o n a t 323 K
14 S_wT3 = m_w * c_pw * log ( T3 / T0 ) ; // Entropy o f w a t e r a t 323
K
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dS_i = S_iT3 - S_iT1 ;
dS_w = S_wT3 - S_wT2 ;
dS_net = dS_i + dS_w
disp ( ” S i n c e dS >0 , p r o c e s s i s
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i r r e v e r s i b l e ”)
Scilab code Exa 5.23 23
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T1 =293; //K
V1 =0.025; //mˆ3
V3 = V1 ;
p1 =1.05*10^5; //N/mˆ2
p2 =4.5*10^5; //N/mˆ2
R =0.287*10^3;
cv =0.718;
cp =1.005;
T3 =293; //K
disp ( ” ( i ) Net h e a t f l o w ” )
m = p1 * V1 / R / T1 ;
T2 = p2 / p1 * T1 ;
Q_12 = m * cv *( T2 - T1 ) ;
Q_23 = m * cp *( T3 - T2 )
disp ( ” Net h e a t f l o w = ” )
Q_net = Q_12 + Q_23 ;
disp ( Q_net )
disp ( ” kJ ” )
disp ( ” ( i i ) Net e n t r o p y c h a n g e ” )
dS_32 = m * cp * log ( T2 / T1 ) ;
dS_12 = m * cv * log ( T2 / T1 ) ;
dS_31 = dS_32 - dS_12 ;
disp ( ” D e c r e a s e i n e n t r o p y = ” )
disp ( dS_31 )
disp ( ” kJ /K” )
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Scilab code Exa 5.24 24
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p1 =1.05*10^5; //N/mˆ2
V1 =0.04; //mˆ3
T1 =288; //K
p2 =4.8*10^5;
T2 = T1 ;
R0 =8314;
M =28;
disp ( ” ( i ) The c h a n g e o f e n t r o p y =” )
R = R0 / M ;
m = p1 * V1 / R / T1 ;
dS = m * R * log ( p1 / p2 )
disp ( ” D e c r e a s e i n e n t r o p y =” )
disp ( - dS )
disp ( ” J /K” )
disp ( ” ( i i ) Heat r e j e c t e d = ” )
Q = T1 *( - dS ) ;
disp ( ”Q=” )
disp ( Q )
disp ( ” J ” )
W=Q;
disp ( ”Work done = ” )
disp ( W )
disp ( ” J ” )
V2 = p1 * V1 / p2 ;
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v1 = V1 / m ; // s p e c i f i c volume
v2 = V2 / m ; // s p e c i f i c volume
v = v2 :0.01: v1 ;
function p = f ( v )
p = p1 * v1 / v
endfunction
plot (v , f )
p = p1
plot (v ,p , ’−− ’ )
p =[0 p2 ]
v =[ v2 v2 ]
plot (v ,p , ’−− ’ )
p =[0 p1 ]
v =[ v1 v1 ]
plot (v ,p , ’−− ’ )
xtitle ( ”p−v d i a g r a m ” , ” v (mˆ3/ kg ) ” , ” p (N/mˆ 2 ) ” )
xset ( ’ window ’ , 1)
T =[288 288]
s =[10 (10 - dS ) ]
plot (s , T )
s =[10 10]
T =[0 288]
plot (s ,T , ’−− ’ )
s =[(10 - dS ) (10 - dS ) ]
T =[0 288]
plot (s ,T , ’−− ’ )
xtitle ( ”T−s d i a g r a m ” , ” s ( kJ / kg K) ” , ”T(K) ” )
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Scilab code Exa 5.25 25
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R =287; // kJ / kg . K
dU =0;
W =0;
Q = dU + W ;
dS = R * log (2) ; // v2 / v1=2
disp ( ” Change i n e n t r o p y = ” )
disp ( dS )
disp ( ” kJ / kg . K” )
Scilab code Exa 5.26 26
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m =0.04; // kg
p1 =1*10^5; //N/mˆ2
T1 =293; //K
p2 =9*10^5; //N/mˆ2
V2 =0.003; //mˆ3
cp =0.88; // kJ / kg . K
R0 =8314;
M =44;
R = R0 / M ;
T2 = p2 * V2 / m / R ;
ds_2A = R /10^3* log ( p2 / p1 ) ;
ds_1A = cp * log ( T2 / T1 ) ;
ds_21 = ds_2A - ds_1A ;
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dS_21 = m * ds_21 ;
disp ( ” D e c r e a s e i n e n t r o p y=” )
disp ( dS_21 )
disp ( ” kJ /K” )
Scilab code Exa 5.27 27
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p1 =7*10^5; //N/mˆ2
T1 =873; //K
p2 =1.05*10^5; //N/M62
n =1.25;
m =1; // kg
R =0.287;
cp =1.005;
T2 = T1 *( p2 / p1 ) ^(( n -1) / n ) ;
// At c o n s t a n t t e m p e r a t u r e from 1 t o A
ds_1A = R * log ( p1 / p2 ) ;
// At c o n s t a n t p r e s s u r e from A t o 2
ds_2A = cp * log ( T1 / T2 ) ;
ds_12 = ds_1A - ds_2A ;
disp ( ” I n c r e a s e i n e n t r o p y = ” )
disp ( ds_12 )
disp ( ” kJ / kg . K” )
Scilab code Exa 5.28 28
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2 p1 =7*10^5; // Pa
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T1 =733; //K
p2 =1.012*10^5; // Pa
T2a =433; //K
y =1.4;
cp =1.005;
disp ( ” ( i ) To p r o v e t h a t t h e p r o c e s s i s i r r e v e r s i b l e ”
)
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
disp ( ”T2 =” )
disp ( T2 )
disp ( ” But t h e a c t u a l t e m p e r a t u r e i s 433K a t t h
e p r e s s u r e o f 1 . 0 1 2 bar , Hence t h e p r o c e s s i s
i r r e v e r s i b l e . Proved . ” )
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16 disp ( ” ( i i ) Change o f e n t r o p y p e r kg o f
17 ds = cp * log ( T2a / T2 ) ;
18 disp ( ” I n c r e a s e o f e n t r o p y=” )
19 disp ( ds )
20 disp ( ” kJ / kg . K” )
Scilab code Exa 5.29 29
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V1 =0.3; //mˆ3
p1 =4*10^5; //N/mˆ2
V2 =0.08; //mˆ3
n =1.25;
p2 = p1 *( V1 / V2 ) ^ n ;
disp ( ” ( i ) Change i n e n t h a l p y ” )
dH = n *( p2 * V2 - p1 * V1 ) /( n -1) /10^3;
disp ( ”dH=” )
disp ( dH )
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a i r ”)
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disp ( ” kJ ” )
disp ( ” ( i i ) Change i n i n t e r n a l e n e r g y ” )
dU = dH -( p2 * V2 - p1 * V1 ) /10^3;
disp ( ”dU=” )
disp ( dU )
disp ( ” kJ ” )
disp ( ” ( i i i ) Change i n e n t r o p y ” )
dS =0;
disp ( ” dS ” )
disp ( dS )
disp ( ” ( i v ) Heat t r a n s f e r ” )
Q =0;
disp ( ”Q=” )
disp ( Q )
disp ( ” ( v ) Work t r a n s f e r ” )
W =Q - dU ;
disp ( ”W=” )
disp ( W )
disp ( ” kJ ” )
Scilab code Exa 5.30 30
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m =20; // kg
p1 =4*10^5; // Pa
p2 =8*10^5; // Pa
V1 =4; //mˆ3
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V2 = V1 ;
cp =1.04; // kJ / kg . K
cv =0.7432; // kJ / kg . K
R = cp - cv ;
T1 = p1 * V1 / R /1000; // kg . K ;
T2 = p2 * V2 / R /1000; // kg . K
T=mass ∗ t e m p e r a t u r e
disp ( ” ( i ) Change i n i n t e r n a l e n e r g y ” )
dU = cv *( T2 - T1 ) ;
disp ( ”dU=” )
disp ( dU )
disp ( ” kJ ” )
disp ( ” ( i i ) Work done ” )
Q =0;
W =Q - dU ;
disp ( ”W” )
disp ( W )
disp ( ” kJ ” )
disp ( ” ( i i i ) Heat t r a n s f e r r e d = ” )
disp ( Q )
disp ( ” ( i v ) Change i n e n t r o p y =” )
dS = m * cv * log ( T2 / T1 ) ;
disp ( dS )
disp ( ” kJ /K” )
Scilab code Exa 5.31 31
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V1 =5; //mˆ3
p1 =2*10^5; // Pa
T1 =300; //K
p2 =6*10^5; // Pa
p3 =2*10^5; // Pa
R =287;
n =1.3;
y =1.4;
m = p1 * V1 / R / T1 ;
T2 = T1 *( p2 / p1 ) ^(( n -1) / n ) ;
T3 = T2 *( p3 / p2 ) ^(( y -1) / y ) ;
W_12 = m * R *( T1 - T2 ) /( n -1) /1000; // p o l y t r o p i c
compression
15 W_23 = m * R *( T2 - T3 ) /( y -1) /1000; // A d i a b a t i c e x p a n s i o n
16
17 W_net = W_12 + W_23 ;
18 disp ( ” Net work done on t h e a i r = ” )
19 disp ( - W_net )
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21 T =[ T1 310 320 330 340 350 360 370 380 T2 ];
22 function s = f ( T )
23
s =( y - n ) /( y -1) /(1 - n ) * R /10^3* log ( T ) ;
24 endfunction
25 s =[ f ( T1 ) f (310) f (320) f (330) f (340) f (350) f (360) f
(370) f (380) f ( T2 ) ]
26 plot (s , T )
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28 T =[ T2 T3 ];
29 s =[ f ( T2 ) f ( T2 ) ];
30 plot (s ,T , ’ r ’ )
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32 xtitle ( ”T−s d i a g r a m ” , ” s ( kJ / kg K) ” , ”T(K) ” )
33 legend ( ” p∗ v ˆ1.3= c o n s t a n t ” , ” p∗ v ˆ y=c o n s t a n t ” )
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Scilab code Exa 5.32 32
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V1 =0.004; //mˆ3
p1 =1*10^5; // Pa
T1 =300; //K
T2 =400; //K
y =1.4;
M =28;
R0 =8.314;
R = R0 / M ;
disp ( ” ( i ) The h e a t s u p p l i e d ” )
m = p1 * V1 / R /1000/ T1 ; // kg
cv = R /( y -1) ;
Q = m * cv *( T2 - T1 ) ;
disp ( ”Q” )
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( i i ) The e n t r o p y c h a n g e ” )
dS = m * cv * log ( T2 / T1 ) ;
disp ( ” dS=” )
disp ( dS )
disp ( ” kJ / kg . K” )
Scilab code Exa 5.33 33
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V1 =0.05; //mˆ3
p1 =1*10^5; // Pa
T1 =280; //K
p2 =5*10^5; // Pa
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disp ( ” ( i ) Change i n e n t r o p y ” )
R0 =8.314;
M =28;
R = R0 / M ;
m = p1 * V1 / R / T1 /1000;
dS = m * R * log ( p1 / p2 ) ;
disp ( ” dS=” )
disp ( dS )
disp ( ” kJ /K” )
disp ( ” ( i i ) Work done ” )
Q = T1 * dS ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
Scilab code Exa 5.34 34
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R =0.287; // kJ / kg . K
m =1; // kg
p1 =8*10^5; // Pa
p2 =1.6*10^5; // Pa
T1 =380; //K
n =1.2;
y =1.4;
disp ( ” ( i ) F i n a l s p e c i f i c volume and t e m p e r a t u r e ” )
v1 = R * T1 / p1 *10^3; //mˆ3/ kg
v2 = v1 *( p1 / p2 ) ^(1/ n ) ;
T2 = T1 *( p2 / p1 ) ^(( n -1) / n ) ;
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disp ( ” v2=” )
disp ( v2 )
disp ( ”mˆ3/ kg ” )
disp ( ”T2=” )
disp ( T2 )
disp ( ” ( i i ) Change o f i n t e r n a l e n e r g y , work done and
heat i n t e r a c t i o n ”)
dU = R /( y -1) *( T2 - T1 ) ;
disp ( ”dU=” )
disp ( dU )
disp ( ” kJ / kg ” )
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28 W = R *( T1 - T2 ) /( n -1) ;
29 disp ( ”W=” )
30 disp ( W )
31 disp ( ” kJ / kg ” )
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33 Q = dU + W ;
34 disp ( ”Q=” )
35 disp ( Q )
36 disp ( ” kJ / kg ” )
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39 disp ( ” ( i i i ) Change i n e n t r o p y ” )
40 dS = R /( y -1) * log ( T2 / T1 ) + R * log ( v2 / v1 )
41 disp ( ” dS=” )
42 disp ( dS )
43 disp ( ” kJ / kg . K” )
Scilab code Exa 5.35 35
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2 y =1.4;
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cv =0.718; // kJ / kg . K
m =1; // kg
T1 =290; //K
n =1.3;
r =16;
y =1.4;
T2 = T1 *( r ) ^( n -1) ;
disp ( ” ( a ) ” )
T =[ T1 300 310 320 330 340 350 360 370 380 390 400
410 420 430 440 450 460 470 480 490 500 510 520
530 540 550 560 570 580 590 600 610 620 630 640
650 660 T2 ];
function s = f ( T )
s =( y - n ) * cv /(1 - n ) /10^3* log ( T ) ;
endfunction
s =[ f ( T1 ) f (300) f (310) f (320) f (330) f (340) f (350)
(360) f (370) f (380) f (390) f (400) f (410) f (420)
(430) f (440) f (450) f (460) f (470) f (480) f (490)
(500) f (510) f (520) f (530) f (540) f (550) f (560)
(570) f (580) f (590) f (600) f (610) f (620) f (630)
(640) f (650) f (660) f ( T2 ) ];
plot (s , T )
T =[0 T2 ];
s =[ f ( T2 ) f ( T2 ) ];
plot (s ,T , ’ r−− ’ )
T =[0 T1 ];
s =[ f ( T1 ) f ( T1 ) ];
plot (s ,T , ’ r−− ’ )
T =[ T1 T2 ];
s =[ f ( T1 ) f ( T2 ) ];
plot (s ,T , ’ r−− ’ )
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f
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xtitle ( ”T−s d i a g r a m ” , ” s ” , ”T” )
legend ( ” p∗ v ˆ n=c ” )
// Heat t r a n s f e r r e d = Area o f t r a p e z i u m = Base ∗mean
ordinate
// Heat t r a n s f e r r e d =dS ∗ ( T1+T2 ) /2
// Hence we g e t
disp ( ” Entropy c h a n g e=Heat t r a n s f e r r e d /Mean a b s o l u t e
temperature ”)
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42 disp ( ” ( b ) Entropy c h a n g e ” )
43 dS = cv *(( n - y ) /( n -1) ) * log ( T2 / T1 ) ;
44 disp ( ” dS=” )
45 disp ( dS )
46 disp ( ” kJ / kg . K” )
47 disp ( ” There i s d e c r e a s e i n e n t r o p y ” )
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49 Q = cv *(( y - n ) /( n -1) ) *( T1 - T2 ) ;
50 Tmean = ( T1 + T2 ) /2;
51 dS_app = Q / Tmean ;
52
53 %error =(( - dS ) - ( - dS_app ) ) /( - dS ) * 100;
54 disp ( ” %age e r r o r =” )
55 disp ( %error )
56 disp ( ”%” )
Scilab code Exa 5.36 36
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cp =1.005; // kJ / kg . K
R =0.287; // kJ / kg . K
V1 =1.2; //mˆ3
p1 =1*10^5; // Pa
p2 = p1 ;
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T1 =300; //K
T2 =600; //K
T3 = T1 ;
p1 =1*10^5; // Pa
cv = cp - R ;
disp ( ” ( i ) The n e t h e a t f l o w ” )
m = p1 * V1 / R /1000/ T1 ; // kg
Q = m * R *( T2 - T1 ) ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( i i ) The o v e r a l l c h a n g e i n e n t r o p y ” )
dS_12 = m * cp * log ( T2 / T1 ) ;
dS_23 = m *( cp - R ) * log ( T3 / T2 ) ; // cv=cp−R
dS_overall = dS_12 + dS_23 ;
disp ( ” O v e r a l l c h a n g e i n e n t r o p y=” )
disp ( dS_overall )
disp ( ” kJ /K” )
s = sqrt (300) :0.1: sqrt (600) ;
T = s ^2;
plot (s , T )
s =22.18:0.1: sqrt (600) ;
T =10*( s -16.725) ^2;
plot (s ,T , ’ r ’ )
s =[17 25];
T =[600 600];
plot (s ,T , ’−− ’ )
s =[17 25];
T =[300 300];
plot (s ,T , ’−− ’ )
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xtitle ( ”T−s d i a g r a m ” , ” S” , ”T” )
legend ( ” p=C” , ”V=C” )
Scilab code Exa 5.37 37
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cv =0.718; // kJ / kg . K
R =0.287; // kJ / kg . K
p1 =1*10^5; // Pa
T1 =300; //K
V1 =0.018; //mˆ3
p2 =5*10^5; // Pa
T3 = T1 ;
cp = cv + R ;
p3 = p2 ;
m = p1 * V1 / R / T1 /1000; // kg
T2 = T1 * p2 / p1 ;
disp ( ” ( i ) c o n s t a n t volume p r o c e s s ” )
disp ( ” dS=” )
dS_12 = m * cv * log ( T2 / T1 ) ;
disp ( dS_12 )
disp ( ” kJ /K” )
disp ( ” ( i i ) C o n s t a n t p r s s u r e p r o c e s s ” )
disp ( ” dS=” )
dS_23 = m * cp * log ( T3 / T2 ) ;
disp ( dS_23 )
disp ( ” kJ /K” )
disp ( ” ( i i i ) I s o t h e r m a l p r o c e s s ” )
disp ( ” dS=” )
dS_31 = m * R * log ( p3 / p1 ) ;
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disp ( dS_31 )
disp ( ” kJ /K” )
disp ( ”T−s d i a g r a m ” )
s = sqrt (300) :0.1: sqrt (600) ;
T = s ^2;
plot (s , T )
s =22.18:0.1: sqrt (600) ;
T =10*( s -16.725) ^2;
plot (s ,T , ’ r ’ )
s =[ sqrt (300) 22.18];
T =[300 300];
plot (s ,T , ’ g ’ )
xtitle ( ”T−s d i a g r a m ” , ” S” , ”T” )
legend ( ” p=C” , ”V=C” , ”T=C” )
disp ( ”p−V d i a g r a m ” )
xset ( ’ window ’ ,1)
V =[0.018 0.018];
p =[1 5];
plot (V , p )
p =[5 5];
V =[0.0036 0.018];
plot (V ,p , ’ r ’ )
V =0.0036:0.0001:0.018;
function p = f ( V )
p =1*0.018/ V ;
endfunction
plot (V ,f , ’ g ’ )
xtitle ( ”p−V d i a g r a m ” , ”V” , ” p” )
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legend ( ”V=C” ,” p=C” ,”T=C” )
Scilab code Exa 5.39 39
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m =4; // kg
T1 =400; //K
T2 =500; //K
dS = integrate ( ’m∗ ( 0 . 4 8 + 0 . 0 0 9 6 ∗T) /T ’ , ’T ’ , T1 , T2 ) ;
disp ( ” dS=” )
disp ( dS )
disp ( ” kJ ” )
Scilab code Exa 5.40 40
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p1 =1*10^5; // Pa
T1 =273; //K
p2 =25*10^5; // Pa
T2 =750; //K
R =0.29; // kJ / kg . K ; cp = 0 . 8 5 + 0 . 0 0 0 2 5 ∗T ; cv
= 0 . 5 6 + 0 . 0 0 0 2 5 ∗T ; R=cp−cv ;
7 v2 = R * T2 / p2 ;
8 v1 = R * T1 / p1 ;
9 ds = integrate ( ’ ( 0 . 5 6 + 0 . 0 0 0 2 5 ∗T) /T ’ , ’T ’ , T1 , T2 ) +
integrate ( ’R/ v ’ , ’ v ’ , v1 , v2 ) ;
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disp ( ” d s=” )
disp ( ds )
disp ( ” kJ / kg K” )
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Scilab code Exa 5.41 41
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cv =0.715; // kJ / kg K
R =0.287; // kJ / kg K
V_A =0.25; //mˆ3
p_Ai =1.4; // b a r
T_Ai =290; //K
V_B =0.25; //mˆ3
p_Bi =4.2; // b a r
T_Bi =440; //K
disp ( ” ( i ) F i n a l e q u i l i b r i u m t e m p e r a t u r e ” )
m_A = p_Ai * 10^5 * V_A / R / 1000/ T_Ai ; // kg
m_B = p_Bi * 10^5 * V_B / R / 1000/ T_Bi ; // kg
T_f =( m_B * T_Bi + m_A * T_Ai ) /( m_A + m_B ) ;
disp ( ” T f = ” )
disp ( T_f )
disp ( ”K” )
disp ( ” ( i i ) F i n a l p r e s s u r e on e a c h s i d e o f t h e
diaphragm ” )
p_Af = p_Ai * T_f / T_Ai ;
disp ( ” p A f=” )
disp ( p_Af )
disp ( ” b a r ” )
p_Bf = p_Bi * T_f / T_Bi ;
disp ( ” p B f=” )
disp ( p_Bf )
disp ( ” b a r ” )
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disp ( ” ( i i i ) Ent ropy c h a n g e o f t h e s y s t e m ” )
dS_A = m_A * cv * log ( T_f / T_Ai ) ;
dS_B = m_B * cv * log ( T_f / T_Bi ) ;
dS_net = dS_A + dS_B ;
disp ( ” Net c h a n g e o f e n t r o p y=” )
disp ( dS_net )
disp ( ” kJ /K” )
Scilab code Exa 5.42 42
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cv =1.25; // kJ / kg . K
T1 =530; //K
v1 =0.0624; //mˆ3/ kg
v2 =0.186; //mˆ3/ kg
dT_31 =25; //K
T3 = T1 - dT_31 ; //K
dT_21 =165; //K
T2 = T1 - dT_21 ; //K
// Path 1−2 : R e v e r s i b l e a d i a b a t i c p r o c e s s
ds_12 =0;
// To c a l c u l a t e ( s 3 s1 ) a r e v e r s i b l e p a t h h a s t o
be s e l e c t e d j o i n i n g 3 and 1 . T h i s i s a c h i e v e d by
s e l e c t i n g t h e r e v e r s i b l e a d i a b a t i c p a t h 1−2 and
t h e r e v e r s i b l e c o n s t a n t volume p r o c e s s 2 −3.
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15 // Path 1−3 : A d i a b a t i c p r o c e s s
16 v3 =0.186; //mˆ3/ kg
17 v3 = v2 ;
18 ds_13 = cv * log ( T3 / T2 ) ;
19 disp ( ” Chang i n e n t r o p y = ” )
20 disp ( ds_13 )
21 disp ( ” kJ /kgK” )
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Scilab code Exa 5.44 44
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T1 =500; //K
T2 =400; //K
T3 =300; //K
Q1 =1500; // kJ / min
W =200; // kJ / min
//Q1/T1 + Q2/T2 + Q3/T3=0
//Q1+Q2+Q3=W
// For s o l v i n g t h e a b o v e two e q u a t i o n s we u s e
f o l l o w i n g method
11 //Q2−Q3=−1300
12 //Q2/ 4 0 0 − Q3/ 3 0 0 =−1500/500=−3
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A =[1 , -1;(1/400) ,( -1/300) ];
B =[( -1300) ;( -3) ];
X = inv ( A ) * B ;
Q2 = X (1 ,1) ;
disp ( ”Q2 =” )
disp ( Q2 )
disp ( ” kJ / min ” )
Q3 = X (2 ,1) ;
disp ( ”Q3 =” )
disp ( Q3 )
disp ( ” kJ / min ” )
disp ( ” ( i i ) Entropy c h a n g e ” )
dS1 =( - Q1 ) / T1 ;
disp ( ” Entropy c h a n g e o f s o u r c e 1 =” )
disp ( dS1 )
disp ( ” kJ /K” )
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33 dS2 =( - Q2 ) / T2 ;
34 disp ( ” Entropy c h a n g e o f s i n k 2 =” )
35 disp ( dS2 )
36 disp ( ” kJ /K” )
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38 dS3 = Q3 / T3 ;
39 disp ( ” Entropy c h a n g e o f s o u r c e 3 =” )
40 disp ( dS3 )
41 disp ( ” kJ /K” )
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44 disp ( ” ( i i i ) Net c h a n g e o f t h e e n t r o p y ” )
45 dSnet = dS1 + dS2 + dS3 ;
46 disp ( ” d S n e t=” )
47 disp ( dSnet )
Scilab code Exa 5.45 45
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T1 =250; //K
T2 =125; //K
// cv = 0 . 0 0 4 5 ∗Tˆ2
Q1 = integrate ( ’ 0 . 0 4 5 ∗Tˆ2 ’ , ’T ’ , T1 , T2 ) ;
dS_system = integrate ( ’ 0 . 0 4 5 ∗T ’ , ’T ’ , T1 , T2 ) ;
// d S r e s e r v o i r =(Q1−W) / T r e s s e r v o i r
// d S u n i v e r s e >= 0
// But f o r maximum work done d S u n i v e r s e =0
dS_universe =0;
W_max =(( - Q1 ) - T2 *( dS_universe - dS_system ) ) /1000;
disp ( ”W max=” )
disp ( W_max )
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disp ( ” kJ ” )
Scilab code Exa 5.46 46
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cp =1.005; // kJ / kg K
T_A =333; //K
T_B =288; //K
p_A =140; // kPa
p_B =110; // kPa
// h=cp ∗T
// v /T= 0 . 2 8 7 / p
ds_system = integrate ( ’ cp /T ’ , ’T ’ , T_A , T_B ) +
integrate ( ’ 0 . 2 8 7 / p ’ , ’ p ’ , p_A , p_B ) ;
ds_surr =0;
ds_universe = ds_system + ds_surr ;
disp ( ” c h a n g e i n e n t r o p y o f u n i v e r s e = ” )
disp ( ds_universe )
disp ( ” kJ /kgK” )
disp ( ” S i n c e c h a n g e i n e n t r o p y o f u n i v e r s e from A t o
B i s −ve ” )
disp ( ” The f l o w i s from B t o A” )
Scilab code Exa 5.47 47
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clc
m1 =3; // kg
m2 =4; // kg
T0 =273; //K
T1 =80+273; //K
T2 =15+273; //K
c_pw =4.187; // kJ /kgK
tm =( m1 * T1 + m2 * T2 ) /( m1 + m2 ) ;
134
9 Si = m1 * c_pw * log ( T1 / T0 ) + m2 * c_pw * log ( T2 / T0 ) ;
10 Sf =( m1 + m2 ) * c_pw * log ( tm / T0 ) ;
11 dS = Sf - Si ;
12 disp ( ” Net c h a n g e i n e n t r o p y =” )
13 disp ( dS )
14 disp ( ” kJ /K” )
Scilab code Exa 5.49 49
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clc
m =1; // kg
T1 =273; //K
T2 =363; //K
c =4.187;
disp ( ” ( a ) ” )
disp ( ” ( i ) Ent ropy o f w a t e r=” )
ds_water = m * c * log ( T2 / T1 ) ;
disp ( ds_water )
disp ( ” kJ /kgK” )
disp ( ” ( i i ) Entropy c h a n g e o f t h e r e s e r v o i r ” )
Q = m * c *( T2 - T1 ) ;
ds_reservoir = - Q / T2 ;
disp ( ” d s r e s e r v o i r =” )
disp ( ds_reservoir )
disp ( ” kJ /K” )
disp ( ” ( i i i ) En tropy c h a n g e o f u n i v e r s e =” )
ds_universe = ds_water + ds_reservoir ;
disp ( ds_universe )
disp ( ” kJ /K” )
135
27
28 disp ( ” ( b ) ” )
29 T3 =313; //K
30 ds_water = m * c *( log ( T3 / T1 ) + log ( T2 / T3 ) ) ;
31 ds_res1 = - m * c *( T3 - T1 ) / T3 ;
32 ds_res2 = - m * c *( T2 - T3 ) / T2 ;
33
34 ds_universe = ds_water + ds_res1 + ds_res2 ;
35 disp ( ” ( i i i ) En tropy c h a n g e o f u n i v e r s e =” )
36 disp ( ds_universe )
37 disp ( ” kJ /K” )
38
39 disp ( ” ( c ) The e n t r o p y c h a n g e o f u n i v e r s e would be
l e s s and l e s s , i f t h e w a t e r i s h e a t e d i n more and
more s t a g e s , by b r i n g i n g t h e w a t e r i n c o n t a c t
s u c c e s s i v e l y w i t h more and more h e a t r e s e r v o i r s ,
each s u c c e e d i n g r e s e r v o i r being at a h i g h e r
t e m p e r a t u r e t h a n t h e p r e c e d i n g one . ” )
40 disp ( ”When w a t e r i s h e a t e d i n i n f i n i t e s t e p s , by
b r i n g i n g i n c o n t a c t w i t h an i n f i n i t e number o f
r e s e r v o i r s i n s u c c e s s i o n , s o t h a t a t any i n s t a n t
t h e t e m p e r a t u r e d i f f e r e n c e b e t w e e n t h e w a t e r and
the r e s e r v o i r in contact i s i n f i n i t e s i m a l l y small
, t h e n t h e e n t r o p y c h a n g e o f t h e u n i v e r s e would
be z e r o and t h e w a t e r would be r e v e r s i b l y h e a t e d .
”)
Scilab code Exa 5.50 50
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clc
cp =2.093; // kJ / kg0C
c =4.187;
Lf =333.33; // kJ / kg
m =1; // kg
T0 =273; //K
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T1 =268; //K
T2 =298; //K
Q_s = m * cp *( T0 - T1 ) ;
Q_f = m * Lf ;
Q_l = m * c *( T2 - T0 ) ;
Q = Q_s + Q_f + Q_l ;
disp ( ” ( i ) Ent ropy i n c r e a s e o f t h e u n i v e r s e ” )
ds_atm = - Q / T2 ;
ds_sys1 = m * cp * log ( T0 / T1 ) ;
ds_sys2 = Lf / T0 ;
ds_sys3 = m * c * log ( T2 / T0 ) ;
ds_total = ds_sys1 + ds_sys2 + ds_sys3 ;
ds_universe = ds_total + ds_atm ;
disp ( ” Entropy i n c r e a s e o f u n i v e r s e=” )
disp ( ds_universe )
disp ( ” kJ /K” )
disp ( ” ( i i ) Minimum amount o f work n e c e s s a r y t o
c o n v e r t t h e w a t e r back i n t o i c e a t
5 C , Wmin
. ”)
28 dS_refrigerator =0;
29
30 // dS atm =(Q+W) /T ;
31 // d S u n i v e r s e >= 0
32 // d S s y s t e m =( s1−s 4 )
33 // d S u n i v e r s e=d S s y s t e m+ d S r e f r i g e r a t o r +dS atm
34
35 dS_system = -1.6263; // kJ / kg K
36 T =298; //K
37
38 // For minimum work
39 W_min = T *( - dS_system ) -Q ;
40 disp ( ”Minimum work done =” )
41 disp ( W_min )
42 disp ( ” kJ ” )
137
138
Chapter 6
Availability and Irreversibility
Scilab code Exa 6.1 1
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clc
T0 =293; //K
T1 =300; //K
T2 =370; //K
cv =0.716;
cp =1.005;
R =0.287;
p1 =1; // b a r
p2 =6.8; // b a r
m =1; // kg
Wmax = -[ cv *( T2 - T1 ) - T0 *[ cp * log ( T2 / T1 ) -R * log ( p2 / p1 )
]];
12 n =1/(1 -( log ( T2 / T1 ) / log ( p2 / p1 ) ) ) ;
13 Wact = m * R *( T1 - T2 ) /( n -1) ;
14
15 I = Wmax - Wact ;
16 disp ( ” I r r e v e r s i b i l i t y = ” )
17 disp ( I )
18 disp ( ” kJ / kg ” )
139
Scilab code Exa 6.2 2
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T1 =1000; //K
T2 =500; //K
T0 =300; //K
Q =7200; // kJ / min
disp ( ” ( i ) Net c h a n g e o f e n t r o p y : ” )
dS_source = - Q / T1 ;
dS_system = Q / T2 ;
dS_net = dS_source + dS_system ;
disp ( ” d S n e t=” )
disp ( dS_net )
disp ( ” kJ / min . K” )
disp ( ” ( i i ) D e c r e a s e i n a v a i l a b l e e n e r g y : ” )
AE_source =( T1 - T0 ) *( - dS_source ) ; // A v a i l a b l e e n e r g y
with the s o u r c e
AE_system =( T2 - T0 ) * dS_system ; // A v a i l a b l e e n e r g y w i t h
the system
dAE = AE_source - AE_system ; // D e c r e a s e i n a v a i l a b l e
energy
disp ( ”dAE=” )
disp ( dAE )
disp ( ” kJ ” )
Scilab code Exa 6.3 3
1 clc
2 m =8; // kg
140
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T1 =650; //K
p1 =5.5*10^5; // Pa
p0 =1*10^5; // Pa
T0 =300; //K
cp =1.005; // kJ / kg . K
cv =0.718;
R =0.287;
// p1 ∗ v1 /T1=p0 ∗ v0 /T0
// L e t r=v1 / v0 = 1 / 2 . 5 4
r =1/2.54;
disp ( ” ( i ) Change i n a v a i l a b l e e n e r g y ( f o r b r i n g i n g
t h e s y s t e m t o dead s t a t e )=” )
16 ds = cv * log ( T1 / T0 ) + R * log ( r ) ;
17 dAE = m *[ cv *( T1 - T0 ) - T0 *[ ds ]];
18 //dAE i s t h e c h a n g e i n a v a i l a b l e e n e r g y i n kJ
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V1 = m * R *10^3* T1 / p1 ;
V0 = V1 / r ;
disp ( ” L o s s o f a v a i l a b i l i t y , L=” )
L = p0 *( V0 - V1 ) /10^3;
disp ( L )
disp ( ” kJ ” )
disp ( ” ( i i ) A v a i l a b l e Energy and E f f e c t i v e n e s s ” )
Q = m * cp *( T1 - T0 ) ;
ds = m * cp * log ( T1 / T0 ) ;
Unavailable_energy = T0 * ds ;
Available_energy = Q - Unavailable_energy ;
disp ( ” A v a i l a b l e e n e r g y = ” )
disp ( Available_energy )
disp ( ” kJ ” )
Effectiveness = Available_energy / dAE ;
disp ( ” E f f e c t i v e n e s s = ” )
disp ( Effectiveness )
141
Scilab code Exa 6.4 4
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clc
c_pg =1; // kJ /kgK
h_fg =1940.7; // kJ / kg
Ts =473; //K ; T e m p e r a t u r e o f s a t u r a t i o n o f steam
T1 =1273; //K ; I n i t i a l t e m p e r a t u r e o f g a s e s
T2 =773; //K ; F i n a l t e m p e r a t u r e o f g a s e s
T0 =293; //K ; a t m o s p h e r i c t e m p e r a t u r e
// Heat l o s t by g a s e s=Heat g a i n e d by 1 kg s a t u r a t e d
w a t e r when i t i s c o n v e r t e d t o steam a t 200 0C
10
11 m_g = h_fg / c_pg /( T1 - T2 ) ;
12 dS_g = m_g * c_pg * log ( T2 / T1 ) ;
13 dS_w = h_fg / Ts ;
14
15 dS_net = dS_g + dS_w ;
16 disp ( ” Net c h a n g e i n e n t r o p y = ” )
17 disp ( dS_net )
18 disp ( ” kJ /K” )
19
20 E = T0 * dS_net ; // I n c r e a s e i n u n a v a i l a b l e e n e r g y due t o
hea t r a n s f e r
21 disp ( ” I n c r e a s e i n u n a v a i l a b l e e n e r g y =” )
22 disp ( E )
23 disp ( ” kJ ” )
Scilab code Exa 6.5 5
1 clc
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m_g =3; // kg
p1 =2.5; // b a r
T1 =1200; //K ; T e m p e r a t u r e o f i n f i n i t e s o u r c e
T1a =400; //K ; I n i t i a l t e m p e r a t u r e
Q =600; // kJ
cv =0.81; // kJ / kg . K
T0 =290; //K ; S u r r o u n d i n g T e m p e r a t u r e
// f i n a l t e m p e r a t u r e = T2a
T2a = Q / m_g / cv + T1a ;
AE =( T1 - T0 ) * Q / T1 ; // A v a i l a b l e e n e r g y w i t h t h e s o u r c e
dS = m_g * cv * log ( T2a / T1a ) ; // Change i n e n t r o p y o f t h e
gas
14
15 UAE = T0 * dS ; // U n a v a i l a b i l i t y o f t h e g a s
16 A =Q - UAE ; // A v a i l a b l e e n e r g y w i t h t h e g a s
17
18 loss = AE - A ;
19 disp ( ” L o s s i n a v a i l a b l e e n e r g y due t o h e a t
20
21
transfer
=” )
disp ( loss )
disp ( ” kJ ” )
Scilab code Exa 6.6 6
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clc
m =60; // kg
T1 =333; //K
T0 =279; //K
p =1; // atm
cp =4.187;
//dW=−m∗ cp ∗(1 −T0/T) dT
//Wmax=A v a i l a b l e e n e r g y
Wmax = integrate ( ’m∗ cp ∗(1 −T0/T) ’ , ’T ’ , T0 , T1 ) ;
143
11 Q1 = m * cp *( T1 - T0 ) ;
12
13 // L e t u n a v a i l a b l e e n e r g y=E
14 E = Q1 - Wmax ;
15 disp ( ” u n a v a i l a b l e e n e r g y = ” )
16 disp ( E )
17 disp ( ” kJ ” )
Scilab code Exa 6.7 7
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clc
m =15; // kg
T1 =340; //K
T0 =300; //K
cp =4.187; // kJ /kgK
// Work added d u r i n g c h u r n i n g = I n c r e a s e i n e n t h a l p y
of water
W = m * cp *( T1 - T0 ) ;
ds = cp * log ( T1 / T0 ) ;
AE = m *[ cp *( T1 - T0 ) - T0 * ds ];
AE_loss =W - AE ; // L o s s i n a v a i l a b i l i t y
disp ( ” L o s s i n a v a i l a b i l i t y ” )
disp ( AE_loss )
disp ( ” kJ ” )
Scilab code Exa 6.8 8
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clc
m =5; // kg
T1 =550; //K
p1 =4*10^5; // Pa
T2 =290; //K
T0 = T2 ;
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p2 =1*10^5; // Pa
p0 = p2 ;
cp =1.005; // kJ / kg K
cv =0.718; // kJ / kg K
R =0.287; // kJ / kg K
disp ( ” ( i ) A v a i l a b i l i t y o f t h e s y s t e m : ” )
ds = cp * log ( T1 / T0 ) - R * log ( p1 / p0 ) ;
Availability = m *[ cv *( T1 - T0 ) - T0 * ds ];
disp ( ” A v a i l a b i l i t y o f t h e s y s t e m =” )
disp ( Availability )
disp ( ” kJ ” )
disp ( ” ( i i ) A v a i l a b l e e n e r g y and E f f e c t i v e n e s s ” )
Q = m * cp *( T1 - T0 ) ;
dS = m * cp * log ( T1 / T0 ) ;
E = T0 * dS ; // U n a v a i l a b l e e n e r g y
AE =Q - E ;
disp ( ” A v a i l a b l e Energy = ” )
disp ( AE )
disp ( ” kJ ” )
disp ( ” E f f e c t i v e n e s s =” )
Effectiveness = AE / Availability ;
disp ( Effectiveness )
Scilab code Exa 6.9 9
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clc
R =0.287; // kJ /kgK
cp =1.005; // kJ /kgK
m =25/60; // kg / s
p1 =1; // b a r
p2 =2; // b a r
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T1 =288; //K
T0 = T1 ;
T2 =373; //K
W_act = cp *( T2 - T1 ) ; // W a c t u a l
W_total = m * W_act ;
disp ( ” T o t a l a c t u a l power r e q u i r e d =” )
disp ( W_total )
disp ( ”kW” )
ds = cp * log ( T2 / T1 ) - R * log ( p2 / p1 ) ;
Wmin = cp *( T2 - T1 ) - T0 *( ds ) ;
disp ( ”Minimuumm work r e q u i r e d = ” )
W = m * Wmin ;
disp ( W )
disp ( ”kW” )
Scilab code Exa 6.10 10
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m_O2 =1; // kg
m_H2 =1; // kg
p =1*10^5; // Pa
T_O2 =450; //K
T_H2 =450; //K
T0 =290; //K
R0 =8.314;
M_O2 =32;
M_H2 =2;
R_O2 = R0 / M_O2 ;
v_O2 = m_O2 * R_O2 * T_O2 / p ;
146
15 R_H2 = R0 / M_H2 ;
16 v_H2 = m_H2 * R_H2 * T_H2 / p ;
17
18 v_f = v_O2 + v_H2 ; // t o t a l volume a f t e r
19
20 dS_O2 = R_O2 * log ( v_f / v_O2 ) ;
21 dS_H2 = R_H2 * log ( v_f / v_H2 ) ;
22
23 dS_net = dS_O2 + dS_H2 ;
24
25 // L e t E be t h e l o s s i n a v a i l a b i l i t y
26 E = T0 * dS_net ;
27 disp ( ” L o s s i n a v a i l a b i l i t y =” )
28 disp ( E )
29 disp ( ” kJ ” )
mixing
Scilab code Exa 6.11 11
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clc
T0 =283; //K
cp =4.18; // kJ /kgK
m1 =20; // kg
T1 =363; //K
m2 =30; // kg
T2 =303; //K
T3 =327; //K
AE1 = integrate ( ’m1∗ cp ∗(1 −T0/T) ’ , ’T ’ , T0 , T1 ) ;
AE2 = integrate ( ’m2∗ cp ∗(1 −T0/T) ’ , ’T ’ , T0 , T2 ) ;
AE_total = AE1 + AE2 ; // b e f o r e m i x i n g
// I f T K i s t h e f i n a l t e m p e r a t u r e a f t e r m i x i n g
T =( m1 * T1 + m2 * T2 ) /( m1 + m2 ) ;
m_total = m1 + m2 ;
147
18
19 // A v a i l a b l e e n e r g y o f 50 kg o f w a t e r a t 54 0C
20 AE3 = m_total * cp *[( T3 - T0 ) - T0 * log ( T3 / T0 ) ];
21
22 // D e c r e a s e i n a v a i l a b l e e n e r g y due t o m i x i n g dAE
23 dAE = AE_total - AE3 ;
24 disp ( ”dAE=” )
25 disp ( dAE )
26 disp ( ” kJ ” )
Scilab code Exa 6.12 12
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T_w1 =323; //K
T_w2 =343; //K
T_o1 =513; //K
T_o2 =363; //K
SG_oil =0.82;
c_po =2.6; // kJ / kg K
c_pw =4.18; // kJ / kg K
T0 =300; //K
m_o =1; // kg
// Heat l o s t by o i l =Heat g a i n e d by w a t e r
m_w =( m_o * c_po *( T_o1 - T_o2 ) ) /( c_pw *( T_w2 - T_w1 ) ) ;
dS_w = m_w * c_pw * log ( T_w2 / T_w1 ) ;
dS_o = m_o * c_po * log ( T_o2 / T_o1 ) ;
dAE_w = m_w *[ c_pw *( T_w2 - T_w1 ) ] - T0 * dS_w ;
dAE_o = m_o *[ c_po *( T_o2 - T_o1 ) ] - T0 * dS_o ;
// L o s s i n a v a i l a b i l i t y E=
E = dAE_w + dAE_o ;
disp ( ” L o s s i n a v a i l a b i l i t y =” )
148
24
25
disp ( E )
disp ( ” kJ ” )
Scilab code Exa 6.13 13
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clc
m_i =1; // kg
T_i =273; //K
m_w =12; // kg
T_w =300; //K
T0 =288; //K
c_pw =4.18; // kJ / kg K
c_pi =2.1; // kJ / kg K
L_i =333.5; // kJ / kg
Tc =( m_w * c_pw * T_w + m_i * c_pw * T_i - L_i ) /( m_w * c_pw +
m_i * c_pw ) ;
12
13 dS_w = m_w * c_pw * log ( Tc / T_w ) ;
14 dS_i = m_i * c_pw * log ( Tc / T_i ) + L_i / T_i ;
15
16 dS_net = dS_w + dS_i ;
17 disp ( ” I n c r e a s e i n e n t r o p y =” )
18 disp ( dS_net )
19 disp ( ” kJ /K” )
20
21 dAE = T0 * dS_net ;
22 disp ( ” I n c r e a s e i n u n a v a i l a b l e e n e r g y = ” )
23 disp ( dAE )
24 disp ( ” kJ ” )
Scilab code Exa 6.14 14
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clc
T1 =673; //K
T2 =473; //K
T0 =303; //K
T1a = T2 ;
// dSa / dS=T1/ T1a
// W=(T1−T0 ) ∗ dS ; Work done by t h e power c y c l e when
t h e r e was no t e m p e r a t u r e d i f f e r e n c e b e t w e e n t h e
v a p o u r c o n d e n s i n g and v a p o u r e v a p o r a t i n g
10 // Wa=(T1−T0 ) ∗ dSa ; Work done by t h e power c y c l e when
t h e v a p o u r c o n d e n s e s a t 400 C and v a p o u r
e v a p o r a t e s a t 200 C
11
12
// F r a c t i o n o f e n e r g y t h a t becomes u n a v a i l a b l e i s
g i v e n by (W−Wa) /W
13
14 UAE = T0 *( T1 - T1a ) / T1a /( T1 - T0 ) ;
15 disp ( ” t h e f r a c t i o n o f e n e r g y t h a t becomes
u n a v a i l a b l e =” )
16 disp ( UAE )
Scilab code Exa 6.15 15
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T1 =293; //K
T2 =353; //K
Tf =1773; //K
T0 =288; //K
c_pl =6.3; // kJ / kg K
dAE = c_pl *( T2 - T1 ) - T0 * c_pl * log ( T2 / T1 ) ;
n =(1 - T0 / Tf ) ; // e f f i c i e n c y
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//W=h e a t s u p p l i e d ∗ e f f i c i e n c y
// The p o s s i b l e work from a h e a t e n g i n e i s a m e a s u r e
of the l o s s of a v a i l a b i l i t y , E
14 E = c_pl *( T2 - T1 ) * n ;
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Effectiveness = dAE / E ;
disp ( ” E f f e c t i v e n e s s o f t h e h e a t i n g p r o c e s s =” )
disp ( Effectiveness )
Scilab code Exa 6.16 16
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T0 =293; //K
T1 =293; //K
T2 =373; //K
T3 =323; //K
cp =1.005;
disp ( ” ( i ) The r a t i o o f mass f l o w ” )
// cp= S p e c i f i c h e a t o f a i r c o n s t a n t p r e s s u r e
// cp ∗T1 + x ∗ cp ∗T2 = (1+ x ) ∗ cp ∗T3
x =( T3 - T1 ) /( T2 - T3 ) ;
disp ( ” x=” )
disp ( x )
disp ( ” ( i i ) The e f f e c t i v e n e s s o f h e a t i n g p r o c e s s ” )
ds_13 = cp * log ( T3 / T1 ) ;
ds_32 = cp * log ( T2 / T3 ) ;
A = cp *( T3 - T1 ) - T1 * ds_13 ; // I n c r e a s e o f a v a i l a b i l i t y
o f system
20 B = x *[ cp *( T2 - T3 ) - T0 *( ds_32 ) ]; // L o s s o f a v a i l a b i l i t y
of surroundings
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Effectiveness = A / B ;
disp ( ” E f f e c t i v e n e s s o f h e a t i n g p r o c e s s=” )
disp ( Effectiveness )
Scilab code Exa 6.17 17
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m =2.5; // kg
p1 =6*10^5; // Pa
r =2; // r=V2/V1
cv =0.718; // kJ / kg K
R =0.287; // kJ / kg K
T1 =363; //K
p2 =1*10^5; // Pa
T2 =278; //K
V1 = m * R * T1 / p1 ;
V2 =2* V1 ;
T0 =278; //K
p0 =1*10^5; // Pa
Q =0; // a d i a b a t i c p r o c e s s
disp ( ” ( i ) The maximum work ” )
dS = m * cv * log ( T2 / T1 ) + m * R * log ( V2 / V1 ) ;
Wmax = m *[ cv *( T1 - T2 ) ] + T0 *( cv * log ( T2 / T1 ) + R * log ( V2 /
V1 ) ) ;
19 disp ( ”Wmax=” )
20 disp ( Wmax )
21 disp ( ” kJ ” )
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24 disp ( ” ( i i ) The c h a n g e i n a v a i l a b i l i t y ” )
25 dA = Wmax + p0 *( V1 - V2 ) ;
26 disp ( ” Change i n a v a i l a b i l i t y =” )
27 disp ( dA )
28 disp ( ” kJ ” )
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31 disp ( ” ( i i i ) The i r r e v e r s i b i l i t y ” )
32
33 I = T0 * m *( cv * log ( T2 / T1 ) + R * log ( V2 / V1 ) ) ;
34
35 disp ( ” I r r e v e r s i b i l i t y =” )
36 disp ( I )
37 disp ( ” kJ ” )
Scilab code Exa 6.18 18
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m =1; // kg
p1 =7*10^5; // Pa
T1 =873; //K
p2 =1*10^5; // Pa
T2 =523; //K
T0 =288; //K
Q = -9; // kJ / kg
cp =1.005; // kJ / kg K
R =0.287; // kJ / kg K
disp ( ” ( i ) The d e c r e a s e i n a v a i l a b i l i t y ” )
dA = cp *( T1 - T2 ) - T0 *( R * log ( p2 / p1 ) - cp * log ( T2 / T1 ) ) ;
disp ( ”dA=” )
disp ( dA )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) The maximum work ” )
Wmax = dA ; // c h a n g e i n a v a i l a b i l i t y
disp ( ”Wmax” )
disp ( Wmax )
disp ( ” kJ / kg ” )
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24
25 disp ( ” The i r r e v e r s i b i l i t y ” )
26 W = cp *( T1 - T2 ) + Q ;
27 I = Wmax - W ;
28 disp ( ” I r r e v e r s i b i l i t y =” )
29 disp ( I )
30 disp ( ” kJ / kg ” )
Scilab code Exa 6.19 19
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cp =1.005; // kJ / kg K
cv =0.718; // kJ / kg K
R =0.287; // kJ / kg K
m =1; // kg
T1 =290; //K
T0 =290; //K
T2 =400; //K
p1 =1; // b a r
p0 =1; // b a r
p2 =6; // b a r
// Wrev=c h a n g e i n i n t e r n a l e n e r g y − T0∗ c h a n g e i n
entropy
disp ( ” ( i ) The i r r e v e r s i b i l i t y ” )
Wrev = -[ cv *( T2 - T1 ) - T0 *[ cp * log ( T2 / T1 ) - R * log ( p2 / p1 )
]];
n =[1/(1 - log ( T2 / T1 ) / log ( p2 / p1 ) ) ];
Wact = m * R *( T1 - T2 ) /( n -1) ;
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20 I = Wrev - Wact ;
21 disp ( ” I r r e v e r s i b i l i t y =” )
22 disp ( I )
23 disp ( ” kJ ” )
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disp ( ” ( i i ) The e f f e c t i v e n e s s = ” )
effectiveness = Wrev / Wact *100;
disp ( effectiveness )
disp ( ”%” )
Scilab code Exa 6.20 20
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I =0.62; // kg /mˆ2
N1 =2500; // rpm
w1 =2* %pi * N1 /60; // r a d / s
m =1.9; // kg ; Water e q u i v a l e n t o f s h a f t b e a r i n g s
cp =4.18;
T0 =293; //K
t0 =20; // 0C
disp ( ” ( i ) R i s e i n t e m p e r a t u r e o f b e a r i n g s ” )
KE =1/2* I * w1 ^2/1000; // kJ
dT = KE /( m * cp ) ; // r i s e i n t e m p e r a t u r e o f b e a r i n g s
disp ( ”dT=” )
disp ( dT )
disp ( ” 0C” )
t2 = t0 + dT ;
disp ( ” F i n a l t e m p e r a t u r e o f t h e b e a r i n g s =” )
disp ( t2 )
disp ( ” 0C” )
T2 = t2 +273;
disp ( ” ( i i ) F i n a l r . p .m. o f t h e f l y w h e e l ” )
AE = integrate ( ’m∗ cp ∗(1 −T0/T) ’ , ’T ’ , T0 , T2 ) ;
UE = KE - AE ;
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27
28 disp ( ” A v a i l a b l e e n e r g y =” )
29 disp ( AE )
30 disp ( ” kJ ” )
31
32 UAE = KE - AE ;
33 disp ( ” U n a v a i l a b l e e n e r g y =” )
34 disp ( UAE )
35 disp ( ” kJ ” )
36
37 w2 = sqrt ( AE *10^3*2/ I ) ;
38 N2 = w2 *60/2/ %pi ;
39 disp ( ” F i n a l rpm o f t h e f l y w h e e l =” )
40 disp ( N2 )
41 disp ( ”rpm” )
Scilab code Exa 6.21 21
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p1 =8; // b a r
T1 =453; //K
p2 =1.4; // b a r
T2 =293; //K
T0 = T2 ;
p0 =1; // b a r
m =1; // kg
C1 =80; //m/ s
C2 =40; //m/ s
cp =1.005; // kJ / kg K
R =0.287; // kJ / kg K
disp ( ” ( i ) R e v e r s i b l e work and a c t u a l work ” )
A1 = cp *( T1 - T0 ) - T0 *( cp * log ( T1 / T0 ) -R * log ( p1 / p0 ) ) + C1
^2/2/10^3; // A v a i l a b i l i t y a t t h e i n l e t
15 A2 = cp *( T2 - T0 ) - T0 *( cp * log ( T2 / T0 ) -R * log ( p2 / p0 ) ) + C2
^2/2/10^3; // A v a i l a b i l i t y a t t h e e x i t
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17 W_rev = A1 - A2 ;
18 disp ( ” W rev =” )
19 disp ( W_rev )
20 disp ( ” kJ / kg ” )
21
22 W_act = cp *( T1 - T2 ) + ( C1 ^2 - C2 ^2) /2/10^3;
23 disp ( ” W act =” )
24 disp ( W_act )
25 disp ( ” kJ / kg ” )
26
27 disp ( ” ( i i ) I r r e v e r s i b i l t y and e f f e c t i v e n e s s =” )
28
29 I = W_rev - W_act ;
30 disp ( ” I r r e v e r s i b i l t y =” )
31 disp ( I )
32 disp ( ” kJ / kg ” )
33
34 Effectiveness = W_act / W_rev *100;
35 disp ( ” E f f e c t i v e n e s s =” )
36 disp ( Effectiveness )
37 disp ( ”%” )
Scilab code Exa 6.22 22
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p1 =20; // b a r
t1 =400; // 0C
p2 =4; // b a r
t2 =250; // 0C
t0 =20; // 0C
T0 = t0 +273;
h1 =3247.6; // kJ / kg
s1 =7.127; // kJ / kg K
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// l e t h2 ’= h2a and s2 ’= s 2 a
h2a =2964.3; // kJ / kg
s2a =7.379; // kJ / kg K
s2 = s1 ;
s1a = s1 ;
//By i n t e r p o l a t i o n , we g e t
h2 =2840.8; // kJ / kg
disp ( ” ( i ) I s e n t r o p i c e f f i c i e n c y ” )
n_isen =( h1 - h2a ) /( h1 - h2 ) ;
disp ( ” I s e n t r o p i c e f f i c i e n c y =” )
disp ( n_isen )
disp ( ” ( i i ) L o s s o f a v a i l a b i l i t y ” )
A = h1 - h2a + T0 *( s2a - s1a ) ;
disp ( ” L o s s o f a v a i l a b i l i t y =” )
disp ( A )
disp ( ” kJ / kg ” )
disp ( ” ( i i i ) E f f e c t i v e n e s s ” )
Effectiveness =( h1 - h2a ) / A ;
disp ( ” E f f e c t i v e n e s s =” )
disp ( Effectiveness )
158
Chapter 7
Thermodynamic Relations
Scilab code Exa 7.17 17
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B =5*10^( -5) ; // /K
K =8.6*10^( -12) ; // mˆ2/N
v =0.114*10^( -3) ; //mˆ3/ kg
p2 =800*10^5; // Pa
p1 =20*10^5; // Pa
T =288; //K
disp ( ” ( i ) Work done on t h e c o p p e r = ” )
W = - v * K /2*( p2 ^2 - p1 ^2) ;
disp ( W )
disp ( ” J / kg ” )
disp ( ” ( i i ) Change i n e n t r o p y =” )
ds = - v * B *( p2 - p1 ) ;
disp ( ds )
disp ( ” J / kg K” )
disp ( ” ( i i i ) The h e a t t r a n s f e r =” )
Q = T * ds ;
disp ( Q )
disp ( ” J / kg ” )
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23 disp ( ” ( i v ) Change i n i n t e r n a l
24 du =Q - W ;
25 disp ( du )
26 disp ( ” J / kg ” )
27
28 disp ( ” ( v ) cp
cv =” )
29 R = B ^2* T * v / K ;
30 disp ( R )
31 disp ( ” J / kg K” )
Scilab code Exa 7.18 18
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vg =0.1274; //mˆ3/ kg
vf =0.001157; //mˆ3/ kg
// dp /dT=32; // kPa /K
T3 =473; //K
h_fg =32*10^3* T3 *( vg - vf ) /10^3;
disp ( ” h f g=” )
disp ( h_fg )
disp ( ” kJ / kg ” )
Scilab code Exa 7.19 19
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h_fg =334; // kJ / kg
v_liq =1; //mˆ3/ kg
v_ice =1.01; //mˆ3/ kg
T1 =273; //K
T2 =263; //K
p1 =1.013*10^5; // Pa
160
e n e r g y =” )
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9 p2 =( p1 + h_fg *10^3/( v_ice - v_liq ) * log ( T1 / T2 ) ) /10^5;
10 disp ( ” p2=” )
11 disp ( p2 )
12 disp ( ” b a r ” )
Scilab code Exa 7.20 20
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h_fg =294.54; // kJ / kg
// l o g ( p ) = 7 . 0 3 2 3 − 3 2 7 6 . 6 /T − 0 . 6 5 2 ∗ l o g (T)
// D i f f e r e n t i a t i n g b o t h s i d e s , we g e t
// 1 / 2 . 3 0 2 / p∗ dp /dT = 3 2 7 6 . 6 /Tˆ 2 − 0 . 6 5 2 / 2 . 3 0 2 /T
// P u t t i n g p =0.1 b a r , we g e t
p =0.1; // b a r
T =523; //K
vg = h_fg *10^3/ T /(2.302*3276.6* p *10^5/ T ^2 - 0.652* p
*10^5/ T ) ;
13 disp ( ” vg=” )
14 disp ( vg )
15 disp ( ”mˆ3/ kg ” )
161
Chapter 8
Ideal and Real Gases
Scilab code Exa 8.1 1
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R =287; // J / kg K
V1 =40; //mˆ3
V2 =40; //mˆ3
p1 =1*10^5; // Pa
p2 =0.4*10^5; // Pa
T1 =298; //K
T2 =278; //K
m1 = p1 * V1 / R / T1 ;
m2 = p2 * V2 / R / T2 ;
// L e t mass o f a i r removed be m
m = m1 - m2 ;
disp ( ” Mass o f a i r removed =” )
disp ( m )
disp ( ” kg ” )
V = m * R * T1 / p1 ;
disp ( ” Volume o f g a s removed =” )
disp ( V )
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22
disp ( ”mˆ3 ” )
Scilab code Exa 8.2 2
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V =0.04; //mˆ3
p =120*10^5; // Pa
T =293; //K
R0 =8314;
disp ( ” ( i ) kg o f n i t r o g e n t h e f l a s k can h o l d ” )
M =28; // m o l e c u l a r w e i g h t o f N i t r o g e n
R = R0 / M ;
m=p*V/R/T;
disp ( ” kg o f n i t r o g e n=” )
disp ( m )
disp ( ” kg ” )
disp ( ” ( i i ) T e m p e r a t u r e a t which f u s i b l e p l u g s h o u l d
melt ”)
18 p =150*10^5; // Pa
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20 T = p * V / R / m ; //K
21 t =T -273; // 0C
22 disp ( ” T e m p e r a t u r e =” )
23 disp ( t )
24 disp ( ” C ” )
Scilab code Exa 8.3 3
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p1 =1*10^5; // Pa
T1 =293; //K
d =6; //m; d i a m e t e r o f t h e s p h e r i c a l b a l l o o n
p2 =0.94* p1 ;
T2 = T1 ;
cv =10400; // J / kg K
R =8314/2;
r =3; //m
disp ( ” ( i ) Mass o f o r i g i n a l g a s e s c a p e d ” )
//dm=m1−m2
//dm=(p1−p2 ) ∗V1/R/T1
//m1=p1 ∗V1/R/T1
%mass_escaped =( p1 - p2 ) / p1 *100;
disp ( ” % m a s s e s c a p e d =” )
disp ( %mass_escaped )
disp ( ”%” )
disp ( ” ( i i ) Amount o f h e a t t o be removed ” )
T2 =0.94* T1 ;
m = p1 *4/3* %pi * r ^3/ R / T1 ;
Q = m * cv *( T1 - T2 ) /10^6;
disp ( ”Q =” )
disp ( Q )
disp ( ”MJ” )
Scilab code Exa 8.4 4
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m =28; // kg
V1 =3; //mˆ3
T1 =363; //K
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R0 =8314;
M =28; // M o l e c u l a r mass o f N2
R = R0 / m ;
V2 = V1 ;
T2 =293; //K
disp ( ” ( i ) P r e s s u r e ( p1 ) and s p e c i f i c volume ( v1 ) o f
the gas ”)
p1 = m * R * T1 / V1 /10^5; // b a r
disp ( ” P r e s s u r e =” )
disp ( p1 )
disp ( ” b a r ” )
v1 = V1 / m ;
disp ( ” s p e c i f i c volume=” )
disp ( v1 )
disp ( ”mˆ3/ kg ” )
disp ( ” ( i i ) cp = ? , cv = ? ” )
// cp−cv=R/ 1 0 0 0 ;
// cp −1.4 cv =0;
// s o l v i n g t h e a b o v e two e q n s
A =[1 , -1;1 , -1.4];
B =[ R /1000;0];
X = inv ( A ) * B ;
cp = X (1 ,1) ;
disp ( ” cp=” )
disp ( cp )
disp ( ” kJ / kg K” )
cv = X (2 ,1) ;
disp ( ” cv=” )
disp ( cv )
disp ( ” kJ / kg K” )
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disp ( ” ( i i i ) F i n a l p r e s s u r e o f t h e g a s a f t e r c o o l i n g
t o 20 C ” )
p2 = p1 * T2 / T1 ;
disp ( ” p2=” )
disp ( p2 )
disp ( ” b a r ” )
disp ( ” ( i v ) du , dh , s , Q” )
du = cv *( T2 - T1 ) ;
disp ( ” I n c r e a s e i n s p e c i f i c
disp ( du )
disp ( ” kJ / kg ” )
i n t e r n a l e n e r g y=” )
dh = cp *( T2 - T1 ) ;
disp ( ” I n c r e a s e i n s p e c i f i c E n t h a l p y =” )
disp ( dh )
disp ( ” kJ / kg ” )
v2 = v1 ;
ds = cv * log ( T2 / T1 ) + R * log ( v2 / v1 ) ;
disp ( ” I n c r e a s e i n s p e c i f i c e n t r o p y =” )
disp ( ds )
disp ( ” kJ / kg K” )
W =0; // c o n s t a n t volume p r o c e s s
Q = m * du + W ;
disp ( ” Heat t r a n s f e r =” )
disp ( Q )
disp ( ” kJ ” )
Scilab code Exa 8.5 5
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disp ( ” P a r t ( a ) ” )
R =0.287; // kJ / kg K
y =1.4;
m1 =1; // kg
p1 =8*10^5; // Pa
T1 =373; //K
p2 =1.8*10^5; // Pa
cv =0.717; // kJ / kg K
n =1.2;
// pv ˆ 1 . 2 = c o n s t a n t
disp ( ” ( i ) The f i n a l s p e c i f i c volume , t e m p e r a t u r e and
i n c r e a s e in entropy ”)
v1 = R *10^3* T1 / p1 ;
v2 = v1 *( p1 / p2 ) ^(1/ n ) ;
disp ( ” v2=” )
disp ( v2 )
disp ( ”mˆ3/ kg ” )
T2 = p2 * v2 / R /10^3; //K
t2 = T2 -273; // 0C
disp ( ” F i n a l t e m p e r a t u r e =” )
disp ( t2 )
disp ( ” 0C” )
ds = cv * log ( T2 / T1 ) + R * log ( v2 / v1 ) ;
disp ( ” d s=” )
disp ( ds )
disp ( ” kJ / kg K” )
disp ( ” ( i i ) Work done and h e a t t r a n s f e r ” )
W = R *( T1 - T2 ) /( n -1) ;
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39 disp ( W )
40 disp ( ” kJ / kg ” )
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42 Q = cv *( T2 - T1 ) + W ;
43 disp ( ” Heat t r a n s f e r =” )
44 disp ( Q )
45 disp ( ” kJ / kg ” )
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48 disp ( ” P a r t ( b ) ” )
49
50 disp ( ” ( i ) Though t h e p r o c e s s
i s assumed now t o be
i r r e v e r s i b l e and a d i a b a t i c , t h e end s t a t e s a r e
g i v e n t o be t h e same a s i n ( a ) . T h e r e f o r e , a l l
t h e p r o p e r t i e s a t t h e end o f t h e p r o c e s s a r e t h e
same a s i n ( a ) . ” )
51
52
53 disp ( ” ( i i ) A d i a b a t i c p r o c e s s ” )
54 Q =0;
55 disp ( ” Heat t r a n s f e r =” )
56 disp ( Q )
57 disp ( ” kJ / kg ” )
58
59 W = - cv *( T2 - T1 ) ;
60 disp ( ”Work done=” )
61 disp ( W )
62 disp ( ” kJ / kg ” )
Scilab code Exa 8.6 6
1 clc
2 d =2.5; //m; d i a m e t e r
3 V1 =4/3* %pi *( d /2) ^3; // volume o f e a c h s p h e r e
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T1 =298; //K
T2 =298; //K
m1 =16; // kg
m2 =8; // kg
V =2* V1 ; // t o t a l volume
m = m1 + m2 ;
R =287; // kJ / kg K
p = m * R * T1 / V /10^5; // b a r
disp ( ” p r e s s u r e i n t h e s p h e r e s when t h e s y s t e m
a t t a i n s e q u i l i b r i u m=” )
14 disp ( p )
15 disp ( ” b a r ” )
Scilab code Exa 8.7 7
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clc
m =6.5/60; // kg / s
cv =0.837; // kJ / kg K
p1 =10*10^5; // Pa
p2 =1.05*10^5; // Pa
T1 =453; //K
R0 =8.314;
M =44; // M o l e c u l a r mass o f CO2
R = R0 / M ;
cp = cv + R ;
y = cp / cv ;
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
t2 = T2 -273;
disp ( ” F i n a l t e m p e r a t u r e=” )
disp ( t2 )
disp ( ” 0C” )
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25
26
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28
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31
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34
35
36
v2 = R *10^3* T2 / p2 ; //mˆ3/ kg
disp ( ” f i n a l s p e c i f i c volume =” )
disp ( v2 )
disp ( ”mˆ3/ kg ” )
ds =0; // R e v e r s i b l e and a d i a b a t i c p r o c e s s
disp ( ” I n c r e a s e i n e n t r o p y=” )
disp ( ds )
Q =0; // A d i a b a t i c p r o c e s s
disp ( ” Heat t r a n s f e r r a t e from t u r b i n e=” )
disp ( Q )
W = m * cp *( T1 - T2 ) ;
disp ( ” Power d e l i v e r e d by t h e t u r b i n e=” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 8.8 8
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15
clc
p1 =8*10^5; // Pa
V1 =0.035; //mˆ3
T1 =553; //K
p2 =8*10^5; // Pa
V2 =0.1; //mˆ3
n =1.4;
R =287; // J / kg K
T3 =553; //K
cv =0.71; // kJ / kg K
m = p1 * V1 / R / T1 ;
T2 = p2 * V2 / m / R ;
p3 = p2 /(( T2 / T3 ) ^( n /( n -1) ) ) ;
V3 = m * R * T3 / p3 ;
170
16
17 disp ( ” ( i ) The h e a t r e c e i v e d i n t h e c y c l e ” )
18
19 // c o n s t a n t p r e s s u r e p r o c e s s 1−2
20 W_12 = p1 *( V2 - V1 ) /10^3; // kJ
21 Q_12 = m * cv *( T2 - T1 ) + W_12 ; // kJ
22
23 // p o l y t r o p i c p r o c e s s 2−3
24 W_23 = m * R /10^3*( T2 - T3 ) /( n -1) ;
25 Q_23 = m * cv *( T3 - T2 ) + W_23 ;
26
27 Q_received = Q_12 + Q_23 ;
28 disp ( ” T o t a l h e a t r e c e i v e d i n t h e c y c l e=” )
29 disp ( Q_received )
30 disp ( ” kJ ” )
31
32
33 disp ( ” ( i i ) The h e a t r e j e c t e d i n t h e c y c l e ” )
34
35 // I s o t h e r m a l p r o c e s s 3−1
36 W_31 = p3 * V3 * log ( V1 / V3 ) /10^3; // kJ
37 Q_31 = m * cv *( T3 - T1 ) + W_31 ;
38 disp ( ” Heat r e j e c t e d i n t h e c y c l e =” )
39 disp ( - Q_31 )
40 disp ( ” kJ ” )
41
42
43 disp ( ” ( i i ) E f f i c i e n c y o f t h e c y c l e ” )
44 n =( Q_received - ( - Q_31 ) ) / Q_received *100;
45 disp ( ” E f f i c i e n c y o f t h e c y c l e =” )
46 disp ( n )
47 disp ( ”%” )
Scilab code Exa 8.9 9
171
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22
clc
v =44; //mˆ3/ kg−mol
T =373; //K
disp ( ” ( i ) U s i n g Van d e r
Waals
equation ”)
a =362850; //N∗mˆ 4 / ( kg−mol ) ˆ2
b =0.0423; //Mˆ3/ kg−mol
R0 =8314; // J / kg K
p =(( R0 * T /( v - b ) ) - a / v ^2) ;
disp ( ” P r e s s u r e u s i n g Van d e r Waals e q u a t i o n=” )
disp ( p )
disp ( ”N/mˆ2 ” )
disp ( ” ( i i ) U s i n g p e r f e c t g a s e q u a t i o n ” )
p = R0 * T / v ;
disp ( ” P r e s s u r e u s i n g p e r f e c t g a s e q u a t i o n=” )
disp ( p )
disp ( ”N/mˆ2 ” )
Scilab code Exa 8.10 10
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8
9
10
clc
V =3; //mˆ3
m =10; // kg
T =300; //K
disp ( ” ( i ) U s i n g p e r f e c t g a s e q u a t i o n ” )
R0 =8314;
M =44;
R = R0 / M ;
p=m*R*T/V;
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disp ( ” P r e s s u r e U s i n g p e r f e c t g a s e q u a t i o n =” )
disp ( p )
disp ( ”N/mˆ2 ” )
disp ( ” ( i i ) U s i n g Van d e r W a a l s
a =362850; //Nmˆ 4 / ( kg−mol ) ˆ2
b =0.0423; //mˆ 3 / ( kg−mol )
v =13.2; //mˆ3/ kg−mol
p = R0 * T /( v - b ) - a / v ^2;
disp ( ” P r e s s u r e U s i n g Van d e r
disp ( p )
disp ( ”N/mˆ2 ” )
equation ”)
Waals
e q u a t i o n=” )
disp ( ” ( i i i ) U s i n g B e a t t i e Bridgeman e q u a t i o n ” )
A0 =507.2836;
a =0.07132;
B0 =0.10476;
b =0.07235;
C =66*10^4;
A = A0 *(1 - a / v ) ;
B = B0 *(1 - b / v ) ;
e = C / v / T ^3;
p = R0 * T *(1 - e ) / v ^2*( v + B ) - A / v ^2;
disp ( ” P r e s s u r e U s i n g B e a t t i e Bridgeman e q u a t i o n = ” )
disp ( p )
disp ( ”N/mˆ2 ” )
Scilab code Exa 8.11 11
1 clc
173
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a =139250; //Nmˆ 4 / ( kg−mol ) ˆ2
b =0.0314; //mˆ3/ kg−mol
R0 =8314; //Nm/ kg−mol K
v1 =0.2*32; //mˆ3/ kg−mol
v2 =0.08*32; //mˆ3/ kg−mol
T =333; //K
disp ( ” ( i ) Work done d u r i n g t h e p r o c e s s ” )
W = integrate ( ’ R0∗T/ ( v−b ) − a / v ˆ2 ’ , ’ v ’ , v1 , v2 ) ;
disp ( ”W=” )
disp ( W )
disp ( ”Nm/ kg−mol ” )
disp ( ” ( i i ) The f i n a l p r e s s u r e ” )
p2 = R0 * T /( v2 - b ) - a / v2 ^2;
disp ( ” p2=” )
disp ( p2 )
disp ( ”N/mˆ2 ” )
Scilab code Exa 8.12 12
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8
9
10
clc
pr =20;
Z =1.25;
Tr =8.0;
Tc =282.4; //K
T = Tc * Tr ;
disp ( ” T e m p e r a t u r e =” )
disp ( T )
disp ( ”K” )
Scilab code Exa 8.13 13
174
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15
clc
p =260*10^5; // Pa
T =288; //K
pc =33.94*10^5; // Pa
Tc =126.2; //K
R =8314/28;
pr = p / pc ;
Tr = T / Tc ;
Z =1.08;
rho = p / Z / R / T ;
disp ( ” D e n s i t y o f N2=” )
disp ( rho )
disp ( ” kg /mˆ3 ” )
Scilab code Exa 8.14 14
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12
clc
p =200*10^5; // Pa
pc =73.86*10^5; // Pa
Tc =304.2; //K
pr = p / pc ;
Z =1;
Tr =2.48;
T = Tr * Tc ;
disp ( ” T e m p e r a t u r e =” )
disp ( T )
disp ( ”K” )
Scilab code Exa 8.15 15
175
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clc
d =12; //m; d i a m e t e r o f s p h e r i c a l b a l l o o n
V =4/3* %pi *( d /2) ^3;
T =303; //K
p =1.21*10^5; // Pa
pc =12.97*10^5; // Pa
Tc =33.3; //K
R =8314/2;
pr = p / pc ;
Tr = T / Tc ;
Z =1;
m=p*V/Z/R/T;
disp ( ” Mass o f H2 i n t h e b a l l o o n =” )
disp ( m )
disp ( ” kg ” )
Scilab code Exa 8.16 16
1 clc
2
3 // d p c / dv=0
4 // d ˆ2 p/ dv ˆ2=0
5
6 // p c p=R0∗ T cp / ( v c p −b ) − a / v c p ˆ2
7
8 // As T cp i s c o n s t a n t
9 // d p c p / d v c p =(−R0∗ T cp ) / ( v c p −b ) ˆ2 + 2∗ a / v c p ˆ3 =
0
10
11
12
13
// d ˆ2 p c p / d v c p =2∗R0∗ T cp / ( v c p −b ) ˆ3 − 6∗ a / v c p ˆ4
= 0
// S o l v i n g t h e s e we g e t v c p =3∗b ;
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22
23
// 2∗ a / v c p ˆ3 − R0∗ T cp / [ v c p −1/3∗ v c p ] ˆ 2
// a =9/8∗R0∗ T cp ∗ v c p
// Z c p=p c p ∗ v c p /R0/ T cp
Z_cp =3/2 -9/8;
disp ( ” Z c p=” )
disp ( Z_cp )
177
Chapter 9
Gases and Vapour Mixtures
Scilab code Exa 9.1 1
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21
clc
V =0.35; //mˆ3
m_CO =0.4; // kg
m_air =1; // kg
m_O2 =0.233; // kg
m_N2 =0.767; // kg
T =293; //K
R0 =8.314; // kJ / kg K
M_O2 =32; // M o l e c u l a r mass o f O2
M_N2 =28; // M o l e c u l a r mass o f N2
M_CO =28; // M o l e c u l a r mass o f CO
disp ( ” P a r t i a l P r e s s u r e s=” )
p_O2 = m_O2 * R0 *10^3* T / M_O2 / V /10^5; // b a r
disp ( ” p a r t i a l p r e s s u r e f o r p O2 ” )
disp ( p_O2 )
disp ( ” b a r ” )
p_N2 = m_N2 * R0 *10^3* T / M_N2 / V /10^5; // b a r
disp ( ” p a r t i a l p r e s s u r e f o r p N2 ” )
178
22 disp ( p_N2 )
23 disp ( ” b a r ” )
24
25 p_CO = m_CO * R0 *10^3* T / M_CO / V /10^5; // b a r
26 disp ( ” p a r t i a l p r e s s u r e f o r p CO” )
27 disp ( p_CO )
28 disp ( ” b a r ” )
29
30
31 disp ( ” ( i i ) T o t a l p r e s s u r e i n t h e v e s s e l ” )
32 p = p_O2 + p_N2 + p_CO ;
33 disp ( ” p=” )
34 disp ( p )
35 disp ( ” b a r ” )
Scilab code Exa 9.2 2
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clc
R0 =8.314;
M_O2 =32;
M_N2 =28;
M_Ar =40;
M_CO2 =44;
R_O2 = R0 / M_O2 ; // kJ / kg K
R_N2 = R0 / M_N2 ; // kJ / kg K
R_Ar = R0 / M_Ar ; // kJ / kg K
R_CO2 = R0 / M_CO2 ; // kJ / kg K
%O2 =0.2314;
%N2 =0.7553;
%Ar =0.0128;
%CO2 =0.0005;
179
19 disp ( ” ( i ) Gas c o n s t a n t f o r a i r ” )
20 R = %O2 * R_O2 + %N2 * R_N2 + %Ar * R_Ar + %CO2 * R_CO2 ;
21 disp ( ”R=” )
22 disp ( R )
23 disp ( ” kJ / kg K” )
24
25 disp ( ” ( i i ) Apparent m o l e c u l a r w e i g h t . ” )
26 M = R0 / R ;
27 disp ( ”M=” )
28 disp ( M )
Scilab code Exa 9.3 3
1 clc
2 p =1; // b a r
3
4 // For o x y g e n
5 m_O2 =0.2314;
6 M_O2 =32;
7 n_O2 = m_O2 / M_O2 ;
8
9 // For N i t r o g e n
10 m_N2 =0.7553;
11 M_N2 =28;
12 n_N2 = m_N2 / M_N2 ;
13
14 // For Argon
15 m_Ar =0.0128;
16 M_Ar =40;
17 n_Ar = m_Ar / M_Ar ;
18
19 // For CO2
20 m_CO2 =0.0005;
21 M_CO2 =44;
22 n_CO2 = m_CO2 / M_CO2 ;
180
23
24
25 n = n_O2 + n_N2 + n_Ar + n_CO2 ;
26
27 // L e t Vi /V be A
28
29 A_O2 = n_O2 / n * 100;
30 disp ( ” Vi /V o f O2=” )
31 disp ( A_O2 )
32 disp ( ”%” )
33
34 A_N2 = n_N2 / n * 100;
35 disp ( ” Vi /V o f N2=” )
36 disp ( A_N2 )
37 disp ( ”%” )
38
39 A_Ar = n_Ar / n *100;
40 disp ( ” Vi /V o f Ar ” )
41 disp ( A_Ar )
42 disp ( ”%” )
43
44 A_CO2 = n_CO2 / n * 100;
45 disp ( ” Vi /V o f CO2=” )
46 disp ( A_CO2 )
47 disp ( ”%” )
48
49
50 P_O2 = n_O2 / n * p ;
51 disp ( ” P a r t i a l p r e s s u r e o f O2=” )
52 disp ( P_O2 )
53 disp ( ” b a r ” )
54
55 P_N2 = n_N2 / n * p ;
56 disp ( ” P a r t i a l p r e s s u r e o f N2=” )
57 disp ( P_N2 )
58 disp ( ” b a r ” )
59
60 P_Ar = n_Ar / n * p ;
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68
disp ( ” P a r t i a l p r e s s u r e o f Ar=” )
disp ( P_Ar )
disp ( ” b a r ” )
P_CO2 = n_CO2 / n * p ;
disp ( ” P a r t i a l p r e s s u r e o f CO2=” )
disp ( P_CO2 )
disp ( ” b a r ” )
Scilab code Exa 9.4 4
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clc
p =1*10^5; // Pa
T =293; //K
n_CO2 =1; // m o l e s o f CO2
n =4; // m o l e s o f a i r
M_CO2 =44;
M_N2 =28;
M_O2 =32;
// L e t A be t h e v o l u m e e t r i c a n a l y s i s
A_O2 =0.21;
A_N2 =0.79;
n_O2 = A_O2 * n ;
n_N2 = A_N2 * n ;
disp ( ” ( i ) The m a s s e s o f CO2 , O2 and N2 , and t h e
t o t a l mass ” )
m_CO2 = n_CO2 * M_CO2 ;
disp ( ” Mass o f CO2=” )
disp ( m_CO2 )
disp ( ” kg ” )
182
24 m_O2 = n_O2 * M_O2 ;
25 disp ( ” Mass o f O2=” )
26 disp ( m_O2 )
27 disp ( ” kg ” )
28
29 m_N2 = n_N2 * M_N2 ;
30 disp ( ” Mass o f N2=” )
31 disp ( m_N2 )
32 disp ( ” kg ” )
33
34 m = m_CO2 + m_O2 + m_N2 ;
35 disp ( ” T o t a l mass =” )
36 disp ( m )
37 disp ( ” kg ” )
38
39
40 disp ( ” ( i i ) The p e r c e n t a g e c a r b o n c o n t e n t by mass ” )
41 // S i n c e t h e m o l e c u l a r w e i g h t o f c a r b o n i s 1 2 ,
t h e r e f o r e , t h e r e a r e 12 kg o f c a r b o n p r e s e n t f o r
e v e r y mole o f CO2
42 m_C =12; // kg
43
44 %C = m_C / m *100;
45 disp ( ” P e r c e n t a g e c a r b o n i n m i x t u r e ” )
46 disp ( %C )
47 disp ( ”%” )
48
49
50 disp ( ” ( i i i ) The a p p a r e n t m o l e c u l a r w e i g h t and t h e
51
52
53
54
55
56
57
58
gas constant f o r the mixture ”)
n = n_CO2 + n_O2 + n_N2 ;
M = n_CO2 / n * M_CO2 + n_O2 / n * M_O2 + n_N2 / n * M_N2 ;
disp ( ” Apparent M o l e c u l a r w e i g h t ” )
disp ( M )
R0 =8.314;
R = R0 / M ;
disp ( ” Gas c o n s t a n t f o r t h e m i x t u r e=” )
183
59 disp ( R )
60 disp ( ” kJ / kg K” )
61
62
63 disp ( ” ( i v ) The s p e c i f i c volume o f t h e m i x t u r e ” )
64 v = R *10^3* T / p ;
65 disp ( ” s p e c i f i c volume=” )
66 disp ( v )
67 disp ( ”mˆ3/ kg ” )
Scilab code Exa 9.5 5
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clc
p =1*10^5; // Pa
T =298; //K
M_H2 =2;
M_O2 =32;
R0 =8314;
// r a t i o = V H2/V O2 =2;
ratio =2;
disp ( ” ( i ) The mass o f O2 r e q u i r e d ” )
// L e t t h e mass o f O2 p e r kg o f H2 = x kg
m_H2 =1; // kg
n_H2 = m_H2 / M_H2 ;
// n O2=x /M O2
x = M_O2 * n_H2 / ratio ;
disp ( ” Mass o f O2 p e r kg o f H2=” )
disp ( x )
disp ( ” kg ” )
disp ( ” ( i i ) The volume o f t h e c o n t a i n e r ” )
184
24 n_O2 = x / M_O2 ;
25 n = n_H2 + n_O2 ;
26 V = n * R0 * T / p ;
27 disp ( ”V=” )
28 disp ( V )
29 disp ( ”mˆ3 ” )
Scilab code Exa 9.6 6
1 clc
2
3 // L e t c o m p o s i t i o n o f m i x t u r e by volume be d e n o t e d by
c1
4 // L e t F i n a l c o m p o s i t i o n d e s i r e d be d e n o t e d by c 2
5
6 c1_H2 =0.78;
7 c1_CO =0.22;
8
9 c2_H2 =0.52;
10 c2_CO =0.48;
11
12 M_H2 =2;
13 M_CO =28;
14
15 M = c1_H2 * M_H2 + c1_CO * M_CO ;
16
17 // L e t x kg o f m i x t u r e be removed and y kg o f CO be
added .
18
19 x =( c1_H2 - c2_H2 ) / c1_H2 * M ;
20 disp ( ” Mass o f m i x t u r e removed =” )
21 disp ( x )
22 disp ( ” kg ” )
23
24 y = M_CO / M * x ;
185
25
26
27
disp ( ” Mass o f CO added=” )
disp ( y )
disp ( ” kg ” )
Scilab code Exa 9.7 7
1 clc
2
3 ratio =1/8; // volume r a t i o ; v1 / v2
4 T1 =1223; //K
5
6 cp_CO2 =1.235; // kJ / kg K
7 cp_O2 =1.088; // kJ / kg K
8 cp_N2 =1.172; // kJ / kg K
9
10 n_CO2 =0.13;
11 n_O2 =0.125;
12 n_N2 =0.745;
13
14 M_CO2 =44;
15 M_O2 =32;
16 M_N2 =28;
17
18 m_CO2 = M_CO2 * n_CO2 ;
19 m_O2 = M_O2 * n_O2 ;
20 m_N2 = M_N2 * n_N2 ;
21
22 m = m_CO2 + m_O2 + m_N2 ;
23
24 // L e t F r a c t i o n by mass be d e n o t e d by F
25 F_CO2 = m_CO2 / m ;
26 F_O2 = m_O2 / m ;
27 F_N2 = m_N2 / m ;
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cp = F_CO2 * cp_CO2 + F_O2 * cp_O2 + F_N2 * cp_N2 ;
R0 =8.314;
R = F_CO2 * R0 / M_CO2 + F_O2 * R0 / M_O2 + F_N2 * R0 / M_N2 ;
cv = cp - R ;
n =1.2;
disp ( ” ( i ) The workdone ” )
T2 = T1 *( ratio ) ^( n -1) ;
W = R *( T1 - T2 ) /( n -1) ;
disp ( ”W=” )
disp ( W )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) The h e a t f l o w ” )
du = cv *( T2 - T1 ) ;
Q = du + W ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ / kg ” )
disp ( ” ( i i i ) Change o f e n t r o p y p e r kg o f m i x t u r e ” )
ds_1A = R * log (1/ ratio ) ; // i s o t h e r m a l p r o c e s s
ds_2A = cv * log ( T1 / T2 ) ;
ds_12 = ds_1A - ds_2A ;
disp ( ” c h a n g e o f e n t r o p y=” )
disp ( ds_12 )
disp ( ” kJ / kg K” )
Scilab code Exa 9.8 8
187
1 clc
2
3 M_CO2 =44;
4 M_H2 =2;
5 M_N2 =28;
6 M_CH4 =16;
7 M_CO =28;
8
9 // L e t v o l u m e t r i c a n a l y s i s be d e n o t e d by V
10 V_CO =0.28;
11 V_H2 =0.13;
12 V_CH4 =0.04;
13 V_CO2 =0.04;
14 V_N2 =0.51;
15
16 Cp_CO =29.27; // kJ / mole K
17 Cp_H2 =28.89; // kJ / mole K
18 Cp_CH4 =35.8; // kJ / mole K
19 Cp_CO2 =37.22; // kJ / mole K
20 Cp_N2 =29.14; // kJ / mole K
21
22 R0 =8.314;
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24 Cp = V_CO * Cp_CO + V_H2 * Cp_H2 + V_CO2 * Cp_CO2 + V_CH4 *
Cp_CH4 + V_N2 * Cp_N2 ;
25 disp ( ”Cp=” )
26 disp ( Cp )
27 disp ( ” kJ / mole K” )
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29 Cv = Cp - R0 ;
30 disp ( ”Cv=” )
31 disp ( Cv )
32 disp ( ” kJ / mole K” )
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34 M = V_CO * M_CO + V_H2 * M_H2 + V_CO2 * M_CO2 + V_CH4 * M_CH4
+ V_N2 * M_N2 ;
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36 cp = Cp / M ;
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37 disp ( ” cp=” )
38 disp ( cp )
39 disp ( ” kJ / kg K” )
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41 cv = Cv / M ;
42 disp ( ” cv ” )
43 disp ( cv )
44 disp ( ” kJ / kg K” )
Scilab code Exa 9.9 9
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clc
p =1.3; // b a r
R0 =8.314;
M_CO2 =44;
M_O2 =32;
M_N2 =28;
M_CO =28;
m_O2 =0.1;
m_N2 =0.7;
m_CO2 =0.15;
m_CO =0.05;
// C o n s i d e r i n g 1 kg o f m i x t u r e
m =1; // kg
// l e t m o l e s be d e n o t e d by n
n_O2 = m_O2 / M_O2 ;
n_N2 = m_N2 / M_N2 ;
n_CO2 = m_CO2 / M_CO2 ;
n_CO = m_CO / M_CO ;
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25 M =1/( m_O2 / M_O2 + m_N2 / M_N2 + m_CO2 / M_CO2 + m_CO / M_CO
);
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27 n = m / M ;
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29 x_O2 = n_O2 / n ;
30 x_N2 = n_N2 / n ;
31 x_CO2 = n_CO2 / n ;
32 x_CO = n_CO / n ;
33
34 disp ( ” ( i ) P a r t i a l p r e s s u r e s o f t h e c o n s t i t u e n t s ” )
35 P_O2 = x_O2 * p ;
36 disp ( ” P a r t i a l p r e s s u r e o f O2=” )
37 disp ( P_O2 )
38 disp ( ” b a r ” )
39
40 P_N2 = x_N2 * p ;
41 disp ( ” P a r t i a l p r e s s u r e o f N2=” )
42 disp ( P_N2 )
43 disp ( ” b a r ” )
44
45 P_CO2 = x_CO2 * p ;
46 disp ( ” P a r t i a l p r e s s u r e o f CO2=” )
47 disp ( P_CO2 )
48 disp ( ” b a r ” )
49
50 P_CO = x_CO * p ;
51 disp ( ” P a r t i a l p r e s s u r e o f CO=” )
52 disp ( P_CO )
53 disp ( ” b a r ” )
54
55 disp ( ” Gas c o n s t a n t o f m i x t u r e =” )
56 R_mix = R0 / M ;
57 disp ( R_mix )
58 disp ( ” kJ / kg K” )
190
Scilab code Exa 9.10 10
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clc
p =4*10^5; // Pa
T =293; //K
R0 =8.314;
m_N2 =4; // kg
m_CO2 =6; // kg
M_N2 =28; // M o l e c u l a r mass
M_CO2 =44; // M o l e c u l a r mass
n_N2 = m_N2 / M_N2 ; // m o l e s o f N2
n_CO2 = m_CO2 / M_CO2 ; // m o l e s o f CO2
x_N2 = n_N2 /( n_N2 + n_CO2 ) ;
disp ( ” x N2=” )
disp ( x_N2 )
x_CO2 = n_CO2 /( n_CO2 + n_N2 ) ;
disp ( ” x CO2=” )
disp ( x_CO2 )
disp ( ” ( i i ) The e q u i v a l e n t m o l e c u l a r w e i g h t o f t h e
mixture ”)
M = x_N2 * M_N2 + x_CO2 * M_CO2 ;
disp ( ”M=” )
disp ( M )
disp ( ” kg / kg−mole ” )
disp ( ” ( i i i ) The e q u i v a l e n t g a s c o n s t a n t o f t h e
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mixture ”)
m = m_N2 + m_CO2 ;
Rmix =( m_N2 *( R0 / M_N2 ) + m_CO2 *( R0 / M_CO2 ) ) / m ;
disp ( ”Rmix=” )
disp ( Rmix )
disp ( ” kJ / kg K” )
disp ( ” ( i v ) The p a r t i a l p r e s s u r e s and p a r t i a l v o l u m e s
”)
P_N2 = x_N2 * p /10^5;
disp ( ” P N2=” )
disp ( P_N2 )
disp ( ” b a r ” )
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45 P_CO2 = x_CO2 * p /10^5;
46 disp ( ”P CO2=” )
47 disp ( P_CO2 )
48 disp ( ” b a r ” )
49
50 V_N2 = m_N2 * R0 / M_N2 * T / p *10^3;
51 disp ( ”V N2” )
52 disp ( V_N2 )
53 disp ( ”mˆ3 ” )
54
55 V_CO2 = m_CO2 * R0 / M_CO2 * T / p *10^3;
56 disp ( ”V CO2” )
57 disp ( V_CO2 )
58 disp ( ”mˆ3 ” )
59
60 disp ( ” ( v ) The volume and d e n s i t y
61
62 V = m * Rmix *10^3* T / p ;
63 disp ( ”V=” )
64 disp ( V )
65 disp ( ”mˆ3 ” )
66
67 rho_mix = m / V ;
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of the mixture ”)
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disp ( ” D e n s i t y o f m i x t u r e=” )
disp ( rho_mix )
disp ( ” kg /mˆ3 ” )
disp ( ” ( v i ) cp and cv o f t h e m i x t u r e ” )
y_N2 =1.4;
cv_N2 =( R0 / M_N2 ) /( y_N2 - 1) ;
cp_N2 = cv_N2 * y_N2 ;
y_CO2 =1.286;
cv_CO2 =( R0 / M_CO2 ) /( y_CO2 - 1) ;
cp_CO2 = cv_CO2 * y_CO2 ;
cp =( m_N2 * cp_N2 + m_CO2 * cp_CO2 ) /( m_N2 + m_CO2 ) ;
disp ( ” cp=” )
disp ( cp )
disp ( ” kJ / kg K” )
cv =( m_N2 * cv_N2 + m_CO2 * cv_CO2 ) /( m_N2 + m_CO2 ) ;
disp ( ” cv=” )
disp ( cv )
disp ( ” kJ / kg K” )
T1 =293; //K
T2 =323; //K
dU = m * cv *( T2 - T1 ) ;
disp ( ” Change i n i n t e r n a l e n e r g y =” )
disp ( dU )
disp ( ” kJ ” )
dH = m * cp *( T2 - T1 ) ;
disp ( ” Change i n e n t h a l p y =” )
disp ( dH )
disp ( ” kJ ” )
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106
107 dS = m * cv * log ( T2 / T1 ) ; // C o n s t a n t volume p r o c e s s
108 disp ( ” Change i n e n t r o p y=” )
109 disp ( dS )
110 disp ( ” kJ / kg K” )
111
112
113 disp ( ”When t h e m i x t u r e i s h e a t e d a t c o n s t a n t
p r e s s u r e ”)
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disp ( ” I f t h e m i x t u r e i s h e a t e d a t c o n s t a n t p r e s s u r e
U and H w i l l r e m a i n t h e same ” )
116
117 dS = m * cp * log ( T2 / T1 ) ;
118 disp ( ” Change i n e n t r o p y =” )
119 disp ( dS )
120 disp ( ” kJ / kg K” )
Scilab code Exa 9.11 11
1 clc
2
3 Cv_O2 =21.07; // kJ / mole K
4 Cv_CO =20.86; // kJ / mole K
5
6 p_O2 =8*10^5; // Pa
7 p_CO =1*10^5; // Pa
8
9 V_O2 =1.8; //mˆ3
10 V_CO =3.6; //mˆ3
11
12 T_O2 =323; //K
13 T_CO =293; //K
14
15 R0 =8314;
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17 n_O2 = p_O2 * V_O2 / R0 / T_O2 ;
18 n_CO = p_CO * V_CO / R0 / T_CO ;
19
20 n =( n_O2 + n_CO ) ;
21 V =( V_O2 + V_CO ) ;
22
23 disp ( ” ( i ) F i n a l t e m p e r a t u r e (T) and p r e s s u r e ( p ) o f
the mixture ”)
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// B e f o r e m i x i n g
U1 = n_O2 * Cv_O2 * T_O2 + n_CO * Cv_CO * T_CO ;
// A f t e r m i x i n g
//U2=T∗ ( n O2 ∗ Cv O2 + n CO∗Cv CO ) ;
//U1=U2
T = U1 /( n_O2 * Cv_O2 + n_CO * Cv_CO ) ;
t =T -273;
disp ( ” F i n a l t e m p e r a t u r e =” )
disp ( t )
disp ( ” C ” )
p = n * R0 * T / V /10^5;
disp ( ” F i n a l p r e s s u r e =” )
disp ( p )
disp ( ” b a r ” )
disp ( ” ( i i ) Change o f e n t r o p y ” )
// For o x y g e n
dS_O1A = n_O2 * R0 * log ( V / V_O2 ) ; // i s o t h e r m a l p r o c e s s
dS_O2A = n_O2 * Cv_O2 * log ( T_O2 / T ) ; // c o n s t a n t volume
process
dS_O12 = dS_O1A - dS_O2A ; // Change o f e n t r o p y o f O2
// For CO
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dS_CO12 = n_CO * R0 * log ( V / V_CO ) + n_CO * Cv_CO * log ( T / T_CO )
; // Change o f e n t r o p y o f CO
54
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56 dS =( dS_O12 + dS_CO12 ) /10^3;
57 disp ( ” Change o f e n t r o p y o f s y s t e m =” )
58 disp ( dS )
59 disp ( ” kJ /K” )
Scilab code Exa 9.12 12
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clc
p_A =16*10^5; // Pa
p_B =6.4*10^5; // Pa
T_A =328; //K
T_B =298; //K
n_A =0.6; // kg−mole
m_B =3; // kg
R0 =8314;
M_A =28;
y =1.4;
V_A = n_A * R0 * T_A / p_A ;
m_A = n_A * M_A ;
R = R0 / M_A ;
V_B = m_B * R * T_B / p_B ;
V = V_A + V_B ;
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m = m_A + m_B ;
T =303; //K
disp ( ” ( a ) ( i ) F i n a l e q u i l i b r i u m p r e s s u r e , p ” )
p = m * R * T / V /10^5;
disp ( ” p=” )
disp ( p )
disp ( ” b a r ” )
cv = R /10^3/( y -1) ;
disp ( ” ( i i ) Amount o f h e a t t r a n s f e r r e d , Q : ” )
U1 = cv *( m_A * T_A + m_B * T_B ) ;
U2 = m * cv * T ;
Q = U2 - U1 ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( b ) I f t h e v e s s e l w e r e i n s u l a t e d : ” )
disp ( ” ( i ) F i n a l t e m p e r a t u r e , ” )
T = cv *( m_A * T_A + m_B * T_B ) /( m * cv ) ;
t =T -273;
disp ( ”T=” )
disp ( t )
disp ( ” C ” )
disp ( ” ( i i ) F i n a l p r e s s u r e ” )
p = m * R * T / V /10^5;
disp ( ” p=” )
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disp ( p )
disp ( ” b a r ” )
Scilab code Exa 9.13 13
1 clc
2
3 m_O2 =3; // kg
4 M_O2 =32;
5
6 m_N2 =9; // kg
7 M_N2 =28;
8
9 R0 =8.314;
10
11 R_O2 = R0 / M_O2 ;
12 R_N2 = R0 / M_N2 ;
13
14 x_O2 =( m_O2 / M_O2 ) /(( m_O2 / M_O2 ) + ( m_N2 / M_N2 ) ) ;
15 x_N2 =( m_N2 / M_N2 ) /(( m_O2 / M_O2 ) + ( m_N2 / M_N2 ) ) ;
16
17 dS = - m_O2 * R_O2 * log ( x_O2 ) - m_N2 * R_N2 * log ( x_N2 ) ;
18 disp ( ” Change i n e n t r o p y =” )
19 disp ( dS )
20 disp ( ” kJ / kg K” )
Scilab code Exa 9.14 14
1 clc
2 m_N2 =2.5; // kg
3 M_N2 =28;
4
5 p_N2 =15; // b a r
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p_total =20; // b a r
n_N2 = m_N2 / M_N2 ;
p_O2 = p_total - p_N2 ;
n_O2 = p_O2 / p_N2 * n_N2 ;
M_O2 =32;
m_O2 = n_O2 * M_O2 ;
disp ( ” Mass o f O2 added =” )
disp ( m_O2 )
disp ( ” kg ” )
Scilab code Exa 9.15 15
1 clc
2 n_O2 =1;
3
4 // V O2 = 0.2 1 ∗V ;
5 // V N2 = 0.7 9 ∗V ;
6 M_N2 =28;
7 M_O2 =32;
8
9 disp ( ” ( i ) M o l e s o f N2 p e r mole o f O2 : ” )
10 n_N2 = n_O2 *0.79/0.21;
11 disp ( ” n N2=” )
12 disp ( n_N2 )
13 disp ( ” m o l e s ” )
14
15 n = n_O2 + n_N2 ;
16 disp ( ” ( i i ) p O2 and p N2 : ” )
17 p =1; // atm
18
19 p_O2 = n_O2 / n * p ;
20 disp ( ” p O2=” )
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21 disp ( p_O2 )
22 disp ( ” atm ” )
23
24 p_N2 = n_N2 / n * p ;
25 disp ( ” p N2=” )
26 disp ( p_N2 ) ;
27 disp ( ” atm ” )
28
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30 disp ( ” ( i i i ) The kg o f n i t r o g e n p e r kg o f m i x t u r e : ” )
31 x = n_N2 * M_N2 /( n_N2 * M_N2 + n_O2 * M_O2 ) ;
32 disp ( ” The kg o f n i t r o g e n p e r kg o f m i x t u r e =” )
33 disp ( x )
34 disp ( ” kg N2/ kg mix ” )
Scilab code Exa 9.16 16
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clc
V =0.6; //mˆ3
p1 =12*10^5; // Pa
p2 =18*10^5; // Pa
T =298; //K
R0 =8.314;
x_O2 =0.23;
x_N2 =0.77;
n = p1 * V / R0 /10^3/ T ;
// C o n s i d e r i n g 100 kg o f a i r
m_O2 =23; // kg
m_N2 =77; // kg
M_O2 =32;
M_N2 =28;
m =100; // kg
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R =( m_O2 / M_O2 + m_N2 / M_N2 ) * R0 / m ; // f o r a i r
M = R0 / R ; // f o r a i r
m = p1 * V / R / T /10^3;
m_O2 = x_O2 * m ;
disp ( ” Mass o f O2=” )
disp ( m_O2 )
disp ( ” kg ” )
m_N2 = x_N2 * m ;
disp ( ” Mass o f N2=” )
disp ( m_N2 )
disp ( ” kg ” )
// A f t e r a d d i n g CO2 i n t h e v e s s e l
p2 =18*10^5; // Pa ;
// p CO2+p N2+p O2 =18∗10ˆ5
// p N2 + p O2 =12∗10ˆ5
p_CO2 =6*10^5; // Pa
M_CO2 =44;
R_CO2 = R0 / M_CO2 ;
m_CO2 = p_CO2 * V /( R_CO2 *10^3* T ) ;
disp ( ” Mass o f CO2 = ” )
disp ( m_CO2 )
disp ( ” kg ” )
Scilab code Exa 9.17 17
1 clc
2 V =6; //mˆ3
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%A =0.45;
%B =0.55;
R_A =0.288; // kJ / kg K
R_B =0.295; // kJ / kg K
m =2; // kg
T =303; //K
disp ( ” ( i ) The p a r t i a l p r e s s u r e s ” )
m_A = %A * m ;
m_B = %B * m ;
p_A = m_A * R_A *10^3* T / V /10^5; // b a r
disp ( ” p A=” )
disp ( p_A )
disp ( ” b a r ” )
p_B = m_B * R_B *10^3* T / V /10^5; // b a r
disp ( ” p B=” )
disp ( p_B )
disp ( ” b a r ” )
disp ( ” ( i i ) The t o t a l p r e s s u r e ” )
p = p_A + p_B ;
disp ( ” p=” )
disp ( p )
disp ( ” b a r ” )
disp ( ” ( i i i ) The mean v a l u e o f R f o r t h e m i x t u r e ” )
Rm =( m_A * R_A + m_B * R_B ) /( m_A + m_B ) ;
disp ( ”Rm=” )
disp ( Rm )
disp ( ” kJ / kg K” )
202
Scilab code Exa 9.18 18
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clc
m_O2 =4; // kg
m_N2 =6; // kg
p =4*10^5; // Pa
T =300; //K
M_O2 =32;
M_N2 =28;
m =10; // kg
disp ( ” ( i ) The mole f r a c t i o n o f e a c h component ” )
n_O2 = m_O2 / M_O2 ;
n_N2 = m_N2 / M_N2 ;
x_O2 = n_O2 /( n_O2 + n_N2 ) ;
disp ( ” x O2=” )
disp ( x_O2 )
x_N2 = n_N2 /( n_N2 + n_O2 ) ;
disp ( ” x N2=” )
disp ( x_N2 )
disp ( ” ( i i ) The a v e r a g e m o l e c u l a r w e i g h t ” )
M =( n_O2 * M_O2 + n_N2 * M_N2 ) /( n_O2 + n_N2 ) ;
disp ( ”M=” )
disp ( M )
disp ( ” ( i i i ) The s p e c i f i c g a s c o n s t a n t ” )
R0 =8.314;
R = R0 / M ;
disp ( ”R=” )
disp ( R )
disp ( ” kJ / kg K” )
disp ( ” ( i v ) The volume and d e n s i t y ” )
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37
38 V = m * R * T *10^3/ p ;
39 disp ( ”V=” )
40 disp ( V )
41 disp ( ”mˆ3 ” )
42
43 rho =( m_O2 / V ) + ( m_N2 / V ) ;
44 disp ( ” d e n s i t y=” )
45 disp ( rho )
46 disp ( ” kg /mˆ3 ” )
47
48
49 disp ( ” ( v ) The p a r t i a l p r e s s u r e s and p a r t i a l v o l u m e s ”
)
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p_O2 = n_O2 * R0 *10^3* T / V /10^5; // b a r
disp ( ” p O2=” )
disp ( p_O2 )
disp ( ” b a r ” )
p_N2 = n_N2 * R0 *10^3* T / V /10^5; // b a r
disp ( ” p N2=” )
disp ( p_N2 )
disp ( ” b a r ” )
V_O2 = x_O2 * V ;
disp ( ”V O2=” )
disp ( V_O2 )
disp ( ”mˆ3 ” )
V_N2 = x_N2 * V ;
disp ( ”V N2=” )
disp ( V_N2 )
disp ( ”mˆ3 ” )
204
Scilab code Exa 9.19 19
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clc
cp_CO2 =0.85; // kJ / kg K
cp_N2 =1.04; // kJ / kg K
m_CO2 =4; // kg
T1_CO2 =313; //K
m_N2 =8; // kg
T1_N2 =433; //K
p2 =0.7; // b a r
p1_CO2 =1.4; // b a r
p1_N2 =1;
R =8.314;
M_CO2 =44;
M_N2 =28;
R_CO2 = R / M_CO2 ;
R_N2 = R / M_N2 ;
disp ( ” ( i ) F i n a l t e m p e r a t u r e , T2” )
T2 =( m_CO2 * cp_CO2 * T1_CO2 + m_N2 * cp_N2 * T1_N2 ) /( m_CO2 *
cp_CO2 + m_N2 * cp_N2 ) ;
19 disp ( ”T2=” )
20 disp ( T2 )
21 disp ( ”K” )
22
23
24 disp ( ” ( i i ) Change i n e n t r o p y ” )
25 n_CO2 =0.0909;
26 n_N2 =0.2857;
27 n = n_CO2 + n_N2 ;
28
29 x_CO2 = n_CO2 / n ;
30 x_N2 = n_N2 / n ;
31
32 p2_CO2 = x_CO2 * p2 ;
33 p2_N2 = x_N2 * p2 ;
34
35
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36 dS = m_CO2 * cp_CO2 * log ( T2 / T1_CO2 ) - m_CO2 * R_CO2 * log (
p2_CO2 / p1_CO2 ) + m_N2 * cp_N2 * log ( T2 / T1_N2 ) - m_N2 *
R_N2 * log ( p2_N2 / p1_N2 ) ;
37 disp ( ” dS=” )
38 disp ( dS )
39 disp ( ” kJ /K” )
Scilab code Exa 9.20 20
1 clc
2
3 cv_O2 =0.39; // kJ / kg K
4 cv_N2 =0.446; // kJ / kg K
5 n_O2 =1;
6 n_N2 =2;
7 M_O2 =32;
8 M_N2 =28;
9 m_O2 =32; // kg
10 m_N2 =2*28; // kg
11 T_O2 =293; //K
12 T_N2 =301; //K
13 R0 =8.314;
14 p_O2 =2.5*10^5; // Pa
15 p_N2 =1.5*10^5; // Pa
16
17 T2 =( m_O2 * cv_O2 * T_O2 + m_N2 * cv_N2 * T_N2 ) /( m_O2 * cv_O2 +
m_N2 * cv_N2 ) ;
18
19 V_O2 = n_O2 * R0 *10^5* T_O2 / p_O2 ;
20 V_N2 = n_N2 * R0 *10^5* T_N2 / p_N2 ;
21 V = V_O2 + V_N2 ;
22
23 dS = m_O2 *[ cv_O2 * log ( T2 / T_O2 ) + R0 / M_O2 * log ( V / V_O2 ) ] +
24
m_N2 *[ cv_N2 * log ( T2 / T_N2 ) + R0 / M_N2 * log ( V / V_N2 ) ];
disp ( ” dS=” )
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25
26
disp ( dS )
disp ( ” kJ ” )
Scilab code Exa 9.21 21
1 clc
2 cv_N2 =0.744; // kJ / kg K
3 cv_H2 =10.352; // kJ / kg K
4 cp_N2 =1.041; // kJ / kg K
5 cp_H2 =14.476; // kJ / kg K
6
7 V =0.45; //mˆ3
8 V_H2 =0.3; //mˆ3
9 V_N2 =0.15; //mˆ3
10
11 p_H2 =3*10^5; // Pa
12 p_N2 =6*10^5; // Pa
13
14 T_H2 =403; //K
15 T_N2 =303; //K
16
17 R_H2 =8.314/2;
18 R_N2 =8.314/28;
19
20 disp ( ” ( i ) T e m p e r a t u r e o f e q u i l i b r i u m m i x t u r e ” )
21
22 m_H2 = p_H2 * V_H2 /( R_H2 *10^3) / T_H2 ;
23 m_N2 = p_N2 * V_N2 /( R_N2 *10^3) / T_N2 ;
24
25 T2 =( m_H2 * cv_H2 * T_H2 + m_N2 * cv_N2 * T_N2 ) /( m_H2 * cv_H2 +
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m_N2 * cv_N2 ) ;
disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
207
30
31 disp ( ” ( i i ) P r e s s u r e o f t h e m i x t u r e ” )
32 p2_H2 = m_H2 * R_H2 *10^3* T2 / V ;
33 p2_N2 = m_N2 * R_N2 *10^3* T2 / V ;
34
35 p2 = p2_H2 + p2_N2 ;
36 disp ( ” p2=” )
37 disp ( p2 /10^5)
38 disp ( ” b a r ” )
39
40 disp ( ” ( i i i ) Change i n e n t r o p y : ” )
41
42 dS_H2 = m_H2 *[ cp_H2 * log ( T2 / T_H2 ) - R_H2 * log ( p2_H2 / p_H2
43
44
45
46
47
) ];
disp ( ” Change i n e n t r o p y o f H2 =” )
disp ( dS_H2 )
disp ( ” kJ /K” )
dS_N2 = m_N2 *[ cp_N2 * log ( T2 / T_N2 ) - R_N2 * log ( p2_N2 / p_N2
) ];
48 disp ( ” Change i n e n t r o p y o f N2 =” )
49 disp ( dS_N2 )
50 disp ( ” kJ /K” )
51
52 dS = dS_H2 + dS_N2 ;
53
54 disp ( ” T o t a l c h a n g e i n e n t r o p y =” )
55 disp ( dS )
56 disp ( ” kJ /K” )
Scilab code Exa 9.22 22
1 clc
2
3 cv_N2 =0.745; // kJ / kg K
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cv_CO2 =0.653; // kJ / kg K
cp_N2 =1.041; // kJ / kg K
cp_CO2 =0.842; // kJ / kg K
m_N2 =4; // kg
m_CO2 =6; // kg
pmix =4; // b a r
m = m_N2 + m_CO2 ;
T1 =298; //K
T2 =323; //K
cv_mix =( m_N2 * cv_N2 + m_CO2 * cv_CO2 ) /( m_N2 + m_CO2 ) ;
disp ( ” c v m i x=” )
disp ( cv_mix )
disp ( ” kJ / kg K” )
cp_mix =( m_N2 * cp_N2 + m_CO2 * cp_CO2 ) /( m_N2 + m_CO2 ) ;
disp ( ” c p m i x=” )
disp ( cp_mix )
disp ( ” kJ / kg K” )
dU = m * cv_mix *( T2 - T1 ) ;
disp ( ” Change i n i n t e r n a l e n e r g y=” )
disp ( dU )
disp ( ” kJ ” )
dH = m * cp_mix *( T2 - T1 ) ;
disp ( ” Change i n e n t h a l p y=” )
disp ( dH )
disp ( ” kJ ” )
dS = m_N2 * cv_N2 * log ( T2 / T1 ) + m_CO2 * cv_CO2 * log ( T2 / T1 ) ;
disp ( ” Change i n e n t r o p y=” )
disp ( dS )
disp ( ” kJ /K” )
209
Chapter 10
Psychrometrics
Scilab code Exa 10.1 1
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clc
t_db =293; //K
W =0.0095; // kg / kg o f d r y a i r
p_t =1.0132;
disp ( ” ( i ) P a r t i a l p r e s s u r e o f v a p o u r ” )
p_v = p_t * W /( W +0.622) ;
disp ( ” p v=” )
disp ( p_v )
disp ( ” b a r ” )
disp ( ” ( i i ) R e l a t i v e h u m i d i t y p h i : ” )
p_vs =0.0234; // b a r ; From steam t a b l e s c o r r e s p o n d i n g
t o 20 0C
14 phi = p_v / p_vs ;
15 disp ( ” r e l a t i v e h m i d i t y =” )
16 disp ( phi )
17
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20
disp ( ” ( i i i ) Dew p o i n t t e m p e r a t u r e ” )
t_dp =13 + (14 -13) /(0.01598 - 0.0150)
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*(0.01524 -0.0150) ; // From s t e a t a b l e by
interpolation
21 disp ( ” t d p=” )
22 disp ( t_dp )
23 disp ( ” 0C” )
Scilab code Exa 10.2 2
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t_db =290; //K
phi =0.6; // r e l a t i v e h u m i d i t y
p_t =1.01325; // b a r
p_vs =0.0194; // b a r
p_v = phi * p_vs ;
W =0.622* p_v /( p_t - p_v ) ;
disp ( ” S p e c i f i c Humidity=” )
disp ( W )
disp ( ” kg / kg o f d r y a i r ” )
t_dp =9 + (10 -9) *(0.01164 -0.01150) /(0.01230 0.01150) ; //By i n t e r p o l a t i o n from steam t a b l e s
16 disp ( ” dew p o i n t t e m p e r a t u r e =” )
17 disp ( t_dp )
18
disp ( ” 0C” )
Scilab code Exa 10.3 3
1 clc
2 phi =0.55;
3 p_vs =0.0425; // b a r
211
4 p_t =1.0132; // b a r
5
6 p_v = phi * p_vs ;
7 W =0.622* p_v /( p_t - p_v ) ;
8
9 // S p e c i f i c h u m i d i t y a f t e r r e m o v i n g o . oo4 kg o f w a t e r
vapour
10 Wnew =W -0.004;
11 p_v = p_t * Wnew /( Wnew +0.622) ;
12 p_vs =0.0234; // b a r
13
14 disp ( ” ( i ) R e l a t i v e h u m i d i t y ” )
15 phi = p_v / p_vs ;
16 disp ( ” p h i=” )
17 disp ( phi )
18
19
20 disp ( ” ( i i ) Dew p o i n t t e m p e r a t u r e ” )
21
22 disp ( ” C o r r e s p o n d i n g t o 0 . 0 1 7 1 bar , from steam t a b l e s
23
24
25
26
”)
t_dp =15; // 0C
disp ( ” t d p=” )
disp ( t_dp )
disp ( ” 0C” )
Scilab code Exa 10.4 4
1 clc
2 t_db =35; // 0C
3 t_wb =25; // 0C
4 p_t =1.0132; // b a r
5
6 // C o r r e s p o n d i n g t o 25 0C i n steam t a b l e s
7 p_vs_wb =0.0317; // b a r
212
8
9 p_v = p_vs_wb - ( p_t - p_vs_wb ) *( t_db - t_wb ) /(1527.4
- 1.3* t_wb ) ;
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disp ( ” ( i ) S p e c i f i c h u m i d i t y ” )
W =0.622* p_v /( p_t - p_v ) ;
disp ( ”W=” )
disp ( W )
disp ( ” kg / kg o f d r y a i r ” )
disp ( ” ( i i ) R e l a t i v e h u m i d i t y ” )
// C o r r e s p o n d i n g t o 35 0C , from steam t a b l e s
p_vs =0.0563;
phi = p_v / p_vs ;
disp ( ” p h i ” )
disp ( phi )
disp ( ” ( i i i ) Vapour d e n s i t y ” )
R_v =8314.3/18;
T_v =308; //K
rho_v = p_v *10^5/( R_v * T_v ) ;
disp ( ” r h o v=” )
disp ( rho_v )
disp ( ” kg /mˆ3 ” )
disp ( ” ( i v ) Dew p o i n t t e m p e r a t u r e ” )
t_dp =21 + (22 -21) *(0.0252 -0.0249) /(0.0264 -0.0249) ;
disp ( ” t d p ” )
disp ( t_dp )
disp ( ” 0C” )
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45 disp ( ” ( v ) E n t h a l p y o f m i x t u r e p e r kg o f d r y a i r ” )
46 cp =1.005;
47 h_g =2565.3; // kJ / kg ; c o r r e s p o n d i n g t o 35 0C
48 h_vapour = h_g + 1.88*( t_db - t_dp ) ;
49
50 h = cp * t_db + W * h_vapour ;
51 disp ( ” h=” )
52 disp ( h )
53 disp ( ” kJ / kg o f d r y a i r ” )
Scilab code Exa 10.5 5
1 clc
2
3 // For t h e a i r a t 35 0C DBT and 60% R . H .
4 p_vs =0.0563; // b a r ; C o r r e s p o n d i n g t o 35 0C from stem
tables
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phi =0.6;
p_t =1.0132; // b a r
cp =1.005;
t_db =35; // 0C
h_g =2565.5; // kJ / kg
m1 =1; // kg
m2 =2; // kg
m = m1 + m2 ;
p_v = phi * p_vs ;
W1 =0.622* p_v /( p_t - p_v ) ;
// C o r r e s p o n d i n g t o 0 . 0 3 8 8 bar , from steam t a b l e s
t_dp =26+(27 -26) *(0.0338 -0.0336) /(0.0356 -0.0336) ;
h_vapour = h_g + 1.88*( t_db - t_dp ) ;
h1 = cp * t_db + W1 * h_vapour ;
214
23
24
// For t h e a i r a t 20 C
temperature :
25 p_v =0.0150; // b a r
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DBT and 13 C
W2 =0.622* p_v /( p_t - p_v ) ;
t_db =20; // 0C
t_dp =13;
h_g =2538.1; // kJ / kg
h_vapour = h_g + 1.88*( t_db - t_dp ) ;
h2 = cp * t_db + W2 * h_vapour ;
// l e t e n t h a l p y p e r kg o f m o i s t a i r be h
h =(( m1 * h1 /(1+ W1 ) ) + ( m2 * h2 /(1+ W2 ) ) ) / m ;
// L e t Mass o f v a p o u r / kg o f m o i s t a i r be M
M =( m1 * W1 /(1+ W1 ) + m2 * W2 /(1+ W2 ) ) / m ;
// L e t s p e c i f i c h u m i d i t y be d e n o t e d by SH
SH = M /(1 - M ) ;
disp ( ” S p e c i f i c h u m i d i t y =” )
disp ( SH )
disp ( ” kg / kg o f d r y a i r ” )
Scilab code Exa 10.6 6
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dew p o i n t
clc
// For a i r a t 20 0C and 75% R . H
p_vs =0.0234; // b a r
phi =0.75;
p_t =1.0132;
cp =1.005;
215
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t_db =20; // 0C
p_v = phi * p_vs ;
t_dp =15 + (16 -15) *(0.01755 -0.017) /(0.0182 -0.017) ;
W =0.622* p_v /( p_t - p_v ) ;
h_g =2538.1; // kJ / kg
h_vapour = h_g + 1.88*( t_db - t_dp ) ;
h1 = cp * t_db + W * h_vapour ;
disp ( ” ( i ) R e l a t i v e h u m i d i t y o f h e a t e d a i r : ” )
// For a i r a t 30 C DBT
p_vs =0.0425; // b a r ; c o r r e s p o n d i n g t o 30 0C
phi = p_v / p_vs ;
disp ( ” R e l a t i v e h u m i d i t y=” )
disp ( phi *100)
disp ( ”%” )
disp ( ” ( i i ) Heat added t o a i r p e r m i n u t e ” )
h_g =2556.3; // kJkg
t_db =30;
h2 = cp * t_db + W * h_vapour ;
V =90; //mˆ3
R =287;
T =293; //K
m =( p_t - p_v ) * V *10^5/ R / T ;
Amt = m *( h2 - h1 ) ;
disp ( ”Amount o f h e a t added p e r m i n u t e=” )
disp ( Amt )
disp ( ” kJ ” )
216
Scilab code Exa 10.7 7
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// For a i r a t 35 0C DBT and 50% RH
p_vs =0.0563; // b a r ; At 35 0C , from steam t a b l e s
phi =0.5;
p_t =1.0132;
t_db1 =35; // 0C
t_dp1 =23; // 0C
cp =1.005;
R =287;
p_v = phi * p_vs ;
W1 =0.622* p_v /( p_t - p_v ) ;
h_g1 =2565.3; // kJ / kg
h_vapour = h_g1 + 1.88*( t_db1 - t_dp1 ) ;
h1 = cp * t_db1 + W1 * h_vapour ;
disp ( ” ( i ) R . H . o f c o o l e d a i r ” )
p_vs =0.0317;
phi = p_v / p_vs ;
disp ( ”RH o f c o o l e d a i r =” )
disp ( phi *100)
disp ( ”%” )
disp ( ” ( i i ) Heat removed from a i r ” )
h_g2 =2547.2; // kJ / kg
t_db2 =25; // 0C
t_dp2 =23; // 0C
W2 = W1 ;
T =308; //K
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V =40; //mˆ3
h_vapour = h_g2 + 1.88*( t_db2 - t_dp2 ) ;
h2 = cp * t_db2 + W2 * h_vapour ;
m =( p_t - p_v ) *10^5* V / R / T ;
// L e t Heat removed be d e n o t e d by H
H = m *( h1 - h2 ) ;
disp ( ” Heat removed =” )
disp ( H )
disp ( ” kJ ” )
Scilab code Exa 10.8 8
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// For t h e a i r a t 35 C DBT and 50% R . H .
p_vs =0.0563; // b a r ; At 35 0C , from steam t a b l e s
phi =0.5;
p_v = phi * p_vs ;
p_t =1.0132; // b a r
t_dp1 =23; // 0C
t_db1 =35; // 0C
W1 =0.622* p_v /( p_t - p_v ) ;
h_g1 =2565.3; // kJ / kg
R =287;
cp =1.005;
h_vapour = h_g1 + 1.88*( t_db1 - t_dp1 ) ;
h1 = cp * t_db1 + W1 * h_vapour ;
disp ( ” ( i ) R e l a t i v e h u m i d i t y o f o u t coming a i r and
i t s wet b u l b t e m p e r a t u r e . ” )
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disp ( ” R e l a t i v e h u m i d i t y o f e x i t a i r i s 100 p e r c e n t .
”)
t_wb =20; // 0C
disp ( ”Wet b u l b t e m p e r t u r e=” )
disp ( t_wb )
disp ( ” 0C” )
p_v =0.0234; // b a r
p_vs = p_v ;
t_db2 =20; // 0C
h_g2 =2538.1; // kJ / kg
t_dp2 = t_db2 ;
W2 =0.622* p_v /( p_t - p_v ) ;
h_vapour = h_g2 + 1.88*( t_db2 - t_dp2 ) ;
h2 = cp * t_db2 + W2 * h_vapour ;
T =308; //K
V =120; //mˆ3
W = W1 - W2 ; // Weight o f w a t e r v v a p o u r removed p e r kg o f
dry a i r
43 h = h1 - h2 ; // Heat removed p e r kg o f d r y a i r
44 m =( p_t - p_v ) *10^5* V / R / T ;
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47
disp ( ” ( i i ) C a p a c i t y o f t h e c o o l i n g c o i l i n t o n n e s o f
r e f r i g e r a t i o n ”)
C = m *( h1 - h2 ) *60/14000;
disp ( ” C a p a c i t y =” )
disp ( C )
disp ( ”TR” )
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54 disp ( ” ( i i i ) Amount o f w a t e r removed p e r h o u r ” )
55 Amt = m *( W1 - W2 ) *60;
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disp ( ”Amount o f w a t e r removed p e r h o u r=” )
disp ( Amt )
disp ( ” kg /h ” )
Scilab code Exa 10.9 9
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p_vs =0.0563; // b a r
phi =0.2;
p_v = phi * p_vs ;
p_t =1.0132; // b a r
W1 =0.622* p_v /( p_t - p_v ) ;
disp ( ” ( i ) Dew p o i n t t e m p e r a t u r e ” )
//
t_dp =8+(9 -8) *(0.01126 -0.01072) /(0.01150 -0.01072) ;
disp ( ” dew p o i n t t e m p e r a t u r e=” )
disp ( t_dp )
disp ( ” 0C” )
disp ( ” ( i i ) R e l a t i v e h u m i d i t y o f t h e e x i t a i r : ” )
p_vs_wb =0.0170; // b a r
p_vs =0.0234; // b a r
t_db =20; // 0C
t_wb =15; // 0C
p_v = p_vs_wb - ( p_t - p_vs_wb ) *( t_db - t_wb ) /(1527.4 -1.3*
t_wb ) ;
24 W2 =0.622* p_v /( p_t - p_v ) ;
25
26 RH = p_v / p_vs ;
27 disp ( ” R e l a t i v e h u m i d i t y=” )
28 disp ( RH )
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p_v =0.01126; // b a r
R =287;
T =308; //K
V =150;
m =( p_t - p_v ) * V *10^5/ R / T ;
disp ( ” ( i i i ) Amount o f w a t e r v a p o u r added t o t h e a i r
per minute ”)
amt = m *( W2 - W1 ) ;
disp ( ”Amount =” )
disp ( amt )
disp ( ” kg / min ” )
Scilab code Exa 10.10 10
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clc
p_s =0.0206; // b a r
p_t =1; // b a r
p_s1 =0.03782; // b a r
W_2s =0.622* p_s /( p_t - p_s ) ;
cp =1.005;
t_db2 =18; // 0C
t_db1 =28; // 0C
h_g2 =2534.4; // kJ / kg
h_f2 =75.6; // kJ / kg
h_g1 =2552.6; // kJ / kg
W1 =( cp *( t_db1 - t_db2 ) + W_2s *( h_g2 - h_f2 ) ) /( h_g1 - h_f2 )
;
16
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17 p_v1 = W1 * p_t /(0.622+ W1 ) ;
18
19 RH = p_v1 / p_s1 ; // R e l a t i v e h u m i d i t y
20 disp ( ” R e l a t i v e h u m i d i t y ” )
21 disp ( RH )
Scilab code Exa 10.11 11
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clc
t_db1 =38; // 0C
t_db2 =18; // 0C
phi_1 =0.75;
phi_2 =0.85;
p_t =1; // b a r
cp =1.005;
// At 38 0C
p_vs =0.0663; // b a r
h_g1 =2570.7; // kJ / kg
p_v = phi_1 * p_vs ;
W1 =0.622* p_v /( p_t - p_v ) ;
// At 18 0C
p_vs =0.0206; // b a r
h_g2 =2534.4; // kJ / kg
h_f2 =75.6; // kJ / kg
p_v = phi_2 * p_vs ;
W2 =0.622* p_v /( p_t - p_v ) ;
q =( W2 * h_g2 - W1 * h_g1 ) + cp *( t_db2 - t_db1 ) + ( W1 - W2 ) *
h_f2 ;
23 disp ( ” Heat t r a n s f e r r a t e=” )
24 disp ( q )
25 disp ( ” kJ / kg o f d r y a i r ” )
222
Scilab code Exa 10.12 12
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clc
// At 38 0C
p_vs =0.0663; // b a r
h_g1 =2570.7; // kJ / kg
phi =0.25;
p_t =1.0132;
p_v = phi * p_vs ;
cp =1.005;
// At 18 0C
h_g2 =2534.4; // kJ / kg
p_vs =0.0206; // b a r
W1 =0.622* p_v /( p_t - p_v ) ;
t_db1 =38; // 0C
t_db2 =18; // 0C
W2 =( cp *( t_db1 - t_db2 ) + W1 * h_g1 ) / h_g2 ;
// amount o f w a t e r added =amt
amt = W2 - W1 ;
disp ( ” amt=” )
disp ( amt )
disp ( ” kg / kg o f d r y a i r ” )
p_v2 = amt * p_t /(0.622+ amt ) ;
RH = p_v2 / p_vs ;
disp ( ” F i n a l r e l a t i v e h u m i d i t y ” )
disp ( RH )
223
Scilab code Exa 10.13 13
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disp ( ” ( i ) Mass o f s p r a y w a t e r r e q u i r e d ” )
// At 22 0 c
p_vs =0.0264; // b a r
phi_3 =0.55;
p_t =1.0132; // b a r
p_v3 = phi_3 * p_vs ;
W3 =0.622* p_v3 /( p_t - p_v3 ) ;
// At 3 0C
p_vs1 =0.0076; // b a r
p_v1 = p_vs1 ;
W1 =0.622* p_v1 /( p_t - p_v1 ) ;
R =287;
T_3 =295; //K
v = R * T_3 /( p_t - p_v3 ) /10^5;
m =( W3 - W1 ) / v ;
disp ( ” Mass o f s p r a y w a t e r r e q u i r e d=” )
disp ( m )
disp ( ” kg m o i s t u r e /mˆ3 ” )
disp ( ” ( i i ) T e m p e r a t u r e t o which t h e a i r must be
heated ”)
31 t_dp =12.5; // 0C
224
32 cp =1.005;
33 t_db3 =22; // 0C
34 h_g3 =2524; // kJ / kg
35 h_vapour3 = h_g3 + 1.88*( t_db3 - t_dp ) ;
36 W2 =0.0047;
37 h_g2 =2524; // kJ / kg
38 h4 =41.87;
39
40 t_db2 =( cp * t_db3 + W3 * h_vapour3 - W2 * h_g2 + 1.88* W2 *
t_dp - ( W3 - W2 ) * h4 ) /( cp - W2 *1.88) ;
41 disp ( ” t d b 2=” )
42 disp ( t_db2 )
43 disp ( ” 0C” )
Scilab code Exa 10.14 14
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clc
disp ( ” ( i ) Make−up w a t e r r e q u i r e d ” )
p_vs =0.0206; // b a r
phi =0.6;
p_t =1.013; // b a r
p_v1 = phi * p_vs ;
p_a1 = p_t - p_v1 ;
V =9; //mˆ3
R =287;
T =291; //K
m_a = p_a1 *10^5* V / R / T ;
m_v1 =0.0828; // kg / s
// At e x i t a t 26 0C
p_vs =0.0336; // b a r
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phi =1;
p_v = p_vs ;
W2 =0.622* p_v /( p_t - p_v ) ;
m_v2 = W2 * m_a ;
m = m_v2 - m_v1 ;
disp ( ”Make−up w a t e r r e q u i r e d=” )
disp ( m )
disp ( ” kg / s ” )
disp ( ” ( i i ) F i n a l t e m p e r a t u r e o f t h e w a t e r ” )
m_w1 =5.5; // kg / s
m_w2 = m_w1 - m ;
Wi =4.75; // kJ / s
h_w1 =184.3; // kJ / kg
h_a1 =18.09; // kJ / kg
h_v1 =2534.74; // kJ / kg
h_v2 =2549; // kJ / kg
h_a2 =26.13; // kJ / kg
h_w2 =( Wi + m_w1 * h_w1 + m_a * h_a1 + m_v1 * h_v1 - m_a *
h_a2 - m_v2 * h_v2 ) / m_w2 ;
45
46 //By i n t e r p o l a t i o n , h w2 c o r r e s p o n d s t o t
47 t =26.7; // 0C
48 disp ( ” f i n a l t e m p e r a t u r e o f w a t e r=” )
49 disp ( t )
50 disp ( ” 0C” )
Scilab code Exa 10.15 15
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m_water =60000; // kg / s
c =4.186;
t1 =30; // 0C
t2 =35; // 0C
Q = m_water * c *( t2 - t1 ) ;
h1 =76.5; // kJ / kg
W1 =0.016; // kg / kg o f a i r
h2 =92.5; // kJ / kg
W2 =0.0246; // kg / kg o f a i r
m_air = Q /( h2 - h1 ) ;
A = m_air /10; // Q u a n t i t y o f a i r h a n d l e d p e r f a n
disp ( ” Q u a n t i t y o f a i r h a n d l e d p e r f a n=” )
disp ( A )
disp ( ” kg /h ” )
B = m_air *( W2 - W1 ) ;
disp ( ” Q u a n t i t y o f make up w a t e r=” )
disp ( B )
disp ( ” kg /h ” )
Scilab code Exa 10.17 17
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h1 =35.4; // kJ / kg
h2 =45.2; // kJ / kg
v_s1 =0.8267; //mˆ3/ kg
m_a =241.9;
disp ( ” ( i ) R . H . o f h e a t e d a i r =” )
227
8 RH =41; // From c h a r t
9 disp ( RH )
10 disp ( ”%” )
11
12 disp ( ” ( i i ) WBT o f h e a t e d a i r =” )
13 WBT =16.1; // 0C
14 disp ( WBT )
15 disp ( ” C ” )
16
17 disp ( ” ( i i i ) Heat added t o a i r p e r m i n u t e =” )
18 Q = m_a *( h2 - h1 ) ;
19 disp ( Q )
20 disp ( ” kJ ” )
Scilab code Exa 10.18 18
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clc
h1 =29.3; // kJ / kg
h2 =42.3; // kJ / kg
h3 = h2 ;
t_db2 =24.5; // 0C
t_db1 =12; // 0C
v_s1 =0.817; //mˆ3/ kg
amt =0.30; // Amount o f a i r c i r c u l a t i o n mˆ3/ min / p e r s o n
capacity =60; // S e a t i n g c a p a c i t y o f o f f i c e
BF =0.4; //By−p a s s f a c t o r
W3 =8.6;
W1 =6.8;
m_a = amt * capacity / v_s1 ;
disp ( ” ( i ) H e a t i n g c a p a c i t y o f t h e h e a t i n g c o i l =” )
Q = m_a *( h2 - h1 ) /60;
disp ( Q )
disp ( ”kW” )
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21 t_db4 =( t_db2 - BF * t_db1 ) /(1 - BF ) ;
22 disp ( ” C o i l s u r f a c e t e m p e r a t u r e =” )
23 disp ( t_db4 )
24 disp ( ” C ” )
25
26 disp ( ” ( i i ) The c a p a c i t y o f t h e h u m i d i f i e r =” )
27 c = m_a *( W3 - W1 ) /1000*60;
28 disp ( c )
29 disp ( ” kg /h ” )
Scilab code Exa 10.19 19
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h1 =82.5; // kJ / kg
h2 =47.5; // kJ / kg
h3 =55.7; // kJ / kg
h5 =36.6; // kJ / kg
W1 =19.6; //gm/ kg
W3 =11.8; //gm/ kg
t_db2 =17.6; // 0C
t_db3 =25; // 0C
v_s1 =0.892; //mˆ3/ kg
amt =250; //mˆ3/ min
m_a = amt / v_s1 ;
disp ( ” ( i ) The c a p a c i t y o f t h e c o o l i n g c o i l =” )
capacity = m_a *( h1 - h2 ) *60/14000;
disp ( capacity )
disp ( ”TR” )
BF =( h2 - h5 ) /( h1 - h5 ) ;
disp ( ” by−p a s s f a c t o r o f t h e c o o l i n g c o i l =” )
disp ( BF )
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disp ( ” ( i i ) The h e a t i n g c a p a c i t y o f t h e h e a t i n g c o i l
=” )
24 Q = m_a *( h3 - h2 ) /60;
25 disp ( Q )
26 disp ( ”kW” )
23
27
28 BF =0.3;
29 t_db6 =( t_db3 - BF * t_db2 ) /(1 - BF ) ;
30 disp ( ” s u r f a c e t e m p e r a t u r e o f h e a t i n g c o i l =” )
31 disp ( t_db6 )
32 disp ( ” C ” )
33
34 disp ( ” ( i i i ) The mass o f w a t e r v a p o u r removed p e r
h o u r =” )
35 m = m_a *( W1 - W3 ) *60/1000;
36 disp ( m )
37 disp ( ” kg /h ” )
230
Chapter 11
Chemical Thermodynamics
Scilab code Exa 11.1 1
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%C =0.88; // F r a c t i o n o f c a r b o n i n c o a l
%H =0.042; // F r a c t i o n o f Hydrogen i n c o a l
w_f =0.848; //gm
w_fw =0.027; //gm
w =1950; //gm
w_e =380; //gm
dt =3.06; // 0C ; O b s e r v e d t e m p e r a t u r e r i s e
tc =0.017; // 0C
dt1 = dt + tc ; // C o r r e c t e d t e m p e r a t u r e r i s e
Cal =6700; // J /gm ; C a l o r i f i c v a l u e o f f u s e w i r e
Q_received =( w + w_e ) *4.18* dt1 ; // Heat r e c e i v e d by
water
15
16 Q_rejected = w_fw * Cal ; // Heat g i v e n o u t by f u s e
17
18 Q_produced = Q_received - Q_rejected ;
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20 HCV = Q_produced / w_f ;
231
wire
21 disp ( ” H i g h e r c a l o r i f i c v a l u e=” )
22 disp ( HCV )
23 disp ( ” kJ / kg ” )
24
25 LCV = HCV - 2465*9* %H ;
26 disp ( ” Lower C a l o r i f i c v a l u e=” )
27 disp ( LCV )
28 disp ( ” kJ / kg ” )
Scilab code Exa 11.2 2
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p1 =75.882; //cm o f Hg
T1 =286; //K
V1 =0.08; //mˆ3
p2 =76; //cm o f Hg
T2 =288; //K
V2 = p1 * V1 * T2 / p2 / T1 ;
m =28; // kg
c =4.18;
t2 =23.5; // 0C
t1 =10; // 0C
Q_received = m * c *( t2 - t1 ) ;
HCV = Q_received / V2 ;
disp ( ” H i g h e r c a l o r i f i c v a l u e =” )
disp ( HCV )
disp ( ” kJ /mˆ3 ” )
amt =0.06/0.08; // Amount o f v a p o u r f o r m e d p e r mˆ3 o f
gas burnt
23 LCV = HCV -2465* amt ;
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26
disp ( ” Lower c a l o r i f i c v a l u e =” )
disp ( LCV )
disp ( ” kJ / kg ” )
Scilab code Exa 11.3 3
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C =0.85; // Weight o f Carbon p r e s e n t
H2 =0.06; // Weight o f Hydrogen p r e s e n t
O2 =0.06; // Weight o f Oxygen p r e s e n t
w_required = C *8/3 + H2 *8; // Weight o f O2 r e q u i r e d
w_needed = w_required - O2 ; // Weight o f O2 t o be
supplied
w_air = w_needed *100/23;
disp ( ” Weight o f a i r n e e d e d=” )
disp ( w_air )
disp ( ” kg ” )
Scilab code Exa 11.4 4
1 clc
2 C =0.848; // kg
3 H2 =0.152; // kg
4 O2_used = C *8/3 + H2 *8;
5
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7 disp ( ” ( i ) Minimum w e i g h t o f
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a i r needed f o r
combustion ”)
w_min = O2_used *100/23;
disp ( ”Minimum w e i g h t o f a i r n e e d e d f o r c o m b u s t i o n=” )
disp ( w_min )
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disp ( ” kg ” )
w_excess = w_min *0.15; // E x c e s s a i r s u p p l i e d
w_O2 = w_excess *23/100; // Weight o f O2 i n e x c e s s a i r
w_total = w_min + w_excess ; // T o t a l a i r s u p p l i e d f o r
combustion
18 w_N2 = w_total *77/100; // Weight o f N2 i n f l u e g a s e s
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disp ( ” ( i i ) t h e v o l u m e t r i c c o m p o s i t i o n o f t h e
products of combustion ”)
// For CO2
x1 =3.109;
y1 =44;
z1 = x1 / y1 ;
// For O2
x2 = w_O2 ;
y2 =32;
z2 = x2 / y2 ;
// For N2
x3 = w_N2 ;
y3 =28;
z3 = x3 / y3 ;
z = z1 + z2 + z3 ;
// For CO2
%V1 = z1 / z *100;
disp ( ” %volume o f CO2 =” )
disp ( %V1 )
disp ( ”%” )
// For O2
234
47 %V2 = z2 / z *100;
48 disp ( ” %volume o f O2 =” )
49 disp ( %V2 )
50 disp ( ”%” )
51
52 // For CO2
53 %V3 = z3 / z *100;
54 disp ( ” %volume o f N2 =” )
55 disp ( %V3 )
56 disp ( ”%” )
Scilab code Exa 11.5 5
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C =0.78;
H2 =0.06;
O2 =0.03;
w_O2 = C *8/3 + H2 *8;
w_min =( w_O2 - O2 ) *100/23; // Minimum wt . o f a i r n e e d e d
f o r combustion
disp ( ” ( i ) Weight o f d r y f l u e g a s e s p e r kg o f f u e l ” )
// For CO2
x1 =0.104;
y1 =44;
z1 = x1 * y1 ;
// For CO
x2 =0.002;
y2 =28;
z2 = x2 * y2 ;
// For N2
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x3 =0.816;
y3 =28;
z3 = x3 * y3 ;
// For O2
x4 =0.078;
y4 =32;
z4 = x4 * y4 ;
z = z1 + z2 + z3 + z4 ;
W_CO2 = z1 / z ; // Weight p e r kg o f
W_CO = z2 / z ; // Weight p e r kg o f
W_N2 = z3 / z ; // Weight p e r kg o f
W_O2 = z4 / z ; // Weight p e r kg o f
flue
flue
flue
flue
gas
gas
gas
gas
amt =3/11* W_CO2 + 3/7* W_CO ;
W = C / amt ; // Weight o f d r y f l u e g a s p e r kg o f f u e l
disp ( ” Weight o f d r y f l u e g a s p e r kg o f f u e l = ” )
disp ( W )
disp ( ” kg ” )
disp ( ” ( i i ) Weight o f e x c e s s a i r p e r kg o f f u e l ” )
m_O2 = W_O2 -4/7* W_CO ; // Weight o f e x c e s s o x y g e n p e r kg
of f l u e gas
47 m_excess = W * m_O2 ; // Weight o f e x c e s s O2 p e r kg o f
fuel
48
49
w_excess = m_excess *100/23; // Weight o f e x c e s s a i r p e r
kg o f f u e l
50 disp ( ” Weight o f e x c e s s a i r p e r kg o f f u e l =” )
51 disp ( w_excess )
52 disp ( ” kg ” )
236
Scilab code Exa 11.6 6
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2 v_CO =0.05;
3 v_CO2 =0.10;
4 v_H2 =0.50;
5 v_CH4 =0.25;
6 v_N2 =0.10;
7
8 V_fuel =1;
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10 V_O2 = v_CO /2+ v_H2 /2+2* v_CH4 ; // Volume o f O2 n e e d e d
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12 V_air = V_O2 *100/21; // Volume o f a i r r e q u i r e d
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14 V_N2 = V_air *79/100; // Volume o f n i t r o g e n i n t h e a i r
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16 V = v_CO + v_CO2 + v_CH4 + v_N2 + V_N2 ; // Dry
combustion products
17
18 O2 =6;
19 V_excess = O2 * V /(21 - O2 ) ;
20
21 V_total = V_air + V_excess ;
22
23 ratio = V_total / V_fuel ;
24 disp ( ” A i r f u e l r a t i o =” )
25 disp ( ratio )
Scilab code Exa 11.7 7
1 clc
2
3 C =0.85;
4 H2 =0.15;
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// For CO2
x1 =0.115;
y1 =44;
z1 = x1 * y1 ;
// For CO
x2 =0.012;
y2 =28;
z2 = x2 * y2 ;
// For O2
x3 =0.009;
y3 =32;
z3 = x3 * y3 ;
// For N2
x4 =0.86;
y4 =28;
z4 = x4 * y4 ;
z = z1 + z2 + z3 + z4 ;
W_CO2 = z1 / z ; // Weight p e r kg o f f l u e g a s
W_CO = z2 / z ; // Weight p e r kg o f f l u e g a s
W_O2 = z3 / z ; // Weight p e r kg o f f l u e g a s
W_N2 =4/ z ; // Weight p e r kg o f f l u e g a s
W_C =3/11* W_CO2 + 3/7* W_CO ; // Weight o f c a r b o n p e r kg
of f l u e gas
34
35 W = C / W_C ; // Weight o f d r y f l u e g a s p e r kg o f
36
37 Vapour =1.35; // kg ; Vapour o f c o m b u s t i o n
38
39 W_total = W + Vapour ; // T o t a l w e i g h t o f g a s
40
41 W_air = W_total -1; // A i r s u p p l i e d
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fuel
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ratio = W_air /1;
disp ( ” R a t i o o f a i r t o p e t r o l =” )
disp ( ratio )
S_air =[ C *8/3 + H2 *8]*100/23; // S t o i c h i o m e t r i c a i r
W_excess = W_air - S_air ; // E x c e s s a i r
%Excess = W_excess / S_air *100; // P e r c e n t a g e e x c e s s a i r
disp ( ” P e r c e n t a g e e x c e s s a i r ” )
disp ( %Excess )
disp ( ”%” )
Scilab code Exa 11.8 8
1
2
3
4
5
6
7
8
9
clc
C =0.86;
H2 =0.08;
S =0.03;
O2 =0.02;
W_O2 = C *8/3 + H2 *8 + S *1;
A = W_O2 - O2 ; // Weight o f o x y g e n t o be s u p p l i e d p e r kg
of fuel
10
11 W_min = A *100/23;
12 r_correct =1/ W_min /1; //
correct
f u e l −a i r
13 r_actual =1/12;
14
15
16 disp ( ” ( i ) M i x t u r e s t r e n g t h ” )
17 s = r_actual / r_correct *100; // M i x t u r e s t r e n g t h
18
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ratio
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richness =s -100;
disp ( ” r i c h n e s s =” )
disp ( richness )
disp ( ”%” )
disp ( ” T h i s show t h a t m i x t u r e i s 6 . 5% r i c h . ” )
D =1/ r_correct -1/ r_actual ;
CO =0.313; // kg
CO2 =2.662; // kg
N2 =9.24; // kg
SO2 =0.06; // kg
disp ( ” ( i i ) The p e r c e n t a g e c o m p o s i t i o n o f d r y f l u e
g a s e s ”)
// For CO
x1 =0.313; // kg
y1 =28;
z1 = x1 / y1 ;
// For CO2
x2 =2.662; // kg
y2 =44;
z2 = x2 / y2 ;
// For N2
x3 =9.24; // kg
y3 =28;
z3 = x3 / y3 ;
// For SO2
x4 =0.06; // kg
y4 =64;
z4 = x4 / y4 ;
z = z1 + z2 + z3 + z4 ;
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// L e t p e r c e n t a g e volume be d e n o t e d by V
V_CO = z1 / z *100;
disp ( ” P e r c e n t a g e volume o f CO=” )
disp ( V_CO )
disp ( ”%” )
V_CO2 = z2 / z *100;
disp ( ” P e r c e n t a g e volume o f CO2=” )
disp ( V_CO2 )
disp ( ”%” )
V_N2 = z3 / z *100;
disp ( ” P e r c e n t a g e volume o f N2=” )
disp ( V_N2 )
disp ( ”%” )
V_SO2 = z4 / z *100;
disp ( ” P e r c e n t a g e volume o f SO2=” )
disp ( V_SO2 )
disp ( ”%” )
Scilab code Exa 11.9 9
1 clc
2
3 A =992/284*100/23; // A i r r e q u i r e d
f o r complete
combustion
4
5 B =13; // kg / kg o f f u e l ; A i r a c t u a l l y
6
7 D =A - B ; // D e f i c i e n c y o f a i r
8
9 W_CO2 =0.466*11/3;
241
supplied
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W_CO =0.379*7/3;
W_H2O =22/142*9;
W_N2 =13*0.77;
// For CO2
x1 = W_CO2
y1 =44;
z1 = x1 / y1 ;
// For CO
x2 = W_CO ;
y2 =28;
z2 = x2 / y2 ;
// For H2O
x3 = W_H2O ;
y3 =18;
z3 = x3 / y3 ;
// For N2
x4 = W_N2 ;
y4 =28;
z4 = x4 / y4 ;
z = z1 + z2 + z3 + z4 ;
%CO2 = z1 / z *100;
disp ( ” P e r c e n t a g e o f CO2=” )
disp ( %CO2 )
disp ( ”%” )
%CO = z2 / z *100;
disp ( ” P e r c e n t a g e o f CO=” )
disp ( %CO )
disp ( ”%” )
%H2O = z3 / z *100;
disp ( ” P e r c e n t a g e o f H2O=” )
242
48 disp ( %H2O )
49 disp ( ”%” )
50
51 %N2 = z4 / z *100;
52 disp ( ” P e r c e n t a g e o f N2=” )
53 disp ( %N2 )
54 disp ( ”%” )
Scilab code Exa 11.11 11
1 clc
2
3 C =80;
4
5 // A n a l y s i s o f g a s e n t e r i n g t h e e c o n o m i s e r
6 CO2_1 =8.3;
7 CO_1 =0;
8 O2_1 =11.4;
9 N2_1 =80.3;
10
11 // A n a l y s i s o f g a s l e a v i n g t h e e c o n o m i s e r
12 CO2_2 =7.9;
13 CO_2 =0;
14 O2_2 =11.5;
15 N2_2 =80.6;
16
17 A1 = N2_1 * C /33/( CO2_1 + CO_1 ) ; // A i r s u p p l i e d on t h e
b a s i s of c o n d i t i o n s at entry to the economiser
18
19 A2 = N2_2 * C /33/( CO2_2 + CO_2 ) ; // A i r a p p l i e d on t h e
b a s i s of c o n d i t i o n s at e x i t
20
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23
leakage = A2 - A1 ; // A i r l e a k a g e
disp ( ” A i r l e a k e g e =” )
disp ( leakage )
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disp ( ” kg o f a i r p e r kg o f f u e l ” )
W_fuel =0.85; // kg ; Weight o f f u e l p a s s i n g up t h e
chimney
c =1.05;
T2 =410;
T1 =0;
W = A1 + W_fuel ; // T o t a l w e i g h t o f p r o d u c t s
Q1 = W * c *( T2 - T1 ) ; // Heat i n f l u e g a s e s p e r kg o f c o a l
Q2 = leakage *1.005*(20 -0) ; // Heat i n l e a k a g e a i r
t =( Q1 + Q2 ) /(1.005* leakage + W *1.05) ;
dT = T2 - t ;
disp ( ” F a l l i n t e m p e r a t u r e a s a r e s u l t o f t h e a i r
leakage i n t o the economiser ”)
40 disp ( dT )
41 disp ( ” C ” )
Scilab code Exa 11.12 12
1 clc
2
3 w_O2 =3*32/46*100/23; // For c o m p l e t e c o m b u s t i o n o f 1
kg o f C2H6O , o x y g e n r e q u i r e d
4
5 ratio = w_O2 ;
6 disp ( ”A : F r a t i o =” )
7 disp ( ratio )
8
9 w1 =88; // kg
10 w2 =54; // kg
11
244
12 w = w1 + w2 ; // kg
13 W =46; // kg
14
15 w_CO2 = w1 / W *100;
16 disp ( ”CO2 p r o d u c e d by f u e l ” )
17 disp ( w_CO2 )
18 disp ( ”%” )
19
20 w_H2O = w2 / W *100;
21 disp ( ”H2O p r o d u c e d by f u e l ” )
22 disp ( w_H2O )
23 disp ( ”%” )
Scilab code Exa 11.13 13
1 clc
2 // C2H2+xO2−−−−>aCO2+bH2O
3 // 2C=aC ; a=2
4 // 2H=2bH ; b=1
5 // x =2.5
6
7 // C2H2 +2.5O2 + 2 . 5 ∗ ( 7 9 / 2 1 ) N2 −−> 2CO2+H2O+ 2 . 5 ∗ ( 7 9 / 2 1 )
N2
8
9
// 26 kg C2H2 + 80 kg O2 + 2 6 3 . 3 N2
88 kg CO2 +
18 kg H2O + 2 6 3 . 3 kg N2
10 // 1 kg C2H2 + 3 . 0 7 6 kg O2 + 1 0 . 1 2 kg N2
3.38
kg CO2 + 0 . 6 9 kg H2O + 1 0 . 1 2 kg N2
11
12
13
Amount = 3.076 + 10.12;
disp ( ” Hence amount o f t h e o r e t i c a l a i r r e q u i r e d f o r
c o m b u s t i o n o f 1 kg a c e t y l e n e =” )
14 disp ( Amount )
15 disp ( ” kg ” )
245
Scilab code Exa 11.14 14
1 clc
2 // C2H2 +2.5O2 + 2 . 5 ∗ ( 7 9 / 2 1 ) N2 −−> 2CO2+H2O+ 2 . 5 ∗ ( 7 9 / 2 1 )
N2
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// 26 kg C2H2 + 160 kg O2 + 5 2 6 . 6 kg N2
+ 18 kg H2O + 5 2 6 . 6 kg N2 + 80 kg O2
88 kg CO2
// 1 kg C2H2 + 6 . 1 5 kg O2 + 2 0 . 2 5 kg N2
3 . 3 8 kg
CO2 + 0 . 6 9 kg H2O + 2 0 . 2 5 kg N2 + 3 . 0 7 kg O2
m_CO2 =3.38; // kg
m_H2O =0.69; // kg
m_O2 =3.07; // kg
m_N2 =20.25; // kg
m_total = m_CO2 + m_H2O + m_O2 + m_N2 ;
CO2 = m_CO2 / m_total *100;
H2O = m_H2O / m_total *100;
O2 = m_O2 / m_total *100;
N2 = m_N2 / m_total *100;
disp ( ” Hence t h e g r a v i m e t r i c a n a l y s i s o f t h e c o m p l e t e
combustion i s : ”)
20 disp ( ”CO2=” )
21 disp ( CO2 )
22 disp ( ”%” )
23
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28
disp ( ”H2O=” )
disp ( H2O )
disp ( ”%” )
disp ( ”O2=” )
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disp ( O2 )
disp ( ”%” )
disp ( ”N2=” )
disp ( N2 )
disp ( ”%” )
Scilab code Exa 11.15 15
1 clc
2 AF_mole =(12.5+12.5*(79/21) ) /1;
3 AF_mass = AF_mole *28.97/(8*12+1*18) ;
4
5 disp ( ” A i r f u e l r a t i o =” )
6 disp ( AF_mass )
7 disp ( ” kg a i r / kg f u e l ” )
Scilab code Exa 11.16 16
1 clc
2 // C8H18 +1 2.5 ∗O2 + 1 2 . 5 ∗ ( 7 9 / 2 1 ) N2 −−> 8CO2+9H2O
+ 1 2 . 5 ∗ ( 7 9 / 2 1 ) ∗N2
3
4
// C8H18 + ( 2 ) ( 1 2 . 5 ) O2 + ( 2 ) ( 1 2 . 5 ) ∗ ( 7 9 / 2 1 ) N2−−>8
CO2 + 9H2O + ( 1 ) ( 1 2 . 5 ) O2 + ( 2 ) ( 1 2 . 5 ) ∗ ( 7 9 / 2 1 ) ∗
N2
5
6 m_fuel =1*(8*12+1*18) ;
7 m_air =2*12.5*(1+79/21) *28.97;
8
9 disp ( ” ( i ) Air − f u e l r a t i o =” )
10 AF = m_air / m_fuel ;
11 disp ( AF )
247
12
13 disp ( ” ( i i ) Dew p o i n t o f t h e p r o d u c t s ” )
14 n =8+9+12.5+2*12.5*(79/21) ;
15
16 x =9/ n ;
17 p =100* x ;
18
19 // Hence
20 t_dp =39.7; // 0C
21
22 disp ( ” t d p=” )
23 disp ( t_dp )
24 disp ( ” C ” )
Scilab code Exa 11.17 17
1 clc
2 // C2H6 + 3 . 5 O2
2CO2 + 3H2O
3 // C2H6 + ( 0 . 9 ) ∗ ( 3 . 5 ) O2 + ( 0 . 9 ) ∗ ( 3 . 5 ) ∗ ( 7 9 / 2 1 ) N 2 a
CO2 + b CO + 3H2O + ( 0 . 9 ) ∗ ( 3 . 5 ) ∗ ( 7 9 / 2 1 ) ∗N2
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//
//
//
//
//
a+b=2
2∗ a+b + 3 = 0 . 9 ∗ 3 . 5 ∗ 2
a =1.3
b =0.7
C2H6 + ( 0 . 9 ) ∗ ( 3 . 5 ) O2 + ( 0 . 9 ) ∗ ( 3 . 5 ) ∗ ( 7 9 / 2 1 ) ∗ N 2
1 . 3 CO2 + 0 . 7CO + 3H2O + ( 0 . 9 ) ∗ ( 3 . 5 ) ∗ ( 7 9 / 2 1 ) N2
n =1.3+0.7+0.9*3.5*(79/21) ;
CO2 =1.3/ n *100;
CO =0.7/ n *100;
N2 =11.85/ n *100;
disp ( ” V o l u m e t r i c a n a l y s i s o f d r y p r o d u c t s o f
248
combustion i s as f o l l o w s ”)
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disp ( ”CO2 =” )
disp ( CO2 )
disp ( ”%” )
disp ( ”CO =” )
disp ( CO )
disp ( ”%” )
disp ( ”N2 =” )
disp ( N2 )
disp ( ”%” )
Scilab code Exa 11.18 18
1 clc
2 disp ( ” ( i ) Combustion e q u a t i o n ” )
3
4 // x CH4 + y O2 + z N2
1 0 . 0 CO2 + 0 . 5 3 CO +
2 . 3 7 O2 + a H2O + 8 7 . 1 N2
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16
z =87.1;
y = z *(79/21) ;
x =10+0.53;
a =2* x ;
// 1 0 . 5 3 CH4 + 2 3 . 1 6 O2 + 8 7 . 1 N2
1 0 . 0 CO2 + 0 . 5 3
CO + 2 . 3 7 O2 + 2 1 . 0 6 H2O + 8 7 . 1 N2
disp ( ”CH4 + 2 . 2 O2 + 8 . 2 7 N2
+ 2H2O + 0 . 2 2 5 O2 + 8 . 2 7 N2” )
disp ( ” ( i i ) Air − f u e l r a t i o ” )
249
0 . 9 5 CO2 + 0 . 0 5 CO
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AF_mole =2.2+8.27;
disp ( ” a i r − f u e l r a t i o on a mole b a s i s =” )
disp ( AF_mole )
disp ( ” m o l e s a i r / mole f u e l ” )
AF_mass = AF_mole *28.97/(12+1*4) ;
disp ( ” a i r − f u e l r a t i o on a mass b a s i s =” )
disp ( AF_mass )
disp ( ” a i r / kg f u e l ” )
// CH4 + 2O2 + 2 ∗ ( 7 9 / 2 1 ) N2
CO2 + 2H2O + ( 2 )
∗ ( 7 9 / 2 1 ) N2
AF_theor =(2+2*(79/21) ) *28.97/(12+1*4) ;
disp ( ” t h e o r e t i c a l a i r − f u e l r a t i o =” )
disp ( AF_theor )
disp ( ” kg a i r / kg f u e l ” )
disp ( ” ( i i i ) P e r c e n t t h e o r e t i c a l a i r =” )
%theo = AF_mass / AF_theor *100;
disp ( %theo )
disp ( ”%” )
Scilab code Exa 11.19 19
1 clc
2 disp ( ” ( i ) The s t o i c h i o m e t r i c A/F r a t i o ” )
3
4 // 1 kg o f c o a l c o n t a i n s 0 . 8 2 kg C and 0 . 1 0 kg H2 .
5 // L e t t h e o x y g e n r e q u i r e d f o r c o m p l e t e c o m b u s t i o n =
x moles
6 // t h e n i t r o g e n s u p p l i e d w i t h t h e o x y g e n = x
∗79/21=3.76∗ x
7 // 0 . 8 2 / 1 2 ∗C+ 0 . 1 0 / 2 ∗ H2 + x CO2 + 3 . 7 6 x N2
+ b H2O + 3 . 7 6 x N2
8 a =0.82/12; // Carbon b a l a n c e
250
a CO2
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b =0.10/2; // Hydrogen b a l a n c e
x =(2* a + b ) /2; // Oxygen b a l a n c e
Stoichiometric_AF_ratio =2.976/0.233;
disp ( ” S t o i c h i o m e t r i c AF r a t i o =” )
disp ( Stoichiometric_AF_ratio )
n = a + b +3.76* x ;
CO2 =0.068/ n *100;
H2 =0.05/ n *100;
N2 =3.76*0.093/ n *100;
disp ( ” t h e a n a l y s i s o f t h e p r o d u c t s i s ” )
disp ( ”CO2 =” )
disp ( CO2 )
disp ( ”%” )
disp ( ”H2 =” )
disp ( H2 )
disp ( ”%” )
disp ( ”N2 =” )
disp ( N2 )
disp ( ”%” )
Scilab code Exa 11.20 20
1 clc
2
3 // C + O2
CO2
4 // 2H2 + O2
2H2O
5 // S + O2
SO2
6
7 O2_req =2.636; // kg
251
8
9 AF = O2_req /0.233;
10 disp ( ” The s t o i c h i o m e t r i c A/F r a t i o =” )
11 disp ( AF )
12
13 disp ( ” ( i ) A c t u a l A/F r a t i o =” )
14 AF_act = AF +0.3* AF ;
15 disp ( AF_act )
16
17 disp ( ” ( i i ) Wet and d r y a n a l y s e s o f p r o d u c t s o f
c o m b u s t i o n by volume ” )
18
19
// As p e r a c t u a l A/F r a t i o , N2 s u p p l i e d = 0 . 7 6 7 ∗
1 4 . 7 = 1 1 . 2 7 kg
20 // A l s o O2 s u p p l i e d = 0 . 2 3 3 ∗ 1 4 . 7 = 3 . 4 2 kg
21
22 // I n t h e p r o d u c t s then , we have
23 // N2 = 1 1 . 2 7 + 0 . 0 1 = 1 1 . 2 8 kg
24 // e x c e s s O2 = 3 . 4 2
2 . 6 3 6 = 0 . 7 8 kg
25
26 n_wet =0.5208;
27 n_dry =0.5008;
28
29 disp ( ” A n a l y s i s o f wet p r o d u c t s i s a s f o l l o w s
30
31 disp ( ”CO2 =” )
32 CO2 =0.0734/ n_wet *100;
33 disp ( CO2 )
34 disp ( ”%” )
35
36 disp ( ”H2O =” )
37 H2O =0.0200/ n_wet *100;
38 disp ( H2O )
39 disp ( ”%” )
40
41 disp ( ”SO2 =” )
42 SO2 =0.0002/ n_wet *100;
43 disp ( SO2 )
252
: ”)
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disp ( ”%” )
disp ( ”O2 =” )
O2 =0.0244/ n_wet *100;
disp ( O2 )
disp ( ”%” )
disp ( ”N2 =” )
N2 =0.4028/ n_wet *100;
disp ( N2 )
disp ( ”%” )
disp ( ” A n a l y s i s o f d r y p r o d u c t s i s a s f o l l o w s : ” )
disp ( ”CO2 =” )
CO2 =0.0734/ n_dry *100;
disp ( CO2 )
disp ( ”%” )
disp ( ”SO2 =” )
SO2 =0.0002/ n_dry *100;
disp ( SO2 )
disp ( ”%” )
disp ( ”O2 =” )
O2 =0.0244/ n_dry *100;
disp ( O2 )
disp ( ”%” )
disp ( ”N2 =” )
N2 =0.4028/ n_dry *100;
disp ( N2 )
disp ( ”%” )
Scilab code Exa 11.21 21
253
1 clc
2
3 // 2H2 + O2
2H2O
4 // 2CO + O2
2CO2
5 // CH4 + 2O2
CO2 + 2H2O
6 // C4H8 + 6O2
4CO2 + 4H2O
7
8 n_O2 =0.853; // t o t a l m o l e s o f O2
9
10 disp ( ” ( i ) S t o i c h i o m e t r i c A/F r a t i o =” )
11 AF = n_O2 /0.21;
12 disp ( AF )
13
14 disp ( ” ( i i ) Wet and d r y a n a l y s e s o f t h e p r o d u c t s o f
c o m b u s t i o n i f t h e a c t u a l m i x t u r e i s 30% weak : ” )
15 AF_act = AF +0.3* AF ;
16 n_N2 =0.79* AF_act ;
17 O2_excess =0.21* AF_act - n_O2 ;
18
19
20
21
22
n_wet =5.899;
n_dry =4.915;
disp ( ” A n a l y s i s by volume o f wet p r o d u c t s i s a s
f o l l o w s : ”)
23
24 disp ( ”CO2 =” )
25 CO2 =0.490/ n_wet *100;
26 disp ( CO2 )
27 disp ( ”%” )
28
29 disp ( ”H2O =” )
30 H2O =0.984/ n_wet *100;
31 disp ( H2O )
32 disp ( ”%” )
33
34 disp ( ”O2 =” )
35 O2 = O2_excess / n_wet *100;
36 disp ( O2 )
254
37 disp ( ”%” )
38
39 disp ( ”N2 =” )
40 N2 = n_N2 / n_wet *100;
41 disp ( N2 )
42 disp ( ”%” )
43
44 disp ( ” A n a l y s i s by volume o f d r y p r o d u c t s
i s as
f o l l o w s : ”)
45
46 disp ( ”CO2 =” )
47 CO2 =0.490/ n_dry *100;
48 disp ( CO2 )
49 disp ( ”%” )
50
51 disp ( ”O2 =” )
52 O2 = O2_excess / n_dry *100;
53 disp ( O2 )
54 disp ( ”%” )
55
56 disp ( ”N2 =” )
57 N2 = n_N2 / n_dry *100;
58 disp ( N2 )
59 disp ( ”%” )
Scilab code Exa 11.22 22
1 clc
2
3 // C2H6O + 3O2 + 3 ∗ 7 9 / 2 1 N2
3 ∗ 7 9 / 2 1 N2
4
5 O2_req =3*32/46;
6
7 AF = O2_req /0.233;
255
2CO2 + 3H2O +
8 disp ( ” S t o i c h i o m e t r i c A/F r a t i o =” )
9 disp ( AF )
10
11 mix =0.8; // m i x t u r e s t r e n g t h
12
13 AF_actual = AF / mix ;
14 disp ( ” A c t u a l A/F r a t i o =” )
15 disp ( AF_actual )
16
17 // C2H6O + 1 . 2 5 ∗ ( 3 O2 + 3 ∗ 7 9 / 2 1 N2 )
+ 0 . 2 5 ∗ 3 O2 + 1 . 2 5 ∗ 3 ∗ 7 9 / 2 1 N2
18
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25
26
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42
43
44
n =2+3+0.75+14.1;
disp ( ” Hence wet a n a l y s i s i s ” )
disp ( ”CO2 =” )
CO2 =2/ n *100;
disp ( CO2 )
disp ( ”%” )
disp ( ”H2O =” )
H2O =3/ n *100;
disp ( H2O )
disp ( ”%” )
disp ( ”O2 =” )
O2 =0.75/ n *100;
disp ( O2 )
disp ( ”%” )
disp ( ”N2 =” )
N2 =14.1/ n *100;
disp ( N2 )
disp ( ”%” )
nd =2+0.75+14.1; // t o t a l d r y m o l e s
256
2CO2 + 3H2O
45
46
47
48
49
50
51
52
53
54
55
56
57
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60
61
62
63
64
65
disp ( ” Hence d r y a n a l y s i s i s : ” )
disp ( ”CO2 =” )
CO2 =2/ nd *100;
disp ( CO2 )
disp ( ”%” )
disp ( ”O2 =” )
O2 =0.75/ nd *100;
disp ( O2 )
disp ( ”%” )
disp ( ”N2 =” )
N2 =14.1/ nd *100;
disp ( N2 )
disp ( ”%” )
mix =1.3;
AF_act = AF / mix ;
disp ( ” A c t u a l A/F r a t i o =” )
disp ( AF_act )
Scilab code Exa 11.23 23
1 clc
2 // C2H6O + 3O2 + 3 ∗ 7 9 / 2 1 N2
2CO2 + 3H2O +
3 ∗ 7 9 / 2 1 N2
3 R0 =8.314*10^3; // kJ / kg K
4 m =46; // kg
5
6 disp ( ” ( i ) Volume o f
7
8 n =1+3+3*79/21;
9 T =323; //K
10 p =1.013*10^5; // Pa
r e a c t a n t s p e r kg o f f u e l ” )
257
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
V = n * R0 * T / p ;
disp ( ” Vr=” )
Vr = V / m ;
disp ( Vr )
disp ( ”mˆ3 ” )
disp ( ” ( i i ) Volume o f p r o d u c t s p e r kg o f f u e l ” )
n =2+3+3*79/21;
T =403; //K
p =1*10^5; // Pa
V = n * R0 * T / p ;
Vp = V / m ;
disp ( ”Vp=” )
disp ( Vp )
disp ( ”mˆ3 ” )
Scilab code Exa 11.24 24
1 clc
2
3 // 0 . 5 0 6 H2 + 0 . 1CO + 0 . 2 6 CH4 + 0 . 0 4 C4H8 + 0 . 0 0 4 O2 +
0 . 0 3 CO2 + 0 . 0 6 N2 + 0 . 2 1
7O2 + 0 . 7 9
a CO2 + b H2O + c O2 + d N2
4
5
6
7
8
9
10
a =0.1*0.26+4*0.04+0.03;
b =(2*0.506+4*0.26+8*0.04) /2;
c =(0.1+2*0.004+2*0.03+0.21*7*2 -2* a - b ) /2;
d =(2*0.06+2*0.79*7) /2;
n =0.55+0.411+5.59;
258
7N2
11
12 disp ( ” a n a l y s i s by volume i s ” )
13 disp ( ”CO2=” )
14 CO2 =0.55/ n *100;
15 disp ( CO2 )
16 disp ( ”%” )
17
18 disp ( ”O2=” )
19 O2 =0.411/ n *100;
20 disp ( O2 )
21 disp ( ”%” )
22
23 disp ( ”N2 =” )
24 N2 =5.59/ n *100;
25 disp ( N2 )
26 disp ( ”%” )
Scilab code Exa 11.25 25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
clc
// C aH bO cN dS e
a =60/12;
b =20;
c =5/16;
d =10/14;
e =5/32;
// C 5 H 20 O 0 . 3 1 2 5 N 0 . 7 1 4 3 S 0 . 1 5 6 2 + x O2 + x
∗ ( 7 9 / 2 1 ) N2
p CO2 + q H2O + r SO2 + s N2
p =5;
q =20/2;
r =0.1562;
x =(2* p + q +2* r -0.3125) /2;
s =(0.7143+2* x *79/21) /2;
259
16
17 air =(9.92*32+ x *79/21*28) /100;
18 disp ( ” S t o i c h i o m e t r i c a i r r e q u i r e d =” )
19 disp ( air )
20 disp ( ” kg / kg o f f u e l ” )
Scilab code Exa 11.26 26
1
2
3
4
5
6
7
8
9
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11
12
13
14
15
16
17
18
19
20
21
22
23
24
clc
disp ( ” ( i ) S t o i c h i o m e t r i c a i r f u e l r a t i o ” )
// C aH bO cN d
a =84/12;
b =10;
c =3.5/16;
d =1.5/14;
// C7 H10 O0 . 2 1 8 N0 . 1 0 7 + x O2 + x ∗ ( 7 9 / 2 1 ) N2
CO2 + q H2O + r N2
p
p =7;
q =10/2;
x =(2* p +q - c ) /2;
r =( d +2* x *(79/21) ) /2;
AF =( x *32+ x *79/21*28) /100;
disp ( ” S t o i c h i o m e t r i c A/F r a t i o =” )
disp ( AF )
disp ( ” ( i i ) P e r c e n t a g e c o m p o s i t i o n o f d r y f l u e g a s e s
by volume w i t h 20 p e r c e n t e x c e s s a i r : ” )
// C7H10O0 . 2 1 8 N0 . 1 0 7 + ( 1 . 2 ) ( 9 . 3 9 ) O2 + ( 1 . 2 ) ( 9 . 3 9 )
∗ ( 7 9 / 2 1 ) N2
7CO2 + 5H2O + ( 0 . 2 ) ( 9 . 3 9 ) O2 +
260
( 1 . 2 ) ( 3 5 . 4 ) N2
25
26 n =7+0.2*9.39+1.2*35.4;
27
28 disp ( ” P e r c e n t a g e c o m p o s i t i o n o f d r y f l u e
g a s e s by
volume i s a s f o l l o w s : ” )
disp ( ”CO2 =” )
CO2 =7/ n *100;
disp ( CO2 )
disp ( ”%” )
29
30
31
32
33
34 disp ( ”O2 =” )
35 O2 =1.878/ n *100;
36 disp ( O2 )
37 disp ( ”%” )
38
39 disp ( ”N2 =” )
40 N2 =42.48/ n *100;
41 disp ( N2 )
42 disp ( ”%” )
Scilab code Exa 11.27 27
1 clc
2 // a C + b H + c O2 + ( 7 9 / 2 1 ) ∗ c N2 = 8CO2 + 0 . 5CO +
6 . 3 O2 + x H2O + 8 5 . 2 N2
3
4
5
6
7
8
9
10
11
a =8+0.5;
c =85.2/(79/21) ;
x =2*( c -8 -0.5/2 -6.3) ;
b =2* x ;
disp ( ” ( i ) Air − f u e l r a t i o =” )
AF =( c *32+(79/21) * c *28) /( a *12+ b *1) ;
disp ( AF )
261
12
13
14
15
16
17
18
19
20
21
disp ( ” kg o f a i r / kg o f f u e l ” )
disp ( ” ( i i ) Per c e n t t h e o r e t i c a l a i r r e q u i r e d f o r
combustion ”)
mf_C =12* a /(12* a + b ) ;
mf_H2 = b *1/(12* a + b ) ;
air = mf_C *8/3*100/23.3 + mf_H2 *8*100/23.3; // a i r
r e q u i r e d f o r complete combustion
percent = AF / air *100;
disp ( ” Per c e n t t h e o r e t i c a l a i r r e q u i r e d f o r
c o m b u s t i o n =” )
disp ( percent )
disp ( ”%” )
Scilab code Exa 11.28 28
1 clc
2 disp ( ” ( i ) By a c a r b o n b a l a n c e ” )
3
4 // a C8H18 + 7 8 . 1 N2 + 7 8 . 1 ∗ ( 2 1 / 7 9 ) O2
8 . 9 CO2 +
8 . 2CO + 4 . 3 H2 + 0 . 5 CH4 + 7 8 . 1 N2 + x H2O
5 a =(8.9+8.2+0.5) /8;
6
7 AF1 =(78.1*28+78.1*21/79*32) / a /(8*12+1*18) ;
8 disp ( ” A i r f u e l r a t i o =” )
9 disp ( AF1 )
10
11
12 disp ( ” ( i i ) By a hydrogen −o x y g e n b a l a n c e ” )
13
14 // a C8H18 + b O2 + b ∗ ( 7 9 / 2 1 ) N2
8 . 9 CO2 + 8 . 2CO +
4 . 3 H2 + 0 . 5 CH4 + b ∗ ( 7 9 / 2 1 ) N2 + x ∗H2O
15
16 a =(8.9+8.2+0.5) /8;
17 x =(18* a -4.3*2 -4*0.5) /2;
262
18 b =(8.9*2+8.2+ x ) /2;
19
20 AF2 =( b *32+ b *(79/21) *28) / a /(8*12+1*18) ;
21 disp ( ” A i r f u e l r a t i o =” )
22 disp ( AF2 )
Scilab code Exa 11.29 29
1 clc
2 // X( 0 . 8 8 / 1 2 C + 0 . 1 2 / 2 H2 ) + Y O2 + 7 9 / 2 1 ∗Y N2
0 . 1 2 CO2 + a O2 + ( 0 . 8 8
3
4
5
6
7
8
9
10
11
12
a ) N2 + b H2O
X =0.12/(0.88/12) ;
b =0.06* X ;
a =0.0513;
Y =0.2203;
Air_supplied =0.2203*32/0.233;
AF = Air_supplied / X ;
disp ( ”A/F r a t i o =” )
disp ( AF )
Scilab code Exa 11.30 30
1 clc
2 // X∗ ( x /12 C + y /2 H2 ) + Y O2 + 7 9 / 2 1 ∗Y/N2
0.15
CO2 + 0 . 0 3CO + 0 . 0 3 CH4 + 0 . 0 1 H2 + 0 . 0 2 O2 + a H2O
+ 0 . 7 6 N2
3
4
5
6
7
Y =0.76/(79/21) ;
a =2*( Y -0.15 -0.03/2 -0.02) ;
Xx =12*(0.15+0.03+0.03) ;
Xy =2*(2*0.03+0.01+ a ) ;
263
8
9
10
11
ratio = Xx / Xy ;
disp ( ” R a t i o o f C t o H2 i n f u e l =” )
disp ( ratio )
Scilab code Exa 11.31 31
1 clc
2 h_fg0 =2441.8; // kJ / kg
3 m =3*18;
4 dH0_liq = -3301000; // kJ / mole
5
6 dH0_vap = dH0_liq + m * h_fg0 ;
7 disp ( ” dH0 vapour =” )
8 disp ( dH0_vap )
9 disp ( ” kJ / mole ” )
Scilab code Exa 11.32 32
1
2
3
4
5
6
7
8
9
10
11
12
13
clc
// C6H6 + 7 . 5 O2
dH0 = -3169100; // kJ
n_R =1+7.5;
n_P =6+3;
R0 =8.314;
T0 =298; //K
6CO2 + 3H2O ( v a p o u r )
dU0 =( dH0 -( n_P - n_R ) * R0 * T0 ) /(6*12+1*6) ;
disp ( ”dU0 =” )
disp ( dU0 )
disp ( ” kJ / kg ” )
264
Scilab code Exa 11.33 33
1 clc
2 // CO+1/2 O2
CO2
3 H_R0 =1*9705+1/2*9696; // kJ
4 H_RT =1*94080+1/2*99790; // kJ
5 H_P0 =1*10760; // kJ
6 H_PT =1*149100; // kJ
7
8 dH_T = -(285200+(143975 -14553) -(149100 -10760) ) ;
9 disp ( ”dH T =” )
10 disp ( dH_T )
11 disp ( ” kJ / mole ” )
Scilab code Exa 11.34 34
1 clc
2 disp ( ” ( i ) H i g h e r h e a t i n g v a l u e a t c o n s t a n t
3
4
5
6
7
8
9
10
11
12
13
14
15
pressure ”
)
m =4*18;
h_fg =2443; // kJ / kg
LHVp =2044009; // kJ / kg
R0 =8.3143; // kJ / kg K
T =298; //K
HHVp = LHVp + m * h_fg ;
disp ( ”HHVp =” )
disp ( HHVp )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) H i g h e r h e a t i n g v a l u e a t c o n s t a n t volume ” )
dn =3 -(1+5) ;
265
16
17
18
19
20
HHVv = HHVp + dn * R0 * T ;
disp ( ”HHVv =” )
disp ( HHVv )
disp ( ” kJ / kg ” )
Scilab code Exa 11.35 35
1 clc
2 HHV =5494977; // kJ / kg
3 m =9*18;
4 u_fg =2305; // kJ / kg
5 LHVv = HHV - m * u_fg ;
6 disp ( ”LHVv =” )
7 disp ( LHVv )
8 disp ( ” kJ / kg ” )
Scilab code Exa 11.36 36
1 clc
2 disp ( ” ( i ) A i r and b e n z e n e v a p o u r ” )
3
4 // C6H6 ( g ) + 7 . 5 O2 ( g ) + 7 . 5 ∗ ( 7 9 / 2 1 ) N2 ( g ) = 6CO2( g ) +
3H2O( g ) + 7 . 5 ∗ ( 7 9 / 2 1 ) ∗N2 ( g )
5
6 LHVp =3169500; // kJ / mole
7
8 LHVv = LHVp /((12*6+6*1) +(7.5*32) +7.5*(79/21) *28)
9 disp ( ”LHVv p e r kg o f m i x t u r e =” )
10 disp ( LHVv )
11 disp ( ” kJ / kg ” )
12
13 m =54; // kg / kg mole o f f u e l
266
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15
16
17
18
19
20
21
22
23
24
h_fg =2442; // kJ / kg
HHVp =( LHVp + m * h_fg ) /(78+240+790) ;
disp ( ”HHVp p e r kg o f m i x t u r e =” )
disp ( HHVp )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) A i r and o c t a n e v a p o u r ” )
LHVp =5116200; // kJ / mole o f C8H18
// C8H18 ( g ) + 1 2 . 5 O2 ( g )
1 2 . 5 ∗ ( 7 9 / 2 1 ) N2 ( g )
8CO2( g ) + 9H2O( g ) +
25
26 LHVp1 = LHVp /((12*8+18*1) +12.5*32+12.5*79/21*28) ;
27 disp ( ”LHVp p e r kg o f m i x t u r e =” )
28 disp ( LHVp1 )
29 disp ( ” kJ / kg ” )
30
31 m =9*18;
32 HHVp = LHVp + m * h_fg ;
33 HHVp1 = HHVp /(114+400+1317) ;
34 disp ( ”HHVp p e r kg o f m i x t u r e =” )
35 disp ( HHVp1 )
36 disp ( ” kJ / kg ” )
Scilab code Exa 11.37 37
1 clc
2 m_CO2 =44/12*0.88; // kg
3 m_H2O =18/2*0.12; // kg
4 u_fg =2304; // kJ / kg
5 h_fg =2442; // kJ / kg
6 HHVv =45670; // kJ / kg
7 R0 =8.3143; // kJ / kg K
8 T =298; //K
267
9 disp ( ” ( i ) (LHV) v =” )
10 LHVv = HHVv - m_H2O * u_fg ;
11 disp ( LHVv )
12 disp ( ” kJ / kg ” )
13
14 disp ( ” ( i i ) (HHV) p , (LHV) p ” )
15
16 // 1 mole f u e l +x /32 O2−−>3.23/44 CO2 + 1 . 0 8 / 1 8 H2O
17
18 x =32*( m_CO2 /44+ m_H2O /18/2) ;
19
20 // 1 kg f u e l + 3 . 3 1 kg O2 = 3 . 2 3 CO2 + 1 . 0 8 H2O
21
22 dn =( m_CO2 /44 - x /32) ;
23
24 HHVp = HHVv - dn * R0 * T ;
25 disp ( ”HHVp =” )
26 disp ( HHVp )
27 disp ( ” kJ / kg ” )
28
29 LHVp = HHVp - m_H2O * h_fg ;
30 disp ( ”LHVp =” )
31 disp ( LHVp )
32 disp ( ” kJ / kg ” )
268
Chapter 12
Vapour Power Cycles
Scilab code Exa 12.1 1
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4
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6
7
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11
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16
17
18
19
20
21
clc
p1 =60; // b a r ; I n l e t t o t u r b i n e
p2 =0.1; // b a r ; E x i t from t u r b i n e
p3 =0.09; // b a r ; E x i t from c o n d e n s e r
p4 =70; // b a r ; E x i t from pump
p5 =65; // b a r ; E x i t from b o i l e r
t1 =380; // 0C
t5 =400; // 0C
x2 =0.9; // Q u a l i t y a t e x i t from t u r b i n e
C =200; //m/ s ; V e l o c i t y a t t h e e x i t from t u r b i n e
disp ( ” ( i ) Power o u t p u t o f t h e t u r b i n e ” )
// At 60 b a r 380 0C , From steam t a b l e s
h1 =3123.5; // kJ / kg ; By i n t e r p o l a t i o n
h_f2 =191.8; // kJ / kg
h_fg2 =2392.8; // kJ / kg
269
22
23
24
25
26
27
28
29
30
31
32
33
x2 =0.9;
h2 = h_f2 + x2 * h_fg2 ;
m_s =10000/3600; // Rate o f stem f l o w i n kg / s
P = m_s *( h1 - h2 ) ;
disp ( ” Power o u t p u t o f t h e t u r b i n e =” )
disp ( P )
disp ( ”kW” )
disp ( ” ( i i ) Heat t r a n s f e r p e r h o u r i n t h e b o i l e r and
condenser ”)
34
35 h_f4 =1267.4; // kJ / kg
36 h_a =3167.6; // kJ / kg
37
38 Q1 =10000*( h_a - h_f4 ) ;
39 disp ( ” Heat t r a n s f e r p e r h o u r i n t h e b o i l e r =” )
40 disp ( Q1 )
41 disp ( ” kJ / h ” )
42
43 h_f3 =183.3; // kJ / kg
44 Q2 =10000*( h2 - h_f3 ) ;
45 disp ( ” Heat t r a n s f e r p e r h o u r i n t h e c o n d e n s e r =” )
46 disp ( Q2 )
47 disp ( ” kJ / h ” )
48
49
50 disp ( ” ( i i i ) Mass o f c o o l i n g w a t e r c i r c u l a t e d p e r
hour i n the c o n d e n s e r ”)
51 c_pw =4.18;
52 t2 =30;
53 t1 =20;
54
55 m_w = Q2 / c_pw /( t2 - t1 ) ;
56 disp ( ”m w=” )
57 disp ( m_w )
270
58
59
60
61
disp ( ” kg /h ” )
disp ( ” T h i s i s t h e e x a c t a n s w e r . ” )
disp ( ” ( i v ) D i a m e t e r o f t h e p i p e c o n n e c t i n g t u r b i n e
with condenser ”)
62
63 v_g2 =14.67; //mˆ3/ kg
64
65 d = sqrt ( m_s * x2 * v_g2 *4/ %pi / C ) *1000;
66 disp ( ” D i a m e t e r =” )
67 disp ( d )
68 disp ( ”mm” )
Scilab code Exa 12.2 2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
clc
p1 =15; // b a r
x1 =1;
p2 =0.4; // b a r
// At 15 b a r
t_s1 =198.3; // 0C
h_g1 =2789.9; // kJ / kg
s_g1 =6.4406; // kJ / kg K
// At 0 . . 4 b a r
t_s2 =198.3; // 0C
h_f2 =317.7; // kJ / kg
h_fg2 =2319.2; // kJ / kg
s_f2 =1.0261; // kJ / kg K
s_fg2 =6.6448; // kJ / kg K
T1 =471.3; //K
T2 =348.9; //K
n_carnot =( T1 - T2 ) / T1 ;
271
21 disp ( ” C a r n o t e f f i c i e n c y =” )
22 disp ( n_carnot )
23
24
25 x2 =( s_g1 - s_f2 ) / s_fg2 ;
26 h2 = h_f2 + x2 * h_fg2 ;
27
28 n_rankine =( h_g1 - h2 ) /( h_g1 - h_f2 ) ;
29 disp ( ” Rankine e f f i c i e n c y =” )
30 disp ( n_rankine )
Scilab code Exa 12.3 3
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p1 =20; // b a r
p2 =0.08; // b a r
// At 20 bar , 360 0C
h1 =3159.3; // kJ / kg
s1 =6.9917; // kJ / kg K
// At 0 . 0 8 b a r
h_f2 =173.88; // kJ / kg
s_f2 =0.5926; // kJ / kg K
h_fg2 =2403.1; // kJ / kg
s_g =8.2287; // kJ / kg K
v_f =0.001008; //mˆ3/ kg
s_fg =7.6361; // kJ / kg K
x2 =( s1 - s_f2 ) / s_fg ;
h2 = h_f2 + x2 * h_fg2 ;
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23 W_pump = v_f *( p1 - p2 ) *100; // kJ / kg
24 W_turbine = h1 - h2 ;
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26 W_net = h1 - h2 ;
27 disp ( ” Net work done=” )
28 disp ( W_net )
29 disp ( ” kJ / kg ” )
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31 h_f4 = W_pump + h_f2 ;
32 Q1 = h1 - h_f4 ;
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34 n_cycle = W_net / Q1 ;
35 disp ( ” C y c l e e f f i c i e n c y =” )
36 disp ( n_cycle )
Scilab code Exa 12.4 4
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n_turbine =0.9;
n_pump =0.8;
p1 =80; // b a r
p2 =0.1; // b a r
v_f =0.0010103; //mˆ3
// At 80 bar , 600 0C
h1 =3642; // kJ / kg
s1 =7.0206; // kJ / kg K
s_f2 =0.6488; // kJ / kg K
s_fg2 =7.5006; // kJ / kg K
h_f2 =191.9; // kJ / kg
h_fg2 =2392.3; // kJ / kg
x2 =( s1 - s_f2 ) / s_fg2 ;
h2 = h_f2 + x2 * h_fg2 ;
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20 W_turbine = n_turbine *( h1 - h2 ) ;
21 W_pump = v_f *( p1 - p2 ) *10^2;
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23 W_actual = W_pump / n_pump ; // A c t u a l pump work
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25 W_net = W_turbine - W_actual ;
26 disp ( ” S p e c i f i c work =” )
27 disp ( W_net )
28 disp ( ” kJ / kg ” )
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30 h_f4 = h_f2 + W_actual ;
31 Q1 = h1 - h_f4 ;
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33 n_thermal = W_net / Q1 ; // Thermal e f f i c i e n c y
34 disp ( ” Thermal e f f i c i e n c y =” )
35 disp ( n_thermal )
Scilab code Exa 12.5 5
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p1 =28; // b a r
p2 =0.06; // b a r
// At 28 b a r
h1 =2802; // kJ / kg
s1 =6.2104; // kJ / kg K
// At 0 . 0 6 b a r
h_f2 =151.5; // kJ / kg
h_f3 = h_f2 ;
h_fg2 =2415.9; // kJ / kg
s_f2 =0.521; // kJ / kg K
s_fg2 =7.809; // kJ / kg K
v_f =0.001; //mˆ3/ kg
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x2 =( s1 - s_f2 ) / s_fg2 ;
h2 = h_f2 + x2 * h_fg2 ;
W_turbine = h1 - h2 ;
W_pump = v_f *( p1 - p2 ) *100; // kJ / kg
h_f4 = h_f2 + W_pump ;
Q1 = h1 - h_f4 ;
W_net = W_turbine - W_pump ;
n_cycle = W_net / Q1 ;
disp ( ” c y c l i c e f f i c i e n c y =” )
disp ( n_cycle )
ratio = W_net / W_turbine ; // Work r a t i o
disp ( ”Work r a t i o =” )
disp ( ratio )
S =3600/ W_net ; // S p e c i f i c steam c o m b u s t i o n
disp ( ” S p e c i f i c steam c o m b u s t i o n=” )
disp ( S )
disp ( ” kg /kWh” )
Scilab code Exa 12.6 6
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p1 =35; // b a r
x =1;
p2 =0.2; // b a r
m =9.5; // kg / s
// At 35 b a r
h1 =2802; // kJ / kg
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h_g1 = h1 ;
s_g1 =6.1228; // kJ / kg K
// At0 . 2 6 b a r
h_f =251.5; // kJ / kg
h_fg =2358.4; // kJ / kg
v_f =0.001017; //mˆ3/ kg
s_f =0.8321; // kJ / kg
s_fg =7.0773; // kJ / kg K
disp ( ” ( i ) The pump work ” )
W_pump = v_f *( p1 - p2 ) *100; // kJ / kg
P = m * W_pump ; // power r e q u i r e d
disp ( ” Power r e q u i r e d t o d r i v e t h e pump” )
disp ( P )
disp ( ”kW” )
disp ( ” ( i i ) The t u r b i n e work ” )
x2 =( s_g1 - s_f ) / s_fg ;
h2 = h_f + x2 * h_fg ;
W_turbine = m *( h1 - h2 ) ;
disp ( ” T u r b i n e work=” )
disp ( W_turbine )
disp ( ”kW” )
disp ( ” ( i i i ) The Rankine e f f i c i e n c y ” )
n_rankine =( h1 - h2 ) /( h1 - h_f ) ;
disp ( ” r a n k i n e e f f i c i e n c y =” )
disp ( n_rankine )
disp ( ” ( i v ) The c o n d e n s e r h e a t f l o w : ” )
Q = m *( h2 - h_f ) ;
disp ( ” The c o n d e n s e r h e a t f l o w=” )
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disp ( Q )
disp ( ”kW” )
disp ( ” ( v ) The d r y n e s s a t t h e end o f e x p a n s i o n=” )
disp ( x2 )
Scilab code Exa 12.7 7
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dh =840; // kJ / kg ; A d i a b a t i c e n t h a l p y d r o p
h1 =2940; // / kJ / kg ;
p2 =0.1; // b a r
h_f2 =191.8; // kJ / kg
n_rankine =( dh ) /( h1 - h_f2 ) *100;
disp ( ” r a n k i n e e f f i c i e n c y =” )
disp ( n_rankine )
S =3600/ dh ; // S p e c i f i c steam c o m b u s t i o n
disp ( ” S p e c i f i c steam c o m b u s t i o n=” )
disp ( S )
disp ( ” kg /kWh” )
Scilab code Exa 12.8 8
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IP =35; // Power d e v e l o p e d by t h e e n g i n e i n kW
S =284; // Steam c o m b u s t i o n i n kg / h
p2 =0.14; // C o n d e n s e r p r e s s u r e i n b a r
p1 =15; // b a r
h1 =2923.3; // kJ / kg
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s1 =6.709; // kJ / kg K
h_f =220; // kJ / kg
h_fg =2376.6; // kJ / kg
s_f =0.737; // kJ / kg K
s_fg =7.296; // kJ / kg K
x2 =( s1 - s_f ) / s_fg ;
disp ( ” ( i ) F i n a l c o n d i t i o n o f steam =” )
disp ( x2 )
h2 = h_f + x2 * h_fg ;
disp ( ” ( i i ) Rankine e f f i c i e n c y =” )
n_rankine =( h1 - h2 ) /( h1 - h_f ) ;
disp ( n_rankine )
disp ( ” ( i i i ) R e l a t i v e e f f i c i e n c y ” )
n_thermal = IP /( S /3600) /( h1 - h_f ) ;
n_relative = n_thermal / n_rankine ;
disp ( ” r e l a t i v e e f f i c i e n c y =” )
disp ( n_relative )
Scilab code Exa 12.9 9
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P =5000; //kW
C =40000; // kJ / kg
n_rankine =0.5;
n_turbine =0.9;
n_heat_transfer =0.85;
n_combustion =0.98;
m_f = P / n_turbine /( C * n_heat_transfer * n_combustion *
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n_rankine ) ;
10 disp ( ” F u e l o i l c o m b u s t i o n=” )
11 disp ( m_f )
12 disp ( ” kg / s ” )
Scilab code Exa 12.10 10
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p2 =2; // b a r
p3 =1.1; // b a r
IP =1;
m =12.8/3600; // kg /kWs
n_mech =0.8; // M e c h a n i c a l e f f i c i e n c y
h1 =3037.6; // kJ / kg
v1 =0.169; //mˆ3/ kg
s1 =6.918; // kJ / kg K
t_s2 =120.2; // 0C
h_f2 =504.7; // kJ / kg
h_fg2 =2201.6; // kJ / kg
s_f2 =1.5301; // kJ / kg K
s_fg2 =5.5967; // kJ / kg K
v_f2 =0.00106; //mˆ3/ kg
v_g2 =0.885; //mˆ3/ kg
t_s3 =102.3; // 0C
h_f3 =428.8; // kJ / kg
h_fg3 =2250.8; // kJ / kg
s_f3 =1.333; // kJ / kg K
s_fg3 =5.9947; // kJ / kg K
v_f3 =0.001; //mˆ3/ kg
v_g3 =1.549; //mˆ3/ kg
x2 =( s1 - s_f2 ) / s_fg2 ;
h2 = h_f2 + x2 * h_fg2 ;
v2 = x2 * v_g2 +(1 - x2 ) * v_f2 ;
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29 disp ( ” ( i ) I d e a l work=” )
30 W =( h1 - h2 ) + ( p2 - p3 ) * v2 *100; // kJ / kg
31 disp ( W )
32 disp ( ” kJ / kg ” )
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35 disp ( ” ( i i ) Rankine e n g i n e e f f i c i e n c y =” )
36 n_rankine = W /( h1 - h_f3 ) ;
37 disp ( n_rankine )
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40 disp ( ” ( i i i ) I n d i c a t e d and b r a k e work p e r kg ” )
41 W_indicated = IP / m ;
42 disp ( ” I n d i c a t e d worK =” )
43 disp ( W_indicated )
44 disp ( ” kJ / kg ” )
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46 W_brake = n_mech * IP / m ;
47 disp ( ” Brake work =” )
48 disp ( W_brake )
49 disp ( ” kJ / kg ” )
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51 disp ( ” ( i v ) Brake t h e r m a l e f f i c i e n c y =” )
52 n_brake = W_brake /( h1 - h_f3 ) ;
53 disp ( n_brake )
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56 disp ( ” ( v ) R e l a t i v e e f f i c i e n c y : ” )
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58 n1 = W_indicated / W ; // on t h e b a s i s o f i n d i c a t e d work
59 disp ( ” R e l a t i v e e f f i c i e n c y on t h e b a s i s o f i n d i c a t e d
work=” )
60 disp ( n1 )
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62 n2 = W_brake / W ; // on t h e b a s i s o f b r a k e work
63 disp ( ” R e l a t i v e e f f i c i e n c y on t h e b a s i s o f b r a k e work
=” )
64 disp ( n2 )
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Scilab code Exa 12.11 11
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p2 =0.75; // b a r
p3 =0.3; // b a r
h1 =3263.9; // kJ / kg
v1 =0.307; //mˆ3/ kg
s1 =7.465; // kJ / kg K
T_s2 =369.7; //K
h_g2 =2670.9; // kJ / kg
s_g2 =7.3954; // kJ / kg K
v_g2 =1.869; //mˆ3/ kg
h_f3 =289.3; // kJ / kg
v_g3 =5.229; //mˆ3/ kg
cp =2.1;
disp ( ” ( i ) Q u a l i t y o f steam a t t h e end o f e x p a n s i o n ” )
T_sup2 = T_s2 *( %e ^(( s1 - s_g2 ) / cp ) ) ;
t_sup2 = T_sup2 -273;
disp ( ” t s u p 2=” )
disp ( t_sup2 )
disp ( ” C ” )
h2 = h_g2 + cp *( T_sup2 -366.5) ;
disp ( ” ( i i ) Q u a l i t y o f steam a t t h e end o f c o n s t a n t
volume o p e r a t i o n , x3 : ” )
v2 = v_g2 / T_s2 * T_sup2 ;
v3 = v2 ;
x3 = v3 / v_g3 ;
disp ( ” x3=” )
disp ( x3 )
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32 disp ( ” ( i i i ) Power d e v e l o p e d ” )
33 P =( h1 - h2 ) + ( p2 - p3 ) * v2 *100;
34 disp ( ”P=” )
35 disp ( P )
36 disp ( ”kW” )
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39 disp ( ” ( i v ) S p e c i f i c steam c o n s u m p t i o n =” )
40 ssc =3600/ P ;
41 disp ( ssc )
42 disp ( ” kg /kWh” )
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45 disp ( ” ( v ) M o d i f i e d Rankine c y c l e e f f i c i e n c y =” )
46 n_mR =(( h1 - h2 ) +( p2 - p3 ) * v2 *100) /( h1 - h_f3 ) ;
47 disp ( n_mR )
Scilab code Exa 12.12 12
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h1 =3100; // kJ / kg
h2 =2100; // kJ / kg
h3 =2500; // kJ / kg
h_f2 =570.9; // kJ / kg
h_f5 =125; // kJ / kg
h_f2 =570.9; // kJ / kg
a =11200; // Q u a n t i t y o f b l e d steam i n kg / h
m =( h_f2 - h_f5 ) /( h2 - h_f5 ) ;
S = a / m ; // Steam s u p p l i e d t o t h e t u r b i n e p e r h o u r
W_net =( h1 - h3 ) + (1 - m ) *( h3 - h2 ) ;
P = W_net * S /3600; // Power d e v e l o p e d by t h e t u r b i n e
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disp ( ” Power d e v e l o p e d by t h e t u r b i n e=” )
disp ( P )
disp ( ”kW” )
Scilab code Exa 12.13 13
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// At 30 bar , 400 0C
h1 =3230.9; // kJ / kg
s1 =6.921; // kJ / kg
s2 = s1 ;
s3 = s1 ;
// At 5 b a r
s_f1 =1.8604;
s_g1 =6.8192; // kJ / kg K
h_f1 =640.1; // kJ / kg
t2 =172 // 0C
h2 =2796; // kJ / kg
// At 0 . 1 b a r
s_f3 =0.649; // kJ / kg K
s_fg3 =7.501; // kJ / kg K
h_f3 =191.8; // kJ / kg
h_fg3 =2392.8; // kJ / kg
x3 =( s2 - s_f3 ) / s_fg3 ;
h3 = h_f3 + x3 * h_fg3 ;
h_f4 =191.8; // kJ / kg
h_f5 = h_f4 ;
h_f6 =640.1; // kJ / kg
h_f7 = h_f6 ;
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s7 =1.8604; // kJ / kg K
s4 =0.649; // kJ / kg K
m =( h_f6 - h_f5 ) /( h2 - h_f5 ) ;
W_T =( h1 - h2 ) + (1 - m ) *( h2 - h3 ) ;
Q1 = h1 - h_f6 ;
disp ( ” ( i ) E f f i c i e n c y o f c y c l e =” )
n_cycle = W_T / Q1 ;
disp ( n_cycle )
SR =3600/ W_T ; // Steam r a t e
disp ( ” Steam r a t e =” )
disp ( SR )
disp ( ” kg /kWh” )
T_m1 =( h1 - h_f7 ) /( s1 - s7 ) ;
T_m1r =( h1 - h_f4 ) /( s1 - s4 ) ; // Without r e g e n e r a t i o n
dT_m1 = T_m1 - T_m1r ;
disp ( ” I n c r e a s e i n T m1 due t o r e g e n e r a t i o n=” )
disp ( dT_m1 )
disp ( ” 0C” )
W_Tr = h1 - h3 ; // Without r e g e n e r a t i o n
SR1 =3600/ W_Tr ; // Steam r a t e w i t h o u t r e g e n e r a t i o n
dSR = SR - SR1 ;
disp ( ” I n c r e a s e i n steam r a t e due t o r e g e n e r a t i o n=” )
disp ( dSR )
disp ( ” kg /kWh” )
n_cycle1 =( h1 - h3 ) /( h1 - h_f4 ) ; // w i t h o u t r e g e n e r a t i o n
dn_cycle = n_cycle - n_cycle1 ;
disp ( ” I n c r e a s e i n c y c l e e f f i c i e n c y due t o
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r e g e n e r a t i o n ”)
68 disp ( dn_cycle *100)
69 disp ( ”%” )
Scilab code Exa 12.14 14
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// At 3 b a r
t_s1 =133.5; // 0C
h_f1 =561.4; // kJ / kg
// At 0 . 0 4 b a r
t_s2 =29; // 0C
h_f2 =121.5; // 0C
h0 =3231; // kJ / kg
h1 =2700; // kJ / kg
h2 =2085; // kJ / kg
t1 =130; // 0C
t2 =27; // 0C
c =4.186;
disp ( ” ( i ) Mass o f steam u s e d ” )
m1 = c *( t1 - t2 ) /( h1 - h_f2 ) ;
disp ( ”m1=” )
disp ( m1 )
disp ( ” kg ” )
disp ( ” ( i i ) Thermal e f f i c i e n c y o f t h e c y c l e ” )
W =( h0 - h1 ) +(1 - m1 ) *( h1 - h2 ) ;
Q = h0 - c * t1 ;
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n_thermal = W / Q ;
disp ( ” n t h e r m a l=” )
disp ( n_thermal )
Scilab code Exa 12.15 15
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h0 =3115.3; // kJ / kg
h1 =2720; // kJ / kg
h2 =2450; // kJ / kg
h3 =2120; // kJ / kg
h_f1 =640.1; // kJ / kg
h_f2 =417.5; // kJ / kg
h_f3 =173.9; // kJ / kg
m1 =( h_f1 - h_f2 ) /( h1 - h_f1 ) ;
disp ( ”m1=” )
disp ( m1 )
disp ( ” kJ / kg ” )
m2 =(( h_f2 - h_f3 ) - m1 *( h_f1 - h_f3 ) ) /( h2 - h_f3 ) ;
disp ( ”m2=” )
disp ( m2 )
disp ( ” kJ / kg ” )
W = h0 - h1 + (1 - m1 ) *( h1 - h2 ) + (1 - m1 - m2 ) *( h2 - h3 ) ;
Q = h0 - h_f1 ;
n=W/Q;
disp ( ” Thermal E f f i c i e n c y o f t h e c y c l e=” )
disp ( n )
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Scilab code Exa 12.16 16
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h0 =2905;
h1 =2600;
h2 =2430;
h3 =2210;
h4 =2000;
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
h_f1 =640.1;
h_f2 =467.1;
h_f3 =289.3;
h_f4 =137.8;
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
disp ( ” ( i ) Mass o f b l e d steam ” )
m1 =( h_f1 - h_f2 ) /( h1 - h_f1 ) ;
disp ( ”m1=” )
disp ( m1 )
disp ( ” kJ / kg ” )
m2 =(( h_f2 - h_f3 ) - ( m1 *( h_f1 - h_f2 ) ) ) /( h2 - h_f2 ) ;
disp ( ”m2=” )
disp ( m2 )
disp ( ” kJ / kg ” )
m3 =(( h_f3 - h_f4 ) -( m1 + m2 ) *( h_f2 - h_f4 ) ) /( h3 - h_f4 ) ;
disp ( ”m3=” )
disp ( m3 )
disp ( ” kJ / kg ” )
W =( h0 - h1 ) + (1 - m1 ) *( h1 - h2 ) +(1 - m1 - m2 ) *( h2 - h3 ) + (1 - m1
- m2 - m3 ) *( h3 - h4 ) ;
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34 disp ( ” ( i i ) Thermal e f f i c i e n c y o f t h e c y c l e=” )
35 n_thermal = W / Q ;
36 disp ( n_thermal )
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38
39 disp ( ” ( i i i ) Thermal e f f i c i e n c y o f Rankine c y c l e =” )
40 n_rankine =( h0 - h4 ) /( h0 - h_f4 ) ;
41 disp ( n_rankine )
42
43
44 disp ( ” ( i v ) T h e o r e t i c a l g a i n due t o r e g e n e r a t i v e f e e d
45
46
47
48
h e a t i n g =” )
gain =( n_thermal - n_rankine ) /( n_thermal ) ;
disp ( gain )
disp ( ” ( v ) Steam c o n s u m p t i o n w i t h r e g e n e r a t i v e f e e d
h e a t i n g =” )
49 S1 =3600/ W ;
50 disp ( S1 )
51 disp ( ” kg /kWh” )
52
53
disp ( ” Steam c o n s u m p t i o n w i t h o u t r e g e n e r a t i v e f e e d
h e a t i n g =” )
54 S2 =3600/( h0 - h4 ) ;
55 disp ( S2 )
56 disp ( ” kg /kWh” )
57
58
disp ( ” ( v i ) Q u a n t i t y o f steam p a s s i n g t h r o u g h t h e
l a s t s t a g e o f a 5 0 0 0 0 kW t u r b i n e w i t h
r e g e n e r a t i v e f e e d −h e a t i n g =” )
59 quantity1 = S1 *(1 - m1 - m2 - m3 ) *50000;
60 disp ( quantity1 )
61 disp ( ” kg /h ” )
62
63
64
disp ( ” q u a n t i t y o f steam w i t h o u t r e g e n e r a t i o n =” )
quantity2 = S2 *50000;
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65
66
disp ( quantity2 )
disp ( ” kg /h ” )
Scilab code Exa 12.17 17
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clc
h1 =3460; // kJ / kg
h2 =3460; // kJ / kg
h3 =3111.5; // kJ / kg
h4 =3585; // kJ / kg
h5 =3207; // kJ / kg
h6 =2466; // kJ / kg
h7 =137.8; // kJ / kg
h8 =962; // kJ / kg
h9 =670.4; // kJ / kg
h10 =962; // kJ / kg
p1 =100; // b a r
p2 =95; // b a r
p3 =25; // b a r
p4 =22; // b a r
p5 =6; // b a r
p6 =0.05; // b a r
n_mech =0.9;
n_gen =0.96;
n_boiler =0.9;
P =120*10^3; //kW
m1 =( h10 - h9 ) /( h3 - h8 ) ;
m2 =( h9 - m1 * h8 -(1 - m1 ) * h7 ) /( h5 - h7 ) ;
W_IP =(1 - m1 - m2 ) *( p5 - p6 ) *0.001*10^2;
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W_HP =( p1 - p5 ) *0.001*10^2;
W_total =( W_IP + W_HP ) / n_mech ;
W_indicated =( h2 - h3 ) + (1 - m1 ) *( h4 - h5 ) + (1 - m1 - m2 ) *( h5
- h6 ) ;
Output =( W_indicated - W_total ) * n_mech * n_gen ; // n e t
e l e c t r i c a l output
rate = P *3600/ Output ;
amt1 = m1 * rate ; // Amounts o f b l e d o f f , s u r f a c e ( h i g h
pressure ) heater
42 disp ( ” Amounts o f b l e d o f f , s u r f a c e ( h i g h p r e s s u r e )
h e a t e r =” )
43 disp ( amt1 )
44 disp ( ” kg /h ” )
45
46
amt2 = m2 * rate ; // Amounts o f b l e d o f f , s u r f a c e ( low
pressure ) heater
47 disp ( ” Amounts o f b l e d o f f , s u r f a c e ( low p r e s s u r e )
heater ”)
48 disp ( amt2 )
49 disp ( ” kg /h ” )
50
51
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53
54
55
56
57
58
59
60
61
62
disp ( ” ( i i i ) O v e r a l l t h e r m a l e f f i c i e n c y ” )
Q_boiler =( h1 - h10 ) / n_boiler ;
Q_reheater =( h4 - h3 ) / n_boiler ;
n_overall = Output /( Q_boiler + Q_reheater ) *100;
disp ( ” O v e r a l l t h e r m a l e f f i c i e n c y =” )
disp ( n_overall )
disp ( ”%” )
disp ( ” ( i v ) S p e c i f i c steam c o n s u m p t i o n =” )
290
63 ssc = rate / P ; // S p e c i f i c steam c o n s u m p t i o n
64 disp ( ssc )
65 disp ( ” kg /kWh” )
Scilab code Exa 12.18 18
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clc
p1 =15; // b a r
p2 =4; // b a r
p4 =0.1; // b a r
h1 =2920;
h2 =2660;
h3 =2960;
h4 =2335;
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
W = h1 - h2 + h3 - h4 ;
disp ( ” work done p e r kg o f steam ” )
disp ( W )
disp ( ” kJ / kg ” )
h_reheat = h3 - h2 ;
disp ( ”Amount o f h e a t s u p p l i e d d u r i n g r e h e a t =” )
disp ( h_reheat )
disp ( ” kJ / kg ” )
h_4a =2125;
// kJ / kg
W1 = h1 - h_4a ;
disp ( ”Work o u t p u t w i t h o u t r e h e a t =” )
disp ( W1 )
disp ( ” kJ / kg ” )
291
Scilab code Exa 12.19 19
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clc
h1 =3450;
h2 =3050;
h3 =3560;
h4 =2300;
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
h_f4 =191.8; // kJ / kg
// From m o l l i e r d i a g r a m
x4 =0.88;
disp ( ” ( i ) Q u a l i t y o f steam a t t u r b i n e e x h a u s t =” )
disp ( x4 )
n_cycle =(( h1 - h2 ) + ( h3 - h4 ) ) /(( h1 - h_f4 ) + ( h3 - h2 ) ) ;
disp ( ” ( i i ) C y c l e e f f i c i e n c y =” )
disp ( n_cycle )
SR =3600/(( h1 - h2 ) + ( h3 - h4 ) ) ;
disp ( ” ( i i i ) Steam r a t e i n kg /kWh =” )
disp ( SR )
disp ( ” kg /kWh” )
Scilab code Exa 12.20 20
1 clc
2
3 h1 =3250; // kJ / kg
4 h2 =2170; // kJ / kg
5 h_f2 =173.9; // kJ / kg
6
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W = h1 - h2 ;
Q = h1 - h_f2 ;
n_thermal = W / Q ;
disp ( ” Thermal e f f i f c i e n c y =” )
disp ( n_thermal ) ;
x2 =0.83; // From m o l l i e r c h a r t
disp ( ” x2=” )
disp ( x2 )
disp ( ” S e c o n d c a s e ” )
h1 =3250; // kJ / kg
h2 =2807; // kJ / kg
h3 =3263; // kJ / kg
h4 =2426; // kJ / kg
h_f4 =173.9; // kJ / kg
W = h1 - h2 + h3 - h4 ;
Q = h1 - h_f4 + h3 - h2 ;
n_thermal = W / Q ;
disp ( ” Thermal e f f i f c i e n c y =” )
disp ( n_thermal ) ;
x4 =0.935; // From m o l l i e r c h a r t
disp ( ” x4=” )
disp ( x4 )
Scilab code Exa 12.21 21
1 clc
2
3 disp ( ” ( a ) The e r o s i o n
o f t h e moving b l a d e s i s c a u s e d
293
by t h e p r e s e n c e o f w a t e r p a r t i c l e s i n ( wet )
steam i n t h e L . P . s t a g e s . The w a t e r p a r t i c l e s
s t r i k e t h e l e a d i n g s u r f a c e o f t h e b l a d e s . Such
impact , i f s u f f i c i e n t l y heavy , p r o d u c e s s e v e r e
l o c a l s t r e s s e s in the blade material causing the
s u r f a c e m e t a l t o f a i l and f l a k e o f f . ” )
4
5
disp ( ” The e r o s i o n , i f any , i s more l i k e l y t o o c c u r
i n t h e r e g i o n where t h e steam i s w e t t e s t , i . e . ,
i n t h e l a s t one o r two s t a g e s o f t h e t u r b i n e .
Moreover , t h e w a t e r d r o p l e t s a r e c o n c e n t r a t e d i n
t h e o u t e r p a r t s o f t h e f l o w a n n u a l s where t h e
v e l o c i t y o f impact i s h i g h e s t . ”)
6 disp ( ” E r o s i o n d i f f i c u l t i e s due t o m o i s t u r e i n t h e
steam may be a v o i d e d by r e h e a t i n g . The w h o l e o f
steam i s t a k e n from t h e t u r b i n e a t a s u i t a b l e
p o i n t 2 , and a f u r t h e r s u p p l y o f h e a t i s g i v e n t o
i t a l o n g 2−3 a f t e r which t h e steam i s r e a d m i t t e d
t o t h e t u r b i n e and expanded a l o n g 3−4 t o
c o n d e n s e r p r e s s u r e . E r o s i o n may a l s o be r e d u c e d
by u s i n g steam t r a p s i n b e t w e e n t h e s t a g e s t o
s e p a r a t e m o i s t u r e from t h e steam . ” )
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disp ( ” ( b ) TTD means
Terminal
temperature
d i f f e r e n c e . I t i s the d i f f e r e n c e between
t e m p e r a t u r e s o f b l e d steam / c o n d e n s a t e and t h e
f e e d w a t e r a t t h e two e n d s o f t h e f e e d w a t e r
heater ”)
11
12
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14 disp ( ” P a r t ( c ) ” )
15
16 h1 =3580; // kJ / kg
17 h2 =3140; // kJ / kg
18 h3 =3675; // kJ / kg
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46
h4 =2335; // kJ / kg
h5 =191.8; // kJ / kg
P =15*10^3; //kW
a =0.104; // m o i s t u r e c o n t e n t i n e x i t from LP t u r b i n e
p =40; // b a r ; From t h e m o l l i e r d i a g r a m
disp ( ” ( i ) Reheat p r e s s u r e=” )
disp ( p )
disp ( ” b a r ” )
disp ( ” ( i i ) Thermal e f f i c i e n c y ” )
W = h1 - h2 + h3 - h4 ;
Q = h1 - h5 + h3 - h2 ;
n_th = W / Q *100;
disp ( ” n t h=” )
disp ( n_th )
disp ( ”%” )
sc = P / W ; // steam c o n s u m p t i o n
ssc = sc *3600/ P ; // s p e c i f i c steam c o n s u m p t i o n
disp ( ” S p e c i f i c steam c o n s u m p t i o n=” )
disp ( ssc )
disp ( ” kg /kWh” )
disp ( ” ( i v ) Rate o f pump work =” )
rate = sc *0.15;
disp ( rate )
Scilab code Exa 12.22 22
1 clc
2
3 h_l =355.988; // kJ / kg
4 s_l =0.5397; // kJ / kg K
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s_f =0.0808; // kJ / kg K
s_g =0.6925; // kJ / kg K
h_f =29.98; // kJ / kg
h_g =329.85; // kJ / kg
p1 =4; // b a r
p2 =0.04; // b a r
v_f2 =76.5*10^( -6) ; //mˆ3/ kg
h1 =2789.9; // kJ / kg
s1 =6.4406; // kJ / kg
h_f =121.5; // kJ / kg
h_fg =2432.9; // kJ / kg
s_f =0.432; // kJ / kg K
s_fg2 =8.052; // kJ / kg K
p4 =15; // b a r
p3 =0.04; // b a r
v_f =0.0001; // kJ / kg K
h_f4 =123; // kJ / kg
h_m =254.88; // kJ / kg
h_fn =29.98; // kJ / kg
h_fk =29.988; // kJ / kg
disp ( ” ( i ) O v e r a l l t h e r m a l e f f i c i e n c y ” )
m =( h1 - h_f4 ) /( h_m - h_fn ) ; // The amount o f m e r c u r y
c i r c u l a t i n g f o r 1 kg o f steam i n t h e bottom c y c l e
33 Q1 = m *( h_l - h_fk ) ; // t o t a l
34
35 x2 =( s1 - s_f ) /( s_fg2 ) ;
36
37 h2 = h_f + x2 * h_fg ;
38
39 W_T = m *( h_l - h_m ) +( h1 - h2 ) ; // t o t a l
40
41 n_overall = W_T / Q1 ; //W P may be n e g l e c t e d
296
42 disp ( ” n o v e r a l l =” )
43 disp ( n_overall )
44
45
46 disp ( ” ( i i ) Flow t h r o u g h m e r c u r y t u r b i n e=” )
47 A =48000; // kg / h
48 m_Hg = m * A ;
49 disp ( m_Hg )
50 disp ( ” kg /h ” )
51
52
53 disp ( ” ( i i i ) U s e f u l work i n b i n a r y v a p o u r c y c l e=” )
54 W_total = A * W_T /3600;
55 disp ( W_total )
56 disp ( ”kW” )
57
58
59 disp ( ” ( i v ) O v e r a l l e f f i c i e n c y u n d e r new c o n d i t i o n s ”
)
60 n_Hg =0.84;
61 n_steam =0.88;
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W_Hg = n_Hg *101.1;
h_m1 = h_l - W_Hg ;
m1 =( h1 - h_f4 ) /( h_m1 - h_fn ) ;
h_g =3037.6; // kJ / kg
s_g =6.918; // kJ / kg
s_f2 =0.423; // kJ / kg K
s_fg2 =8.052; // kJ / kg K
Q1 = m1 *( h_l - h_fk ) + ( h_g - h1 ) ;
x2 =( s_g - s_f2 ) / s_fg2 ;
h2 = h_f + x2 * h_fg ;
W_steam = n_steam *( h_g - h2 ) ;
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W_total = m1 * W_Hg + W_steam ;
n_overall = W_total / Q1 ;
disp ( ” n o v e r a l l ” )
disp ( n_overall )
Scilab code Exa 12.23 23
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clc
p1 =60; // b a r
t1 =450; // 0C
p2 =3; // b a r
p3 =0.07; // b a r ; p3 =( 7 6 0 − 7 07 . 5) / 7 6 0 ∗ 1 . 0 1 3
n_turbine =0.87;
n_boiler =0.86;
n_alt =0.94;
n_mech =0.97;
P =22500; //kW
h1 =3300; // kJ / kg
h2 =2607; // kJ / kg
h2a = h1 - n_turbine *( h1 - h2 ) ;
h3 =2165; // kJ / kg
h3a = h2a - n_turbine *( h2a - h3 ) ;
h_f4 =163.4; // kJ / kg
h_f5 =561.4; // kJ / kg
disp ( ” ( i ) The steam b l e d p e r kg o f steam s u p p l i e d t o
the t u r b i n e ”)
26 m =( h_f5 - h_f4 ) /( h2a - h_f4 ) ;
298
27 disp ( ”m=” )
28 disp ( m )
29 disp ( ” kJ / kg ” )
30
31
32 disp ( ” ( i i ) Steam g e n e r a t e d p e r h o u r ” )
33 W =( h1 - h2a ) + (1 - m ) *( h2a - h3a ) ; // Work d e v e l o p e d p e r
kg o f steam i n t h e t u r b i n e
34 W_act = P / n_alt / n_mech ; // a c t u a l work
35
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43
steam = W_act / W *3600/1000; // t o n n e s /h
disp ( ” Steam g e n e r a t e d=” )
disp ( steam )
disp ( ” t o n n e s / h ” )
disp ( ” ( i i i ) The o v e r a l l e f f i c i e n c y o f t h e p l a n t ” )
P_avail = P *(1 -0.09) ; // Net power a v a i l a b l e d e d u c t i n g
pump power
44 Q = steam *1000*( h1 - h_f5 ) / n_boiler /3600; //kW
45
46
47
48
n_overall = P_avail / Q
disp ( ” n o v e r a l l =” )
disp ( n_overall )
Scilab code Exa 12.24 24
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clc
t1 =350; // 0C
t_s =350; // 0C
p2 =7; // b a r
p3 =7; // b a r
p4 =0.4; // b a r
t3 =350; // 0C
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h1 =2985;
h2 =2520;
h3 =3170;
h4 =2555;
// kJ / kg
// kJ / kg
// kJ / kg
// kJ / kg
h_f2 =697.1; // kJ / kg
h_f4 =317.7; // kJ / kg
P =110*10^3; //kW
disp ( ” ( i ) The r a t i o o f steam b l e d t o steam g e n e r a t e d
”)
21 m =( h_f2 - h_f4 ) /( h2 - h_f4 ) ;
22
23 ratio =1/ m ;
24 disp ( ” r a t i o =” )
25 disp ( ratio )
26
27
28 disp ( ” ( i i ) The b o i l e r g e n e r a t i n g c a p a c i t y =” )
29 m_s = P /( h1 - h2 +(1 - m ) *( h3 - h4 ) ) *3600/1000; // t o n n e s / h o u r
30 disp ( m_s )
31 disp ( ” t o n n e s / h o u r ” )
32
33
34 disp ( ” ( i i i ) Thermal e f f i c i e n c y o f t h e c y c l e =” )
35 n_thermal =(( h1 - h2 ) + (1 - m ) *( h3 - h4 ) ) /(( h1 - h_f2 ) +(1 - m )
*( h3 - h2 ) ) ;
36 disp ( n_thermal )
Scilab code Exa 12.25 25
1 clc
2 h1 =3315; // kJ / kg
300
3 h2 =2716; // kJ / kg
4 h3 =3165; // kJ / kg
5 h4 =2236; // kJ / kg
6 h_f2 =697.1; // kJ / kg
7 h_f6 = h_f2 ;
8 h_f4 =111.9; // kJ / kg
9 h_f5 = h_f4 ;
10
11 disp ( ” ( i ) Amount o f steam b l e d
o f f for feed heating
=” )
12 m =( h_f2 - h_f4 ) /( h2 - h_f4 ) ;
13 disp ( m )
14 disp ( ” steam b l e d o f f i s 2 2 . 5% o f steam g e n e r a t e d by
the b o i l e r . ”)
15
16
17
disp ( ” ( i i ) Amount o f steam s u p p l i e d t o L . P . t u r b i n e
=” )
18 amt =100 - m *100;
19 disp ( amt )
20 disp ( ” 7 7 . 5% o f t h e steam g e n e r a t e d by t h e b o i l e r . ” )
21
22
23
disp ( ” ( i i i ) Heat s u p p l i e d i n t h e b o i l e r and r e h e a t e r
”)
Q_boiler = h1 - h_f6 ;
disp ( ” Q b o i l e r=” )
disp ( Q_boiler )
disp ( ” kJ / kg ” )
24
25
26
27
28
29 Q_reheater =(1 - m ) *( h3 - h2 ) ;
30 disp ( ” Q r e h e a t e r=” )
31 disp ( Q_reheater )
32 disp ( ” kJ / kg ” )
33
34 Qs = Q_boiler + Q_reheater ;
35
36 disp ( ” ( i v ) C y c l e e f f i c i e n c y ” )
301
37 W = h1 - h2 + (1 - m ) *( h3 - h4 ) ;
38
39 n_cycle = W / Qs ;
40 disp ( ” n c y c l e=” )
41 disp ( n_cycle )
42
43
44 disp ( ” ( v ) Power d e v e l o p e d by t h e s y s t e m ” )
45 ms =50; // kg / s
46 Power = ms * W /1000; //MW
47 disp ( ” Power=” )
48 disp ( Power )
49 disp ( ”MW” )
Scilab code Exa 12.26 26
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clc
h1 = 3578; // kJ / kg
h2 = 3140; // kJ / kg
h3 = 3678; // kJ / kg
h4 = 3000; // kJ / kg
h5 = 2330; // kJ / kg
h_f1 =1611; // kJ / kg
h_f2 =1087.4; // kJ / kg
h_f4 =640.1; // kJ / kg
h_f5 =191.8; // kJ / kg
h_f6 = h_f5 ;
disp ( ” ( i ) F r a c t i o n o f steam e x t r a c t e d from t h e
t u r b i n e s a t e a c h b l e d h e a t e r =” )
15
16 disp ( ” c l o s e d f e e d h e a t e r ” )
17 m1 =( h_f2 - h_f4 ) /( h2 - h_f4 ) ;
18 disp ( m1 )
302
19 disp ( ” kg / kg o f steam s u p p l i e d by
20
21 disp ( ” open f e e d h e a t e r ” )
22 m2 =(1 - m1 ) *( h_f4 - h_f5 ) /( h4 - h_f6 ) ;
23 disp ( m2 )
24 disp ( ” kg / kg o f steam s u p p l i e d by
25
26
27 disp ( ” ( i i ) Thermal e f f i c i e n c y o f
28
29 W_total =( h1 - h2 ) + (1 - m1 ) *( h3 - h4 )
30
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45
46
the b o i l e r ”)
the b o i l e r ”)
the system ”)
+ (1 - m1 - m2 ) *( h4 - h5 )
;
p1 =150; // b a r
p2 =40; // b a r
p4 =5; // b a r
p5 =0.1; // b a r
v_w1 =1/1000; //mˆ3/ kg
v_w2 = v_w1 ;
v_w3 = v_w1 ;
W_P1 = v_w1 *(1 - m1 - m2 ) *( p4 - p5 ) *100; // kJ / kg
W_P2 = v_w2 *(1 - m1 ) *( p1 - p4 ) *100; // kJ / kg
W_P3 = v_w3 * m1 *( p1 - p2 ) *100; // kJ / kg
W_P = W_P1 + W_P2 + W_P3 ; // T o t a l pump work
W_net = W_total - W_P ;
Q =(1 - m1 ) * h_f1 + m1 *( h_f1 ) ; // Heat o f f e e d w a t e r
e x t e r i n g the b o i l e r
47 Qs1 = h1 - Q ;
48 Qs2 =(1 - m1 ) *( h3 - h2 ) ;
49 Qst = Qs1 + Qs2 ;
50
51
52
53
54
n_thermal = W_net / Qst *100;
disp ( ” n t h e r m a l=” )
disp ( n_thermal )
disp ( ”%” )
303
Scilab code Exa 12.27 27
1 clc
2
3 disp ( ” ( i ) The minimum p r e s s u r e a t which b l e e d i n g
is
n e c e s s a r y=” )
4
5
// I t would be assumed t h a t t h e f e e d w a t e r h e a t e r i s
an open h e a t e r . Feed w a t e r i s h e a t e d t o 180 C .
So p s a t a t 180 C ˜= 10 b a r i s t h e p r e s s u r e a t
which t h e h e a t e r o p e r a t e s . Thus , t h e p r e s s u r e a t
which b l e e d i n g i s n e c e s s a r y i s 10 b a r .
6 p_min =10; // b a r
7 disp ( p_min )
8 disp ( ” b a r ” )
9
10
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12
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15
16
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18
19
20
21
22
h1 =3285; // kJ / kg
h2 =2980; // kJ / kg
h3 =3280; // kJ / kg
h4a =3072.5; // kJ / kg
h5 =2210; // kJ / kg
h5a =2356.6; // kJ / kg
h_f6 =163.4; // kJ / kg
h_f8 =762.6; // kJ / kg
h2a =3045.6; // kJ / kg
disp ( ” ( i i ) The q u a n t i t y o f steam b l e d p e r kg o f f l o w
a t t h e t u r b i n e i n l e t =” )
23 m =( h_f8 - h_f6 ) /( h4a - h_f6 ) ;
24 disp ( m )
25 disp ( ” kg o f steam f l o w a t t u r b i n e i n l e t . ” )
26
304
27
28
29
disp ( ” ( i i i ) C y c l e e f f i c i e n c y =” )
n_cycle =(( h1 - h2a ) +( h3 - h4a ) +(1 - m ) *( h4a - h5a ) ) /(( h1 h_f8 ) + ( h3 - h2a ) ) *100;
30 disp ( n_cycle )
31 disp ( ”%” )
305
Chapter 13
Gas Power Cycles
Scilab code Exa 13.1 1
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19
clc
T1 =671; //K
T2 = T1 ;
T3 =313; //K
T4 = T3 ;
W =130; // kJ
disp ( ” ( i ) E n g i n e t h e r m a l e f f i c i e n c y =” )
n_th =( T2 - T3 ) / T2 ;
disp ( n_th )
disp ( ” ( i i ) Heat added =” )
Q = W / n_th ;
disp ( Q )
disp ( ” kJ ” )
disp ( ” ( i i i ) The e n t r o p y c h a n g e s d u r i n g h e a t
r e j e c t i o n p r o c e s s ”)
20 Q_rejected =Q - W ;
306
21 dS = Q_rejected / T3 ;
22 disp ( ” dS=” )
23 disp ( dS )
24 disp ( ” kJ /K” )
Scilab code Exa 13.2 2
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23
clc
cv =0.721; // kJ / kg K
cp =1.008; // kJ / kg K
m =0.5; // kg
n_th =0.5;
Q_isothermal =40; // kJ
p1 =7*10^5; // Pa
V1 =0.12; //mˆ3
R =287; // J / kg K
disp ( ” ( i ) The maximum and minimum t e m p e r a t u r e s ” )
T1 = p1 * V1 / m / R ;
disp ( ”Maximun t e m p e r a t u r e =” )
disp ( T1 )
disp ( ”K” )
T2 =(1 - n_th ) * T1 ;
disp ( ”Minimum t e m p e r a t u r e =” )
disp ( T2 )
disp ( ”K” )
disp ( ” ( i i ) The volume a t t h e end o f i s o t h e r m a l
e x p a n s i o n =” )
24 V2 = V1 * %e ^( Q_isothermal *10^3/ m / R / T1 ) ;
25 disp ( V2 )
26 disp ( ”mˆ3 ” )
27
307
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46
disp ( ” ( i i i ) The h e a t t r a n s f e r f o r e a c h o f t h e f o u r
p r o c e s s e s ”)
Q1 = Q_isothermal ;
disp ( ” I s o t h e r m a l e x p a n s i o n ” )
disp ( Q1 )
disp ( ” kJ ” )
Q2 =0;
disp ( ” A d i a b a t i c r e v e r s i b l e e x p a n s i o n ” )
disp ( Q2 )
Q3 = - Q_isothermal ;
disp ( ” I s o t h e r m a l c o m p r e s s i o n ” )
disp ( Q3 )
Q4 =0;
disp ( ” A d i a b a t i c r e v e r s i b l e c o m p r e s s i o n ” )
disp ( Q4 )
Scilab code Exa 13.3 3
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2
3
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8
9
10
clc
p1 =18*10^5; // Pa
T1 =683; //K
T2 = T1 ;
r1 =6; // r a t i o V4/V1 ; I s e n t r o p i c c o m p r e s s i o n
r2 =1.5; // r a t i o V2/V1 ; I s o t h e r m a l e x p a n s i o n
y =1.4;
V1 =0.18; //mˆ3
disp ( ” ( i ) T e m p e r a t u r e s and p r e s s u r e s a t t h e main
p o i n t s in the c y c l e ”)
11
308
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49
T4 = T1 /( r1 ) ^( y -1) ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
T3 = T4 ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
p2 = p1 / r2 ;
disp ( ” p2=” )
disp ( p2 /10^5)
disp ( ” b a r ” )
p3 = p2 /( r1 ) ^ y ;
disp ( ” p3=” )
disp ( p3 /10^5)
disp ( ” b a r ” )
p4 = p1 /( r1 ) ^ y ;
disp ( ” p4=” )
disp ( p4 /10^5)
disp ( ” b a r ” )
disp ( ” ( i i ) Change i n e n t r o p y =” )
dS = p1 * V1 / T1 /10^3* log ( r2 ) ;
disp ( dS )
disp ( ” kJ /K” )
disp ( ” ( i i i ) Mean t h e r m a l e f f i c i e n c y o f t h e c y c l e ” )
Qs = T1 *( dS ) ;
Qr = T4 *( dS ) ;
n =1 - Qr / Qs ;
disp ( ” n=” )
309
50 disp ( n )
51
52
53 disp ( ” ( i v ) Mean e f f e c t i v e p r e s s u r e
54 pm =( Qs - Qr ) /8/ V1 /100; // b a r
55 disp ( pm )
56 disp ( ” b a r ” )
57
58
59 n =210; // c y c l e s p e r m i n u t e
60 disp ( ” ( v ) Power o f t h e e n g i n e =” )
61 P =( Qs - Qr ) * n /60; //kW
62 disp ( P )
63 disp ( ”kW” )
Scilab code Exa 13.4 4
1 clc
2
3 // F i r s t c a s e
4 // ( T1−T2 ) /T1=1/6
5 //T1 =1.2∗ T2
6
7
8 // S e c o n d c a s e
9 // ( T1−(T2−(70+273) ) ) /T3=1/3
10
11 T2 =1029/0.6;
12 T1 =1.2* T2 ;
13
14 disp ( ” T e m p e r a t u r e o f t h e s o u r c e =” )
15 disp ( T1 )
16 disp ( ”K” )
17
18
310
o f t h e c y c l e =” )
19
20
21
disp ( ” T e m p e r a t u r e o f t h e s i n k=” )
disp ( T2 )
disp ( ”K” )
Scilab code Exa 13.5 5
1
2
3
4
5
6
7
8
9
clc
T1 =1990; //K
T2 =850; //K
Q =32.5/60; // kJ / s
P =0.4; //kW
n_carnot =( T1 - T2 ) / T1 ;
disp ( ” most e f f i c i e n t e n g i n e i s one t h a t w o r k s on
Carnot c y c l e ”)
10 disp ( n_carnot )
11
12
13
14
15
16
n_th = P / Q ;
disp ( ” n t h e r m a l =” )
disp ( n_th )
disp ( ” which i s n o t f e a s i b l e a s no e n g i n e can be more
e f f i c i e n t t h a n t h a t w o r k i n g on C a r n o t ” )
17 disp ( ” Hence c l a i m s o f t h e i n v e n t o r i s n o t t r u e . ” )
Scilab code Exa 13.7 7
1 clc
2
3 n =0.6;
4 y =1.5;
5
311
6 r =(1/(1 - n ) ) ^(1/( y -1) ) ;
7 disp ( ” C o m p r e s s i o n r a t i o =” )
8 disp ( r )
Scilab code Exa 13.8 8
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25
clc
D =0.25; //m
L =0.375; //m
Vc =0.00263; //mˆ3
p1 =1; // b a r
T1 =323; //K
p3 =25; // b a r
Vs = %pi /4* D ^2* L ;
r =( Vs + Vc ) / Vc ;
y =1.4;
disp ( ” ( i ) A i r s t a n d a r d e f f i c i e n c y =” )
n_otto =1 -1/( r ^( y -1) ) ;
disp ( n_otto )
disp ( ” ( i i ) Mean e f f e c t i v e p r e s s u r e ” )
p2 = p1 *( r ) ^( y ) ;
r_p = p3 / p2 ;
p_m = p1 * r *( r ^( y -1) - 1) *( r_p - 1) /( y -1) /( r -1) ;
disp ( ”Mean e f f e c t i v e p r e s s u r e =” )
disp ( p_m )
disp ( ” b a r ” )
Scilab code Exa 13.9 9
312
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38
clc
cv =0.72; // kJ / kg K
y =1.4;
p1 =1; // b a r
T1 =300; //K
Q =1500; // kJ / kg
r =8;
y =1.4;
disp ( ” ( i ) P r e s s u r e s and t e m p e r a t u r e s a t a l l p o i n t s ” )
T2 = T1 *( r ) ^( y -1) ;
disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
p2 = p1 *( r ) ^ y ;
disp ( ” p2=” )
disp ( p2 )
disp ( ” b a r ” )
T3 = Q / cv + T2 ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
p3 = p2 * T3 / T2 ;
disp ( ” p3=” )
disp ( p3 )
disp ( ” b a r ” )
T4 = T3 / r ^( y -1) ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
p4 = p3 / r ^( y ) ;
disp ( ” p4=” )
disp ( p4 )
313
39 disp ( ” b a r ” )
40
41
42 disp ( ” ( i i ) S p e c i f i c work and t h e r m a l
43 SW = cv *[( T3 - T2 ) - ( T4 - T1 ) ];
44 disp ( ” S p e c i f i c work =” )
45 disp ( SW )
46 disp ( ” kJ / kg ” )
47
48 n_th =1 -1/ r ^( y -1) ;
49 disp ( ” Thermal e f f i c i e n c y =” )
50 disp ( n_th )
e f f i c i e n c y ”)
Scilab code Exa 13.10 10
1
2
3
4
5
6
7
8
clc
r =6; // v1 / v2=v4 / v3=r
p1 =1; // b a r
T1 =300; //K
T3 =1842; //K
y =1.4;
disp ( ” ( i ) T e m p e r a t u r e and p r e s s u r e a f t e r t h e
i s e n t r o p i c expansion ”)
9 p2 = p1 *( r ) ^ y ;
10 T2 = T1 * r ^( y -1) ;
11 p3 = p2 *( T3 / T2 ) ;
12
13 T4 = T3 / r ^( y -1) ;
14 disp ( ”T4=” )
15 disp ( T4 )
16 disp ( ”K” )
17
18 p4 = p3 /( r ) ^( y ) ;
19 disp ( ” p4 =” )
314
20
21
22
23
24
25
disp ( p4 )
disp ( ” b a r ” )
disp ( ” ( i i ) P r o c e s s r e q u i r e d t o c o m p l e t e t h e c y c l e ” )
disp ( ” P r o c e s s r e q u i r e d t o c o m p l e t e t h e c y c l e i s t h e
c o n s t a n t p r e s s u r e s c a v e n g i n g . The c y c l e i s c a l l e d
Atkinson c y c l e ”)
26
27
disp ( ” ( i i i ) P e r c e n t a g e improvement / i n c r e a s e i n
e f f i c i e n c y ”)
28 p5 =1; // b a r
29 T5 = T3 *( p5 / p3 ) ^(( y -1) / y ) ;
30
31 n_otto =(1 -1/ r ^( y -1) ) *100;
32 disp ( ” n o t t o = ” )
33 disp ( n_otto )
34 disp ( ”%” )
35
36 n_atkinson =(1 - y *( T5 - T1 ) /( T3 - T2 ) ) *100;
37 disp ( ” n a t k i n s o n=” )
38 disp ( n_atkinson )
39 disp ( ”%” )
40
41 dn = n_atkinson - n_otto ; // Improvement i n
42 disp ( ” Improvement i n e f f i c i e n c y =” )
43 disp ( dn )
44 disp ( ”%” )
Scilab code Exa 13.11 11
1
2
3
4
clc
p1 =1; // b a r
T1 =343; //K
p2 =7; // b a r
315
efficiency
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25
Qs =465; // kJ / kg o f a i r
cp =1; // kJ / kg K
cv =0.706; // kJ / kg K
y =1.41;
disp ( ” ( i ) C o m p r e s s i o n r a t i o o f e n g i n e =” )
r =( p2 / p1 ) ^(1/ y ) ;
disp ( r )
disp ( ” ( i i ) T e m p e r a t u r e a t t h e end o f c o m p r e s s i o n =” )
T2 = T1 *( r ) ^( y -1) ;
t2 = T2 -273;
disp ( t2 )
disp ( ” 0C” )
disp ( ” ( i i i ) T e m p e r a t u r e a t t h e end o f h e a t a d d i t i o n
=” )
T3 = Qs / cv + T2 ;
t3 = T3 -273;
disp ( t3 )
disp ( ” 0C” )
Scilab code Exa 13.12 12
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2
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5
6
7
8
9
10
clc
y =1.4;
R =0.287; // kJ / kg K
T1 =311; //K
T3 =2223; //K
// p2 / p1=15
disp ( ” ( i ) C o m p r e s s i o n r a t i o =” )
r =15^(1/1.4) ;
316
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29
disp ( r )
disp ( ” ( i i ) Thermal e f f i c i e n c y =” )
n_th =1 -1/ r ^( y -1) ;
disp ( n_th )
disp ( ” ( i i i ) Work done ” )
T2 = T1 *( r ) ^( y -1) ;
T4 = T3 / r ^( y -1) ;
cv = R /( y -1) ;
Q_supplied = cv *( T3 - T2 ) ;
Q_rejected = cv *( T4 - T1 ) ;
W = Q_supplied - Q_rejected ;
disp ( ”Work done=” )
disp ( W )
disp ( ” kJ ” )
Scilab code Exa 13.13 13
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8
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10
11
12
clc
V1 =0.45; //mˆ3
p1 =1; // b a r
T1 =303; //K
p2 =11; // b a r
Qs =210; // kJ
n =210; // number o f w o r k i n g c y c l e s / min
R =287; // J / kg K
cv =0.71; // kJ / kg K
y =1.4;
disp ( ” ( i ) P r e s s u r e s , t e m p e r a t u r e s and v o l u m e s a t
s a l i e n t p o i n t s ”)
317
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50
r =( p2 / p1 ) ^(1/ y ) ;
T2 = T1 *( r ) ^( y -1) ;
disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
V2 = T2 / T1 * p1 / p2 * V1 ;
disp ( ”V2=” )
disp ( V2 )
disp ( ”mˆ3 ” )
m = p1 *10^5* V1 / R / T1 ;
T3 = Qs / m / cv + T2 ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
p3 = T3 / T2 * p2 ;
disp ( ” p3=” )
disp ( p3 )
disp ( ” b a r ” )
V3 = V2 ;
disp ( ”V3=” )
disp ( V3 )
disp ( ”mˆ3 ” )
p4 = p3 / r ^ y ;
disp ( ” p4=” )
disp ( p4 )
disp ( ” b a r ” )
T4 = T3 / r ^( y -1) ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
318
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V4 = V1 ;
disp ( ”V4=” )
disp ( V4 )
disp ( ”mˆ3 ” )
disp ( ” ( i i ) P e r c e n t a g e c l e a r a n c e =” )
%clearance = V2 /( V1 - V2 ) *100;
disp ( %clearance )
disp ( ”%” )
disp ( ” ( i i i ) E f f i c i e n c y =” )
Qr = m * cv *( T4 - T1 ) ;
n_otto =( Qs - Qr ) / Qs ;
disp ( n_otto )
disp ( ” ( i v ) Mean e f f e c t i v e p r e s s u r e =” )
p_m =( Qs - Qr ) /( V1 - V2 ) /100; // b a r
disp ( p_m )
disp ( ” b a r ” )
disp ( ” ( v ) Power d e v e l o p e d =” )
P =( Qs - Qr ) * n /60;
disp ( P )
disp ( ”kW” )
Scilab code Exa 13.14 14
1 clc
2
3 // W=Qs−Qr=cv ∗ ( T3−T2 ) − cv ∗ ( T4−T1 )
4 // T2=T1 ∗ ( r ˆ ( y −1) )
319
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// T3=T4 ∗ ( r ˆ ( y −1) )
// W=cv ∗ [ T3−T1∗ r ˆ ( y −1) − T3/ r ˆ ( y −1)+T1 ] ;
// dW/ d r=−T1 ∗ ( y −1) ∗ r ˆ ( y −2) − T3∗(1 − y ) ∗ r ˆ(−y ) =0
//By s o l v i n g t h i s we g e t
disp ( ” r =(T3/T1 ) ˆ ( 1 / 2 / ( y −1) ) ” )
disp ( ” ( b ) Change i n e f f i c i e n c y ” )
T3 =1220; //K
T1 =310; //K
// For a i r
y =1.4;
r1 =( T3 / T1 ) ^(1/2/( y -1) ) ;
n1 =1 -1/ r1 ^( y -1) ; // a i r s t a n d a r d E f f i c i e n c y
disp ( ” A i r s t a n d a r d E f f i c i e n c y =” )
disp ( n1 )
// For h e l i u m
cp =5.22; // kJ / kg K
cv =3.13; // kJ / kg K
y = cp / cv ;
r2 =( T3 / T1 ) ^(1/2/( y -1) ) ;
n2 =1 -1/ r2 ^( y -1) ;
disp ( ” A i r s t a n d a r d e f f i c i e n c y f o r h e l i u m =” )
disp ( n2 )
change = n1 - n2 ;
disp ( ” Change i n e f f i c i e n c y =” )
disp ( change )
disp ( ” Hence c h a n g e i n e f f i c i e n c y
320
is
n i l ”)
Scilab code Exa 13.15 15
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2
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// W=cv ∗ [ T3−T1∗ r ˆ ( y −1) − T3/ r ˆ ( y −1)+T1 ]
// r =(T3/T1 ) ˆ ( 1 / 2 / ( y −1) )
// T2=T1∗ r ˆ ( y −1)
// T4=T3/ r ˆ ( y −1)
// T2=T1 ∗ [ ( T3/T1 ) ˆ ( 1 / 2 / ( y −1) ) ] ˆ ( y −1)
//T2=s q r t ( T1∗T3 )
// S i m i l a r l y T4=T3 / [ ( T3/T1 ) ˆ ( 1 / 2 / ( y −1) ) ] ˆ ( y −1)
//T4=s q r t ( T1∗T3 )
disp ( ”T2=T4=s q r t ( T1∗T3 ) ” )
disp ( ” ( b ) Power d e v e l o p e d ” )
T1 =310; //K
T3 =1450; //K
m =0.38; // kg
cv =0.71; // kJ / kg K
T2 = sqrt ( T1 * T3 ) ;
T4 = T2 ;
W1 = cv *[( T3 - T2 ) - ( T4 - T1 ) ]; // Work done
W = m /60* W1 ; // Work done p e r s e c o n d
disp ( ” Power =” )
disp ( W )
disp ( ”kW” )
321
Scilab code Exa 13.17 17
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r =15;
y =1.4;
//V3−V2 = 0 . 0 6 ∗ ( V1−V2 )
rho =1.84; // c u t o f f r a t i o r h o=V3/V2
n_diesel =1 -1/ y / r ^( y -1) *(( rho ^y -1) /( rho -1) ) ;
disp ( ” e f f i c i e n c y =” )
disp ( n_diesel )
Scilab code Exa 13.18 18
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L =0.25; //m
D =0.15; //m
V2 =0.0004; //mˆ3
Vs = %pi /4* D ^2* L ;
V_total = Vs + V2 ;
y =1.4;
V3 = V2 +5/100* Vs ;
rho = V3 / V2 ;
r =( Vs + V2 ) / V2 ; //V1=Vs+V2
n_diesel =1 -1/ y / r ^( y -1) *(( rho ^y -1) /( rho -1) ) ;
disp ( ” e f f i c i e n c y =” )
disp ( n_diesel )
322
Scilab code Exa 13.19 19
1 clc
2 r =14; // l e t c l e a r a n c e volume be u n i t y
3 y =1.4;
4
5 //When t h e f u e l i s cut − o f f a t 5%
6 rho1 =5/100*( r -1) +1;
7 n_diesel1 =1 -1/ y / r ^( y -1) *(( rho1 ^y -1) /( rho1 -1) ) ;
8
9 //When t h e f u e l i s cut − o f f a t 8%
10 rho2 =8/100*( r -1) +1;
11 n_diesel2 =1 -1/ y / r ^( y -1) *(( rho2 ^y -1) /( rho2 -1) ) ;
12
13 %loss =( n_diesel1 - n_diesel2 ) *100;
14 disp ( ” p e r c e n t a g e l o s s i n e f f i c i e n c y due t o d e l a y i n
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f u e l c u t o f f =” )
disp ( %loss )
disp ( ”%” )
Scilab code Exa 13.20 20
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pm =7.5; // b a r
r =12.5;
p1 =1; // b a r
y =1.4;
// pm = p1 ∗ r ˆ y ∗ [ y ∗ ( rho −1) − r ˆ(1 − y ) ∗ ( r h o ˆy −1) ] / ( y −1)
/ ( r −1)
9 // S o l v i n g a b o v e e q u a t i o n we g e t
323
10 rho =2.24;
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12 %cutoff =( rho -1) /( r -1) *100;
13 disp ( ” % c u t o f f=” )
14 disp ( %cutoff )
15 disp ( ”%” )
Scilab code Exa 13.21 21
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D =0.2; //m
L =0.3; //m
p1 =1; // b a r
T1 =300; //K
R =287;
r =15;
y =1.4;
disp ( ” ( i ) P r e s s u r e s and t e m p e r a t u r e s a t s a l i e n t
p o i n t s ”)
11 Vs = %pi /4* D ^2* L ;
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V1 = r /( r -1) * Vs ;
disp ( ”V1=” )
disp ( V1 )
disp ( ”mˆ3 ” )
m = p1 *10^5* V1 / R / T1 ;
p2 = p1 * r ^ y ;
disp ( ” p2=” )
disp ( p2 )
disp ( ” b a r ” )
T2 = T1 * r ^( y -1) ;
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disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
V2 = Vs /( r -1) ;
disp ( ”V2=” )
disp ( V2 )
disp ( ”mˆ3 ” )
rho =8/100*( r -1) + 1;
V3 = rho * V2 ;
disp ( ”V3=” )
disp ( V3 )
disp ( ”mˆ3 ” )
T3 = T2 * V3 / V2 ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
p3 = p2 ;
disp ( ” p3=” )
disp ( p3 )
disp ( ” b a r ” )
p4 = p3 *( rho / r ) ^ y ;
disp ( ” p4=” )
disp ( p4 )
disp ( ” b a r ” )
T4 = T3 *( rho / r ) ^( y -1) ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
V4 = V1 ;
disp ( ”V4=” )
disp ( V4 )
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64 disp ( ”mˆ3 ” )
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66 disp ( ” ( i i ) T h e o r e t i c a l a i r s t a n d a r d e f f i c i e n c y =” )
67 n_diesel =1 -1/ y / r ^( y -1) *(( rho ^y -1) /( rho -1) ) ;
68 disp ( ” e f f i c i e n c y =” )
69 disp ( n_diesel )
70
71
72 disp ( ” ( i i i ) Mean e f f e c t i v e p r e s s u r e =” )
73 pm =( p1 * r ^ y *( y *( rho -1) - r ^(1 - y ) *( rho ^y -1) ) ) /( y -1) /( r
-1) ;
74 disp ( pm )
75 disp ( ” b a r ” )
76
77 disp ( ” ( i v ) Power o f t h e e n g i n e =” )
78 n =380; // number o f c y c l e s p e r min
79 P = n /60* pm * Vs *100; //kW
80 disp ( P )
81 disp ( ”kW” )
Scilab code Exa 13.22 22
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r1 =15.3; //V1/V2
r2 =7.5; //V4/V3
p1 =1; // b a r
T1 =300; //K
n_mech =0.8;
C =42000; // kJ / kg
y =1.4;
R =287;
cp =1.005;
cv =0.718;
V2 =1; // // Assuming V2=1 mˆ3
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T2 = T1 * r1 ^( y -1) ;
p2 = p1 * r1 ^ y ;
T3 = r1 / r2 * T2 ;
m = p2 *10^5* V2 / R / T2 ;
T4 = T3 / r2 ^( y -1) ;
Q_added = m * cp *( T3 - T2 ) ;
Q_rejected = m * cv *( T4 - T1 ) ;
W = Q_added - Q_rejected ;
pm = W /( r1 -1) / V2 /100;
disp ( ”Mean e f f e c t i v e p r e s s u r e =” )
disp ( pm )
disp ( ” b a r ” )
ratio = p2 / pm ;
disp ( ” R a t i o o f maximum p r e s s u r e t o mean e f f e c t i v e
p r e s s u r e =” )
31 disp ( ratio )
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33 n_cycle = W / Q_added ;
34 disp ( ” C y c l e e f f i c i e n c y =” )
35 disp ( n_cycle )
36
37 n_thI =0.5;
38 n_cycle1 = n_thI * n_cycle ;
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40 n_thB = n_mech * n_cycle1 ;
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42 BP =1;
43 mf = BP / C / n_thB *3600;
44 disp ( ” F u e l c o n s u m p t i o n p e r kWh =” )
45 disp ( mf )
46 disp ( ” kg /kWh” )
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Scilab code Exa 13.23 23
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Vs =0.0053; //mˆ3
Vc =0.00035; //mˆ3
V3 = Vc ;
V2 = V3 ;
p3 =65; // b a r
p4 =65; // b a r
T1 =353; //K
p1 =0.9; // b a r
y =1.4;
r =( Vs + Vc ) / Vc ;
rho =(5/100* Vs + V3 ) / V3 ;
p2 = p1 *( r ) ^ y ;
B = p3 / p2 ;
n_dual =1 -1/ r ^( y -1) *[( B * rho ^y -1) /(( B -1) + B * y *( rho -1) )
];
18 disp ( ” E f f i c i e n c y o f t h e c y c l e =” )
19 disp ( n_dual )
Scilab code Exa 13.24 24
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r =14;
B =1.4;
rho =6/100*( r -1) + 1;
y =1.4;
n_dual =1 -1/ r ^( y -1) *[( B * rho ^y -1) /(( B -1) + B * y *( rho -1) ) ]
disp ( ” E f f i c i e n c y o f t h e c y c l e =” )
disp ( n_dual )
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Scilab code Exa 13.25 25
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D =0.25; //m
r =9;
L =0.3; //m
cv =0.71; // kJ / kg K
cp =1; // kJ / kg K
p1 =1; // b a r
T1 =303; //K
p3 =60; // b a r
p4 = p3 ;
n =3; // number o f w o r k i n g c y c l e s / s e c
y =1.4;
R =287;
disp ( ” ( i ) A i r s t a n d a r d e f f i c i e n c y ” )
Vs = %pi /4* D ^2* L ;
Vc = Vs /( r -1) ;
V1 = Vs + Vc ;
p2 = p1 *( r ) ^ y ;
T2 = T1 * r ^( y -1) ;
T3 = T2 * p3 / p2 ;
rho =4/100*( r -1) +1;
T4 = T3 * rho ;
T5 = T4 *( rho / r ) ^( y -1) ;
p5 = p4 *( r / rho ) ^( y ) ;
Qs = cv *( T3 - T2 ) + cp *( T4 - T3 )
Qr = cv *( T5 - T1 ) ;
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33 n_airstandard =( Qs - Qr ) / Qs ;
34 disp ( ” e f f i c i e n c y =” )
35 disp ( n_airstandard )
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38 disp ( ” ( i i ) Power d e v e l o p e d by t h e e n g i n e ” )
39 m = p1 *10^5* V1 / R / T1 ;
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41 W = m *( Qs - Qr ) ;
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43 P = W * n ;
44 disp ( ”P=” )
45 disp ( P )
46 disp ( ”kW” )
Scilab code Exa 13.26 26
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clc
p1 =1; // b a r
T1 =363; //K
r =9;
p3 =68; // b a r
p4 =68; // b a r
Q =1750; // kJ / kg
y =1.4;
cv =0.71;
cp =1.0;
disp ( ” ( i ) P r e s s u r e s and t e m p e r a t u r e s a t s a l i e n t
p o i n t s ”)
p2 = p1 *( r ) ^ y ;
disp ( ” p2=” )
disp ( p2 )
disp ( ” b a r ” )
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T2 = T1 * r ^( y -1) ;
disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
disp ( ” p3=” )
disp ( p3 )
disp ( ” b a r ” )
disp ( ” p4=” )
disp ( p4 )
disp ( ” b a r ” )
T3 = T2 *( p3 / p2 ) ;
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
Q1 = cv *( T3 - T2 ) ; // h e a t added a t c o n s t a n t volume
Q2 =Q - Q1 ; // h e a t added a t c o n s t a n t p r e s s u r e
T4 = Q2 / cp + T3 ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
rho = T4 / T3 ; //V4/V3=T4/T3
p5 = p4 *( rho / r ) ^ y ;
disp ( ” p5=” )
disp ( p5 )
disp ( ” b a r ” )
T5 = T4 *( rho / r ) ^( y -1) ;
disp ( ”T5=” )
disp ( T5 )
disp ( ”K” )
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57 disp ( ” ( i i ) A i r s t a n d a r d e f f i c i e n c y =” )
58 Qr = cv *( T5 - T1 ) ;
59 n_airstandard =( Q - Qr ) / Q ;
60 disp ( n_airstandard )
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63 disp ( ” ( i i i ) Mean e f f e c t i v e p r e s s u r e =” )
64 pm =1/( r -1) *( p3 *( rho -1) + ( p4 * rho - p5 * r ) /( y -1) - ( p2 -
p1 * r ) /( y -1) ) ;
65 disp ( pm )
66 disp ( ” b a r ” )
Scilab code Exa 13.27 27
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T1 =300; //K
r =15;
y =1.4;
// p3 / p1=70
T2 = T1 *( r ) ^( y -1) ;
// p2 / p1=r ˆ y
// p2 = 44. 3 ∗ p1
T3 =1400; //K ; T3=T2∗ p3 / p2
T4 = T3 + ( T3 - T2 ) / y ;
// v1 / v3 =15
// v4 = 0 . 0 8 4 ∗ v1
// v5=v1
//T5=T4 ∗ ( v5 / v1 ) ˆ ( y −1)
T5 =656.9; //K
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n_airstandard =1 -( T5 - T1 ) /(( T3 - T2 ) + y *( T4 - T3 ) ) ;
disp ( ” E f f i c i e n c y =” )
disp ( n_airstandard )
disp ( ” R e a s o n s f o r a c t u a l t h e r m a l e f f i c i e n c y b e i n g
d i f f e r e n t from t h e t h e o r e t i c a l v a l u e : ” )
disp ( ” 1 . I n t h e o r e t i c a l c y c l e w o r k i n g s u b s t a n c e i s
taken a i r whereas in a c t u a l c y c l e a i r with f u e l
a c t s as working substance ”)
disp ( ” 2 . The f u e l c o m b u s t i o n phenomenon and
a s s o c i a t e d problems l i k e d i s s o c i a t i o n of gases ,
d i l u t i o n of charge during suction stroke , etc .
have n o t b e e n t a k e n i n t o a c c o u n t ” )
disp ( ” 3 . E f f e c t o f v a r i a b l e s p e c i f i c h e a t , h e a t l o s s
t h r o u g h c y l i n d e r w a l l s , i n l e t and e x h a u s t
v e l o c i t i e s o f a i r / g a s e t c . have n o t b e e n t a k e n
i n t o account . ”)
Scilab code Exa 13.28 28
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T1 =373; //K
p1 =1; // b a r
p3 =65; // b a r
p4 = p3 ;
Vs =0.0085; //mˆ3
ratio =21; // A i r f u e l r a t i o
r =15;
C =43890; // kJ / kg
cp =1;
cv =0.71;
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V2 =0.0006; //mˆ3
V1 =0.009; //mˆ3
y =1.41;
V5 = V1 ;
V3 = V2 ;
R =287;
p2 = p1 *( r ) ^ y ;
T2 = T1 * r ^( y -1) ;
T3 = T2 * p3 / p2 ;
m = p1 *10^5* V1 / R / T1 ;
Q1 = m * cv *( T3 - T2 ) ; // Heat added d u r i n g c o n s t a n t volume
p r o c e s s 2−3
25 amt = Q1 / C ; // Amount o f f u e l added d u r i n g t h e c o n s t a n t
volume p r o c e s s 2−3
26 total = m / ratio ; // T o t a l amount o f f u e l added
27 quantity = total - amt ; // Q u a n t i t y o f f u e l added d u r i n g
t h e p r o c e s s 3−4
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29 Q2 = quantity * C ; // Heat added d u r i n g c o n s t a n t
pressure
process
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T4 = Q2 /( m + total ) / cp + T3 ;
V4 = V3 * T4 / T3 ;
T5 = T4 *( V4 / V5 ) ^( y -1) ;
Q3 =( m + total ) * cv *( T5 - T1 ) ; // Heat r e j e c t e d d u r i n g
c o n s t a n t volume p r o c e s s 5−1
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37 W =( Q1 + Q2 ) - Q3 ;
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39 n_th = W /( Q1 + Q2 ) ;
40 disp ( ” Thermal e f f i c i e n c y =” )
41 disp ( n_th )
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Scilab code Exa 13.29 29
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T1 =303; //K
p1 =1; // b a r
rc =9;
re =5;
n =1.25;
D =0.25; //m
L =0.4; //m
R =287;
cv =0.71;
cp =1;
num =8; // no . 0 f c y c l e s / s e c
disp ( ” ( i ) P r e s s u r e and t e m p e r a t u r e s a t a l l
p o i n t s =” )
p2 = p1 *( rc ) ^ n ;
disp ( ” p2=” )
disp ( p2 )
disp ( ” b a r ” )
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20 T2 = T1 *( rc ) ^( n -1) ;
21 disp ( ”T2=” )
22 disp ( T2 )
23 disp ( ”K” )
24
25 //T4 =1.8∗ T3
26 // Heat l i b e r a t e d a t c o n s t a n t
p r e s s u r e= 2
l i b e r a t e d a t c o n s t a n t volume
27 // cp ∗ ( T4−T3 ) =2∗ cv ∗ ( T3−T2 )
28 //T4/T3 =1.8
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30 rho = rc / re ;
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salient
heat
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T3 =1201.9; //K
disp ( ”T3=” )
disp ( T3 )
disp ( ”K” )
p3 = p2 * T3 / T2 ;
disp ( ” p3=” )
disp ( p3 )
disp ( ” b a r ” )
p4 = p3 ;
disp ( ” p4=” )
disp ( p4 )
disp ( ” b a r ” )
T4 =1.8* T3 ;
disp ( ”T4=” )
disp ( T4 )
disp ( ”K” )
p5 = p4 *(1/ re ) ^( n ) ;
disp ( ” p5=” )
disp ( p5 )
disp ( ” b a r ” )
T5 = T4 *(1/ re ) ^( n -1)
disp ( ”T5=” )
disp ( T5 )
disp ( ”K” )
disp ( ” ( i i ) Mean e f f e c t i v e p r e s s u r e = ” )
pm =1/( rc -1) *[ p3 *( rho -1) +( p4 * rho - p5 * rc ) /( n -1) -( p2 - p1 *
rc ) /( n -1) ];
64 disp ( pm )
65 disp ( ” b a r ” )
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disp ( ” ( i i i ) E f f i c i e n c y o f t h e c y c l e ” )
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Vs = %pi /4* D ^2* L ;
W = pm *10^5* Vs /1000;
V1 = rc /( rc -1) * Vs
m = p1 *10^5* V1 / R / T1 ;
Q = m *( cv *( T3 - T2 ) + cp *( T4 - T3 ) ) ;
Efficiency = W / Q ;
disp ( ” E f f i c i e n c y =” )
disp ( Efficiency )
disp ( ” ( i v ) Power o f t h e e n g i n e =” )
P = W * num ;
disp ( P )
disp ( ”kW” )
Scilab code Exa 13.30 30
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v =10:1:100;
function p = f ( v )
p =1/ v ^1.4;
endfunction
plot (v , f )
v =[10 20]
p =[ f (10) f (10) ]
plot (v ,p , ’ r ’ )
v =20:1:100;
function p = fa ( v )
p =2.6515/ v ^1.4;
endfunction
plot (v , fa , ’ g ’ )
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v =[100 100]
p =[ f (100) fa (100) ]
plot (v ,p , ’−−p ’ )
v =[15 15]
p =[ f (15) 0.040]
plot (v ,p , ’−− ’ )
v =[20 20]
p =[ f (20) 0.040]
plot (v ,p , ’−−r ’ )
xtitle ( ”p−v d i a g r a m ” , ” v ” , ” p” )
legend ( ”1−2b ” ,” 2b−3” , ”3−4” , ”4−1” , ” 2 a−3a ” , ”2−3” )
// The a i r −s t a n d a r d Otto , Dual and D i e s e l c y c l e s a r e
drawn on common p−v and T−s d i a g r a m s f o r t h e same
maximum p r e s s u r e and maximum t e m p e r a t u r e , f o r
the purpose of comparison .
34 // Otto 1−2−3−4−1
35 // Dual 1−2a−3a−3−4−1
36 // D i e s e l 1−2b−3−4−1
37
38
39 xset ( ’ window ’ , 1)
40
41 s =10:1:50;
42 function T = fb ( s )
43
T = s ^2
44 endfunction
45 plot (s , fb )
46
47 s =10:1:50;
48 function T = fc ( s )
49
T =( s +30) ^2
50 endfunction
51 plot (s , fc , ’ r ’ )
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s =[12 12];
T =[ fb (12) fc (12) ];
plot (s ,T , ’−−p ’ )
s =[45 45];
T =[ fb (45) fc (45) ]
plot (s ,T , ’m ’ )
s =10:1:27;
T =5*( s ) ^2;
plot (s ,T , ’ g ’ )
s =10:1:20;
T =7* s ^2;
plot (s ,T , ’−−r ’ )
xtitle ( ”T−s d i a g r a m ” , ” s ” , ”T” )
legend ( ”1−4” , ” 2b−3” , ”1−2b ” , ”3−4” , ”2−3” , ” 2 a−3a ” )
// The c o n s t r u c t i o n o f c y c l e s on T−s d i a g r a m p r o v e s
that f o r the given c o n d i t i o n s the heat r e j e c t e d
i s same f o r a l l t h e t h r e e c y c l e s ( a r e a u n d e r
p r o c e s s l i n e 4 −1) .
73 //
=1−(Heat r e j e c t e d ) / ( Heat s u p p l i e d )=1− c o n s t a n t /
Qs
74
75
// The c y c l e w i t h g r e a t e r h e a t a d d i t i o n w i l l be more
efficient .
76 // From t h e T−s d i a g r a m
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// Qs ( d i e s e l ) = Area u n d e r 2b−3
// Qs ( d u a l ) = Area u n d e r 2 a−3a−3
// Qs ( o t t o ) = Area u n d e r 2 −3.
// Qs ( d i e s e l ) > Qs ( d u a l ) > Qs ( o t t o )
disp ( ” Thus ,
diesel
>
dual
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>
otto
”)
Scilab code Exa 13.31 31
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cp =0.92;
cv =0.75;
y =1.22; // y=cp / cv
p1 =1; // b a r
p2 = p1 ;
p3 =4; // b a r
p4 =16; // b a r
T2 =300; //K
T3 = T2 *( p3 / p2 ) ^(( y -1) / y ) ;
T4 = p4 / p3 * T3 ;
T1 = T4 /( p4 / p1 ) ^(( y -1) / y ) ;
disp ( ” ( i ) Work done p e r kg o f g a s ” )
Q_supplied = cv *( T4 - T3 ) ;
Q_rejected = cp *( T1 - T2 ) ;
W = Q_supplied - Q_rejected ;
disp ( ”W=” )
disp ( W )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) E f f i c i e n c y o f t h e c y c l e =” )
n = W / Q_supplied ;
disp ( n )
Scilab code Exa 13.32 32
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p1 =101.325; // kPa
T1 =300; //K
rp =6;
y =1.4;
T2 = T1 * rp ^(( y -1) / y ) ;
//T3/T4=r p ˆ ( ( y −1) / y )
//T4=T3 / 1 . 6 6 8
//W T=2.5∗W C
T3 =2.5*( T2 - T1 ) /(1 -1/1.668) ;
disp ( ” ( i ) Maximum t e m p e r a t u r e i n t h e c y c l e =” )
disp ( T3 )
disp ( ”K” )
disp ( ” ( i i ) C y c l e e f f i c i e n c y ” )
T4 = T3 /1.668;
n_cycle =(( T3 - T4 ) - ( T2 - T1 ) ) /( T3 - T2 ) ;
disp ( ” C y c l e e f f i c i e n c y =” )
disp ( n_cycle )
Scilab code Exa 13.33 33
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p1 =1; // b a r
p2 =5; // b a r
T3 =1000; //K
cp =1.0425; // kJ / kg K
cv =0.7662; // kJ / kg K
y = cp / cv ;
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disp ( ” ( i ) T e m p e r a t u r e e n t r o p y d i a g r a m ” )
s =10:1:50;
function T = fb ( s )
T = s ^2
endfunction
plot (s , fb , ’−− ’ )
s =10:1:50;
function T = fc ( s )
T =( s +30) ^2
endfunction
plot (s , fc , ’ r ’ )
s =[12 12];
T =[ fb (12) fc (12) ];
plot (s ,T , ’m ’ )
s =[45 45];
T =[ fb (45) fc (45) ]
plot (s ,T , ’ g ’ )
xtitle ( ”T−s d i a g r a m ” , ” s ” , ”T” )
legend ( ” p1=1 b a r ” , ” p2=5 b a r ” , ”1−2” , ”3−4” )
disp ( ” ( i i ) Power r e q u i r e d =” )
T4 = T3 *( p1 / p2 ) ^(( y -1) / y ) ;
P = cp *( T3 - T4 ) ;
disp ( ”P=” )
disp ( P )
disp ( ”kW” )
Scilab code Exa 13.34 34
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clc
m =0.1; // kg / s
p1 =1; // b a r
T4 =285; //K
p2 =4; // b a r
cp =1; // kJ / kg K
y =1.4;
T3 = T4 *( p2 / p1 ) ^(( y -1) / y ) ;
disp ( ” T e m p e r a t u r e a t t u r b i n e i n l e t =” )
disp ( T3 )
disp ( ”K” )
P = m * cp *( T3 - T4 ) ;
disp ( ” Power d e v e l o p e d =” )
disp ( P )
disp ( ”kW” )
Scilab code Exa 13.35 35
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y =1.4;
cp =1.005; // kJ / kg K
p1 =1; // b a r
T1 =293; //K
p2 =3.5; // b a r
T3 =873; //K
rp = p2 / p1 ;
disp ( ” ( i ) E f f i c i e n c y o f t h e c y c l e =” )
n_cycle =1 -1/ rp ^(( y -1) / y ) ;
disp ( n_cycle )
disp ( ” ( i i ) Heat s u p p l i e d t o a i r =” )
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T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
Q1 = cp *( T3 - T2 ) ;
disp ( Q1 )
disp ( ” kJ / kg ” )
disp ( ” ( i i i ) Work a v a i l a b l e a t t h e s h a f t =” )
W = n_cycle * Q1 ;
disp ( W )
disp ( ” kJ / kg ” )
disp ( ” ( i v ) Heat r e j e c t e d i n t h e c o o l e r =” )
Q2 = Q1 - W ;
disp ( Q2 )
disp ( ” kJ / kg ” )
disp ( ” ( v ) T e m p e r a t u r e o f a i r l e a v i n g t h e t u r b i n e =” )
T4 = T3 / rp ^(( y -1) / y ) ;
disp ( T4 )
disp ( ”K” )
Scilab code Exa 13.36 36
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clc
T1 =303; //K
T3 =1073; //K
C =45000; // kJ / kg
cp =1; // kJ / kg K
y =1.4;
T2 = sqrt ( T1 * T3 ) ;
T4 = T2 ;
// W turbine −W c om pr e ss or=m f ∗C∗n =100;
m_f =100/ C /(1 -( T4 - T1 ) /( T3 - T2 ) ) ;
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14 disp ( ” m f=” )
15 disp ( m_f )
16 disp ( ” kg / s ” )
17
18 m_a =(100 - m_f *( T3 - T4 ) ) /( T3 - T4 - T2 + T1 ) ;
19 disp ( ” m a=” )
20 disp ( m_a )
21 disp ( ” kg / s ” )
Scilab code Exa 13.37 37
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clc
T1 =300; //K
p1 =1; // b a r
rp =6.25;
T3 =1073; //K
n_comp =0.8;
n_turbine =0.8;
cp =1.005; // kJ / kg K
y =1.4;
T2 = T1 *( rp ) ^(( y -1) / y ) ;
// L e t T2’= T2a
T2a =( T2 - T1 ) / n_comp + T1 ;
W_comp = cp *( T2a - T1 ) ;
disp ( ” C o m p r e s s o r work =” )
disp ( W_comp )
disp ( ” kJ / kg ” )
T4 = T3 / rp ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
W_turbine = cp *( T3 - T4a ) ;
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25 disp ( ” T u r b i n e work =” )
26 disp ( W_turbine )
27 disp ( ” kJ / kg ” )
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29 Q_s = cp *( T3 - T2a ) ;
30 disp ( ” Heat s u p p l i e d =” )
31 disp ( Q_s )
32 disp ( ” kJ / kg ” )
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34 W_net = W_turbine - W_comp ;
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36 n_cycle = W_net / Q_s *100;
37 disp ( ” n c y c l e ” )
38 disp ( n_cycle )
39 disp ( ”%” )
40
41 t4a = T4a -273;
42 disp ( ” T u r b i n e e x h a u s t t e m p e r a t u r e =” )
43 disp ( t4a )
44 disp ( ” 0C” )
Scilab code Exa 13.38 38
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clc
n_turbine =0.85;
n_compressor =0.80;
T3 =1148; //K
T1 =300; //K
cp =1; // kJ / kg K
y =1.4;
p1 =1; // b a r
p2 =4; // b a r
C =42000; // kJ / kg K
n_cc =0.90;
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13 T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
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15 T2a =( T2 - T1 ) / n_compressor + T1 ;
16
17 ratio =0.9* C / cp /( T3 - T2a ) - 1; // r a t i o =ma/ mf
18 disp ( ”A/F r a t i o =” )
19 disp ( ratio )
Scilab code Exa 13.39 39
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clc
cp =1.005; // kJ / kg K
y1 =1.4;
y2 =1.333;
p1 =1; // b a r
p4 = p1 ;
T1 =300; //K
p2 =6.2; // b a r
p3 = p2 ;
n_compressor =0.88;
C =44186; // kJ / kg
ratio =0.017; // Fuel −a i r r a t i o ; kJ / kg o f a i r
n_turbine =0.9; //
cpg =1.147;
T2 = T1 *( p2 / p1 ) ^(( y1 -1) / y1 ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ; //T2 ’
T3 = ratio * C /(1+ ratio ) / cp + T2a ;
T4 = T3 *( p4 / p3 ) ^(( y2 -1) / y2 ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
W_compressor = cp *( T2a - T1 ) ;
W_turbine = cpg *( T3 - T4a ) ;
W_net = W_turbine - W_compressor ;
Qs = ratio * C ;
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n_th = W_net / Qs *100;
disp ( ” Thermal e f f i c i e n c y =” )
disp ( n_th )
disp ( ”%” )
Scilab code Exa 13.40 40
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clc
cp =1; // kJ / kg K
y =1.4;
C =41800; // kJ / kg
p1 =1; // b a r
T1 =293; //K
p2 =4; // b a r
p4 = p1 ;
p3 = p2 ;
n_compressor =0.80;
n_turbine =0.85;
ratio =90; // Air −F u e l r a t i o
m_a =3; // kg / s
disp ( ” ( i ) Power d e v e l o p e d ” )
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ;
T3 = C /(1+ ratio ) / cp + T2a ;
T4 = T3 *( p4 / p3 ) ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
W_turbine =( ratio +1) / ratio * cp *( T3 - T4a ) ;
W_compressor = cp *( T2a - T1 ) ;
W_net = W_turbine - W_compressor ;
Qs =1/ ratio * C ;
P = m_a * W_net ;
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disp ( ” Power=” )
disp ( P )
disp ( ”kW/ kg o f a i r ” )
disp ( ” ( i i ) Thermal e f f i c i e n c y o f c y c l e =” )
n_thermal = W_net / Qs ;
disp ( n_thermal )
disp ( ”%” )
Scilab code Exa 13.41 41
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clc
T1 =288; //K
T3 =883; //K
rp =6; // r p=p2 / p1
n_compressor =0.80;
n_turbine =0.82;
m_a =16; // kg / s
cp1 =1.005; // kJ / kg K, For c o m p r e s s i o n p r o c e s s
y1 =1.4; // For c o m p r e s s i o n p r o c e s s
cp2 =1.11; // kJ / kg K
y2 =1.333;
T2 = T1 *( rp ) ^(( y1 -1) / y1 ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ;
T4 = T3 / rp ^(( y2 -1) / y2 ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
W_compressor = cp1 *( T2a - T1 ) ;
W_turbine = cp2 *( T3 - T4a ) ;
W_net = W_turbine - W_compressor ;
Power = m_a * W_net ;
disp ( ” Power =” )
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disp ( Power )
disp ( ”kW” )
Scilab code Exa 13.42 42
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cp =1.11;
T3 =883; //K
T2a =529; //K
W_turbine =290.4; // kJ / kg
W_net =48.2; // kJ / kg
Qs = cp *( T3 - T2a ) ;
n_thermal = W_net / Qs *100;
disp ( ” Thermal e f f i c i e n c y =” )
disp ( n_thermal )
disp ( ”%” )
W_ratio = W_net / W_turbine ; // Work r a t i o =n e t work
o u t p u t / G r o s s work o u t p u t
16 disp ( ”Work r a t i o =” )
17 disp ( W_ratio )
Scilab code Exa 13.43 43
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p1 =1; // b a r
p2 =5; // b a r
p3 =4.9; // b a r
p4 =1; // b a r
T1 =293; //K
T3 =953; //K
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n_compressor =0.85;
n_turbine =0.80;
n_combustion =0.85;
y =1.4;
cp =1.024; // kJ / kg K
P =1065; //kW
disp ( ” ( i ) The q u a n t i t y o f a i r c i r c u l a t i o n ” )
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ;
T4 = T3 *( p4 / p3 ) ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
W_compressor = cp *( T2a - T1 ) ;
W_turbine = cp *( T3 - T4a ) ;
W_net = W_turbine - W_compressor ;
m_a = P / W_net ;
disp ( ” m a =” )
disp ( m_a )
disp ( ” kg ” )
disp ( ” ( i i ) Heat s u p p l i e d p e r kg o f a i r c i r c u l a t i o n =
”)
32 Qs = cp *( T3 - T2a ) / n_combustion ;
33 disp ( Qs )
34 disp ( ” kJ / kg ” )
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disp ( ” ( i i i ) Thermal e f f i c i e n c y o f t h e c y c l e =” )
n_thermal = W_net / Qs *100;
disp ( n_thermal )
disp ( ”%” )
351
Scilab code Exa 13.44 44
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m_a =20; // kg / s
T1 =300; //K
T3 =1000; //K
rp =4; // r p=p2 / p1
cp =1; // kJ / kg K
y =1.4;
T2 = T1 *( rp ) ^(( y -1) / y ) ;
T4 = T3 - T2 + T1 ;
// p5 / p4=(p5 / p3 ) ∗ ( p3 / p4 )
// l e t p3 / p4=r 1
r1 =( T3 / T4 ) ^( y /( y -1) ) ;
// r 2=p5 / p4 ;
r2 =1/4* r1 ;
P_ratio =1/ r2 ; // P r e s s u r e r a t i o o f low p r e s s u r e
turbine
19 disp ( ” P r e s s u r e r a t i o o f low p r e s s u r e t u r b i n e =” )
20 disp ( P_ratio )
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22 T5 = T4 /( P_ratio ) ^(( y -1) / y ) ;
23 disp ( ” T e m p e r a t u r e o f t h e e x h a u s t from t h e u n i t =” )
24 disp ( T5 )
25 disp ( ”K” )
Scilab code Exa 13.45 45
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T1 =288; //K
p1 =1.01; // b a r
rp =7;
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p2 = rp * p1 ;
p3 = p2 ;
p5 = p1 ;
n_compressor =0.82;
n_turbine =0.85;
n_turbine =0.85;
T3 =883; //K
cpa =1.005;
cpg =1.15;
y1 =1.4;
y2 =1.33;
disp ( ” ( i ) P r e s s u r e and t e m p e r a t u r e o f t h e g a s e s
e n t e r i n g t h e power t u r b i n e =” )
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19 T2 = T1 * rp ^(( y1 -1) / y1 ) ;
20 T2a =( T2 - T1 ) / n_compressor + T1 ;
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22 W_compressor = cpa *( T2a - T1 ) ;
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24 T4a =( cpg * T3 - W_compressor ) / cpg ;
25 disp ( ” T e m p e r a t u r e o f g a s e s e n t e r i n g t h e power
t u r b i n e =” )
26 disp ( T4a )
27 disp ( ”K” )
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29 T4 = T3 -( T3 - T4a ) / n_turbine ;
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31 p4 = p3 /( T3 / T4 ) ^( y2 /( y2 -1) ) ;
32 disp ( ” P r e s s u r e o f g a s e s e n t e r i n g t h e power t u r b i n e =
”)
33 disp ( p4 )
34 disp ( ” b a r ” )
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37 disp ( ” ( i i ) Net power d e v e l o p e d p e r kg / s mass f l o w ” )
38 T5 = T4a /( p4 / p5 ) ^(( y2 -1) / y2 ) ;
39 T5a = T4a - n_turbine *( T4a - T5 ) ;
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41 W_turbine = cpg *( T4a - T5a ) ;
42 disp ( ” Net power d e v e l o p e d p e r kg / s mass f l o w =” )
43 disp ( W_turbine )
44 disp ( ”kW” )
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47 disp ( ” ( i i i ) Work r a t i o =” )
48 W_ratio = W_turbine /( W_turbine + W_compressor ) ;
49 disp ( W_ratio )
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52 disp ( ” ( i v ) Thermal e f f i c i e n c y o f t h e u n i t ” )
53 Qs = cpg *( T3 - T2a ) ;
54 n_thermal = W_turbine / Qs *100;
55 disp ( ” n t h e r m a l =” )
56 disp ( n_thermal )
57 disp ( ”%” )
Scilab code Exa 13.46 46
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T1 =288; //K
rp =4; // r p=p2 / p1=p3 / p4
n_compressor =0.82;
e =0.78; // E f f e c t i v e n e s s o f t h e h e a t e x c h a n g e r
n_turbine =0.70;
T3 =873; //K
y =1.4;
R =0.287;
T2 = T1 *( rp ) ^(( y -1) / y ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ;
T4 = T3 / rp ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
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16 cp = R * y /( y -1) ;
17 W_compressor = cp *( T2a - T1 ) ;
18 W_turbine = cp *( T3 - T4a ) ;
19 W_net = W_turbine - W_compressor ;
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21 T5 = e *( T4a - T2a ) + T2a ;
22 Qs = cp *( T3 - T5 ) ;
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24 n_cycle = W_net / Qs *100;
25 disp ( ” E f f i c i e n c y =” )
26 disp ( n_cycle )
27 disp ( ”%” )
Scilab code Exa 13.47 47
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// S i m p l e c y c l e
p2 =4; // b a r
p1 =1; // b a r
T1 =293;
n_compressor =0.8;
n_turbine =0.85;
ratio =90; // A i r F u e l r a t i o
C =41800; // kJ / kg
cp =1.024;
p4 =1.01; // b a r
p3 =3.9; // b a r
y =1.4;
e =0.72; // t h e r m a l r a t i o
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
T2a =( T2 - T1 ) / n_compressor + T1 ;
T3 = C / cp /( ratio +1) +471;
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T4 = T3 *( p4 / p3 ) ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
n_thermal1 =(( T3 - T4a ) -( T2a - T1 ) ) /( T3 - T2a ) *100;
disp ( ” Thermal e f f i c i e n c y o f s i m p l e c y c l e=” )
disp ( n_thermal1 )
disp ( ”%” )
// Heat e x c h a n g e r c y c l e
T2a =471; // K ( a s f o r s i m p l e c y c l e )
T3 =919.5; // K ( a s f o r s i m p l e c y c l e )
p3 =4.04 -0.14 -0.05; // b a r
p4 =1.01+0.05; // b a r
T4 = T3 *( p4 / p3 ) ^(( y -1) / y ) ;
T4a = T3 - n_turbine *( T3 - T4 ) ;
T5 = e *( T4a - T2a ) + T2a ;
n_thermal2 =(( T3 - T4a ) - ( T2a - T1 ) ) /( T3 - T5 ) *100;
disp ( ” Thermal e f f i c i e n c y o f h e a t e x c h a n g e r c y c l e =” )
disp ( n_thermal2 )
disp ( ”%” )
dn = n_thermal2 - n_thermal1 ;
disp ( ” I n c r e a s e i n t h e r m a l e f f i c i e n c y =” )
disp ( dn )
disp ( ”%” )
Scilab code Exa 13.48 48
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T1 =293; //K
T6 =898; //K
T8 = T6 ;
n_c =0.8; // E f f i c i e n c y o f e a c h c o m p r e s s o r s t a g e
n_t =0.85; // E f f i c i e n c y o f e a c h t u r b i n e s t a g e
n_mech =0.95;
e =0.8;
cpa =1.005; // kJ / kg K
cpg =1.15; // kJ / kg K
y1 =1.4;
y2 =1.333;
disp ( ” ( i ) Thermal e f f i c i e n c y ” )
T3 = T1 ;
// p2 / p1=s q r t ( 9 ) =3
T2 = T1 *(3) ^(( y1 -1) / y1 ) ;
T2a =( T2 - T1 ) / n_c + T1 ;
T4a = T2a ;
W_c = cpa *( T2a - T1 ) ; // Work i n p u t p e r c o m p r e s s o r s t a g e
W_t =2* W_c / n_mech ; // Work o u t p u t o f H . P . t u r b i n e
T7a = T6 - W_t / cpg ;
T7 = T6 -( T6 - T7a ) / n_t ;
// ( p6 / p7 ) =(T6/T7 ) ˆ ( y2 / ( y2 −1) ) = 4 . 8 2 ;
// p8 / p9 = 9 / 4 . 8 2 = 1 . 8 6
T9 = T8 /(1.86) ^(( y2 -1) / y2 ) ;
T9a = T8 - n_t *( T8 - T9 ) ;
W = cpg *( T8 - T9a ) * n_mech ; // Net work o u t p u t
T5 = e *( T9a - T4a ) + T4a ;
Q = cpg *( T6 - T5 ) + cpg *( T8 - T7a ) ; // Heat s u p p l i e d
n_thermal = W / Q *100;
disp ( ” n t h e r m a l =” )
disp ( n_thermal )
disp ( ”%” )
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40 disp ( ” ( i i ) Work r a t i o ” )
41 Gross_work = W_t + W / n_mech ;
42 W_ratio = W / Gross_work ;
43 disp ( ”Work r a t i o =” )
44 disp ( W_ratio )
45
46
47 disp ( ” ( i i i ) Mass f l o w r a t e =” )
48 m =4500/ W ;
49 disp ( m )
50 disp ( ” kg / s ” )
Scilab code Exa 13.49 49
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T1 =293; //K
T5 =1023; //K
T7 = T5 ;
p1 =1.5; // b a r
p2 =6; // b a r
n_c =0.82;
n_t =0.82;
e =0.70;
P =350; //kW
cp =1.005; // kJ / kg K
y =1.4;
T3 = T1 ;
px = sqrt ( p1 * p2 ) ;
T2 = T1 *( px / p1 ) ^(( y -1) / y ) ;
T2a = T1 +( T2 - T1 ) / n_c ;
T4a = T2a ;
p5 = p2 ;
T6 = T5 /( p5 / px ) ^(( y -1) / y ) ;
T6a = T5 - n_t *( T5 - T6 ) ;
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T8a = T6a ;
Ta = T4a + e *( T8a - T4a ) ;
W_net =2* cp *[( T5 - T6a ) -( T2a - T1 ) ];
Q1 = cp *( T5 - T4a ) + cp *( T7 - T6a ) ; // Without r e g e n e r a t o r
Q2 = cp *( T5 - Ta ) + cp *( T7 - T6a ) ;
disp ( ” n t h e r m a l w i t h o u t r e g e n e r a t o r =” )
n1 = W_net / Q1 *100;
disp ( n1 )
disp ( ”%” )
disp ( ” n t h e r m a l woth r e g e n e r a t o r =” )
n2 = W_net / Q2 *100;
disp ( n2 )
disp ( ”%” )
disp ( ” ( i i i ) Mass o f f l u i d c i r c u l a t e d =” )
m = P / W_net ;
disp ( m )
disp ( ” kg / s ” )
359
Chapter 14
Refrigeration Cycles
Scilab code Exa 14.1 1
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T2 =235; //K
P =1.3; //kW
disp ( ” ( i ) C . O . P . o f C a r n o t r e f r i g e r a t o r =” )
COP =14000/ P /60/60;
disp ( COP )
disp ( ” ( i i ) H i g h e r t e m p e r a t u r e o f t h e c y c l e =” )
T1 = T2 / COP + T2 ;
t1 = T1 -273;
disp ( t1 )
disp ( ” 0C” )
disp ( ” ( i i i ) Heat d e l i v e r e d a s h e a t pump” )
Qabs =14000/60; // Heat a b s o r b e d
W = P *60;
Q = Qabs + W ;
disp ( ”Q=” )
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22 disp ( Q )
23 disp ( ” kJ / min ” )
24
25 COP = Q / W ;
26 disp ( ”COP o f h e a t pump =” )
27 disp ( COP )
Scilab code Exa 14.2 2
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T1 =308; //K
T2 =258; //K
capacity =12; // t o n n e
COP = T2 /( T1 - T2 ) ;
disp ( ” ( i ) Co− e f f i c i e n t o f p e r f o r m a n c e =” )
disp ( COP )
disp ( ” ( i i ) Heat r e j e c t e d from t h e s y s t e m p e r h o u r ” )
W = capacity *14000/5.16;
Q = capacity *14000+ W ;
disp ( ”Q=” )
disp ( Q )
disp ( ” kJ / h ” )
disp ( ” ( i i i ) Power r e q u i r e d =” )
P = W /60/60;
disp ( P )
disp ( ”kW” )
Scilab code Exa 14.3 3
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T2 =268; //K
T1 =308; //K
Q =29; // Heat l e a k a g e from t h e s u r r o u n d i n g s i n t o t h e
c o l d s t o r a g e i n kW
5 COP_ideal = T2 /( T1 - T2 ) ;
6 COP_actual =1/3* COP_ideal ;
7
8 W = Q / COP_actual ;
9 disp ( ” Power r e q u i r e d =” )
10 disp ( W )
11 disp ( ”kW” )
Scilab code Exa 14.4 4
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T1 =293; //K
T2 =265; //K
T0 =273; //K
L =335; // L a t e n t h e a t o f i c e i n kJ / kg
cpw =4.18;
COP = T2 /( T1 - T2 ) ;
Rn = cpw *( T1 - T0 ) + L ;
m_ice = COP *3600/ Rn ;
disp ( ” i c e f o r m e d p e r kWh =” )
disp ( m_ice )
disp ( ” kg ” )
Scilab code Exa 14.5 5
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2 T1 =291; //K
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T2 =265; //K
T0 =273; //K
cpw =4.18; // kJ / kg
cpi =2.09; // kJ / kg
L =334; // kJ / kg
m =400; // kg
COP = T2 /( T1 - T2 ) ;
Rn = cpw *( T1 - T0 ) + L + cpi *( T0 - T2 ) ;
W = Rn * m / COP /3600; // kJ / s
disp ( ” L e a s t power =” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 14.6 6
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cpw =4.18; // kJ / kg
disp ( ” ( i ) Q u a n t i t y o f i c e p r o d u c e d ” )
t =20; // 0C
L =335; // kJ / kg
capacity =280; // t o n n e s
Q1 = cpw * t + L ; // Heat t o be e x t r a c t e d p e r kg o f w a t e r
( t o form i c e a t 0 C )
10 Rn = capacity *14000; // kJ /h
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m_ice = Rn *24/ Q1 /1000;
disp ( ” Q u a n t i t y o f i c e p r o d u c e d i n 24 h o u r s =” )
disp ( m_ice )
disp ( ” t o n n e s ” )
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disp ( ” ( i i ) Minimum power r e q u i r e d =” )
T1 =298; //K
T2 =263; //K
COP = T2 /( T1 - T2 ) ;
W = Rn / COP /3600; // kJ / s
disp ( ” Power r e q u i r e d =” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 14.7 7
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cp1 =1.25; // kJ / kg 0C
cp2 =2.93; // kJ / kg 0C
L =232; // kJ / kg
T1 = -3; // 0C
T2 = -8; // 0C
T3 =25; // 0C
Q1 = cp2 *( T3 - T1 ) + L + cp1 *( T1 - T2 ) ; // Heat removed i n
8 h o u r s from e a c h kg o f f i s h
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11 Q = Q1 *20*1000/8; // Heat removed by t h e p l a n t / min
12
13 disp ( ” ( i ) C a p a c i t y o f t h e r e f r i g e r a t i n g p l a n t =” )
14 capacity = Q /14000; // t o n n e s
15 disp ( capacity )
16 disp ( ” t o n n e s ” )
17
18 disp ( ” ( i i ) C a r n o t c y c l e C . O. P . b e t w e e n t h i s
temperature range . ”)
19 T1 =298; //K
20 T2 =265; //K
21
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22 COP = T2 /( T1 - T2 ) ;
23 disp ( ”COP o f r e v e r s e d c a r n o t c y c l e =” )
24 disp ( COP )
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27 disp ( ” ( i i i ) Power r e q u i r e d ” )
28 COP_actual =1/3* COP ;
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30 W = Q / COP_actual /3600; // kJ / s
31 disp ( ” Power =” )
32 disp ( W )
33 disp ( ”kW” )
Scilab code Exa 14.8 8
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T1 =1273; //K
T2 =298; //K
T3 =268; //K
T4 =298; //K
// L e t Q2/Q1=r1 , r 2=Q3/Q4 ;
r1 =298/1273; //Q2/Q1
r2 =268/298; //Q3/Q4
// L e t Q4/Q1=r
r =(1 - r1 ) /(1 - r2 ) ;
disp ( ” The r a t i o i n which t h e h e a t pump and h e a t
e n g i n e s h a r e t h e h e a t i n g l o a d =” )
14 disp ( r )
Scilab code Exa 14.9 9
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y =1.4;
n =1.35;
cp =1.003; // kJ / kg K
p2 =1; // b a r
p1 =8; // b a r
T3 =282; //K
T4 =302; //K
T1 = T4 ;
T4 = T3 *( p1 / p2 ) ^(( n -1) / n ) ;
T2 = T1 *( p2 / p1 ) ^(( n -1) / n ) ;
Q1 = cp *( T3 - T2 ) ; // Heat e x t r a c t e d from c o l d chamber
p e r kg o f a i r
Q2 = cp *( T4 - T1 ) ; // Heat r e j e c t e d i n t h e c o o l i n g
chamber p e r kg o f a i r
cv = cp / y ;
R = cp - cv ;
W = n /( n -1) * R *(( T4 - T3 ) - ( T1 - T2 ) ) ;
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19 COP = Q1 / W ;
20 disp ( ”COP=” )
21 disp ( COP )
Scilab code Exa 14.10 10
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p1 =1000; // kPa
p2 =100; // kPa
p4 = p1 ;
p3 = p2 ;
E =2000; // R e f r i g e r a t i n g e f f e c t p r o d u c e d i n kJ / min
T3 =268; //K
T1 =303; //K
y =1.4;
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11 disp ( ” ( i ) Mass o f a i r c i r c u l a t e d p e r m i n u t e ” )
12 T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
13 e = cp *( T3 - T2 ) ; // R e f r i g e r a t i n g e f f e c t p e r kg ; kJ / kg
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15 m = E / e ;
16 disp ( ”m=” )
17 disp ( m )
18 disp ( ” kg / min ” )
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21 disp ( ” ( i i ) C o m p r e s s o r work (Wcomp . ) , e x p a n d e r work (
Wexp . ) and c y c l e work ( Wcycle ) ” )
22 T4 = T3 *( p4 / p3 ) ^(( y -1) / y ) ;
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24 Wcomp = y /( y -1) * m * R *( T4 - T3 ) ;
25 disp ( ” C o m p r e s s o r work =” )
26 disp ( Wcomp )
27 disp ( ” kJ / min ” )
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29 Wexp = y /( y -1) * m * R *( T1 - T2 ) ;
30 disp ( ” Expander work =” )
31 disp ( Wexp )
32 disp ( ” kJ / min ” )
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34 W_cycle = Wcomp - Wexp ;
35 disp ( ” Wcycle=” )
36 disp ( W_cycle )
37 disp ( ” kJ / min ” )
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40 disp ( ” ( i i i ) C . O . P . and power r e q u i r e d ” )
41 COP = E / W_cycle ;
42 disp ( ”COP =” )
43 disp ( COP )
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45 P = W_cycle /60;
46 disp ( ” Power r e q u i r e d =” )
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disp ( P )
disp ( ”kW” )
Scilab code Exa 14.11 11
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y =1.4;
cp =1.003; // kJ / kg K
T3 =289; //K
T1 =314; //K
p1 =5.2; // b a r
p2 =1; // b a r
capacity =6; // t o n n e s
R =287; // J / kg K
l =0.2; //m
T4 = T3 *( p1 / p2 ) ^(( y -1) / y ) ;
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
disp ( ” ( i ) C . O . P . =” )
COP = T2 /( T1 - T2 ) ;
disp ( COP )
disp ( ” ( i i ) Mass o f a i r i n c i r c u l a t i o n ” )
e = cp *( T3 - T2 ) ; // R e f r i g e r a t i n g e f f e c t p e r kg o f a i r
E = capacity *14000; // R e f r i g e r a t i n g e f f e c t p r o d u c e d by
t h e r e f r i g e r a t i n g machine i n kJ / h
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24 m = E / e /60;
25 disp ( ” mass o f a i r
26 disp ( m )
27 disp ( ” kg / min ” )
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29
i n c i r c u l a t i o n =” )
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30 disp ( ” P i s t o n d i s p l a c e m e n t o f c o m p r e s s o r ” )
31 V3 = m * R * T3 / p2 /10^5;
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33 V_swept = V3 /2/240;
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35 d_c = sqrt ( V_swept / l / %pi *4) ;
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37 disp ( ” D i a m e t e r o r b o r e o f t h e c o m p r e s s o r c y l i n d e r =”
)
38 disp ( d_c *1000)
39 disp ( ”mm” )
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41 disp ( ” P i s t o n d i s p l a c e m e n t o f e x p a n d e r ” )
42 V2 = m * R * T2 / p2 /10^5;
43 V_swept = V2 /2/240;
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45 d_c = sqrt ( V_swept / l / %pi *4) ;
46 disp ( ” D i a m e t e r o r b o r e o f t h e e x p a n d e r c y l i n d e r =” )
47 disp ( d_c *1000)
48 disp ( ”mm” )
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51 disp ( ” ( v ) Power r e q u i r e d t o d r i v e t h e u n i t ” )
52 W = capacity *14000/ COP /3600;
53 disp ( ” power =” )
54 disp ( W )
55 disp ( ”kW” )
Scilab code Exa 14.12 12
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m =6; // kg / min
n_relative =0.50;
cpw =4.187; // kJ / kg K
L =335; // kJ / kg
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h_f2 =31.4; // kJ / kg
h_fg2 =154; // kJ / kg
h_f3 =59.7; // kJ / kg
h_fg3 =138; // kJ / kg
h_f4 =59.7; // kJ / kg
x2 =0.6;
s_f3 =0.2232; // kJ / kg K
s_f2 =0.1251; // kJ / kg K
T2 =268; //K
T3 =298; //K
h2 = h_f2 + x2 * h_fg2 ;
x3 =(( s_f2 - s_f3 ) + x2 *( h_fg2 / T2 ) ) * T3 / h_fg3 ;
h3 = h_f3 + x3 * h_fg3 ;
h1 = h_f4 ;
COP_th =( h2 - h1 ) /( h3 - h2 ) ; // T h e o r i t i c a l COP
COP = n_relative * COP_th ;
Q = cpw *(20 -0) + L ; // Heat e x t r a c t e d from 1 kg o f
w a t e r a t 20 C f o r t h e f o r m a t i o n o f 1 kg o f i c e
at 0 C
m_ice = COP * m *( h3 - h2 ) / Q *60*24/1000; // i n 24 h o u r s
disp ( ” m i c e=” )
disp ( m_ice )
disp ( ” t o n n e s ” )
Scilab code Exa 14.13 13
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L =335; // kJ / kg
h3 =1319.22; // kJ / kg
h1 =100.04; // kJ / kg
h4 = h1 ;
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6 s_f2 = -2.1338; // kJ / kg K
7 s_g2 =5.0585; // kJ / kg K
8 s_g3 =4.4852; // kJ / kg K
9 h_f2 = -54.56; // kJ / kg
10 h_g2 =1304.99; // kJ / kg
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12 x2 =( s_g3 - s_f2 ) /( s_g2 - s_f2 ) ;
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14 h2 = h_f2 + x2 *( h_g2 - h_f2 ) ;
15 COP_theoritical =( h2 - h1 ) /( h3 - h2 ) ;
16 COP_actual =0.62* COP_theoritical ;
17 RE = COP_actual *( h3 - h2 ) ; // A c t u a l r e f r i g e r a t i n g
effect
p e r kg
18 Q =28*1000* L /24/3600; // Heat t o be e x t r a c t e d p e r
second
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20 m = Q / RE ; // Mass o f r e f r i g e r a n t
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22 W = m *( h3 - h2 ) ;
23 disp ( ” Power r e q u i r e d =” )
24 disp ( W )
25 disp ( ”kW” )
Scilab code Exa 14.14 14
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h_f2 =158.2; // kJ / kg
x2 =0.62;
h_fg2 =1280.8;
h1 =298.9; // kJ / kg
h_f4 = h1 ;
s_f2 =0.630; // kJ / kg K
T2 =268; //K
T3 =298; //K
s_f3 =1.124; // kJ / kg K
371
c i r c u l a t e d per second
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h_fg3 =1167.1; // kJ / kg
m =6.4; // kg / min
cp =4.187;
L =335; // kJ / kg
h_f3 =298.9; // kJ / kg
h2 = h_f2 + x2 * h_fg2 ;
x3 =(( s_f2 - s_f3 ) + x2 * h_fg2 / T2 ) / h_fg3 * T3 ;
h3 = h_f3 + x3 * h_fg3 ;
COP_theoritical =( h2 - h1 ) /( h3 - h2 ) ;
COP_actual =0.55* COP_theoritical ;
W1 = h3 - h2 ; // Work done p e r kg o f r e f r i g e r a n t
W = m * W1 /60; // Work done p e r s e c o n d kJ / s
Q =15* cp + L ;
m_ice = W *3600*24/ Q ;
disp ( ”Amount o f i c e f o r m e d i n 24 h o u r s =” )
disp ( m_ice )
disp ( ” kg ” )
Scilab code Exa 14.15 15
1 clc
2 RE =5*14000/3600; // T o t a l
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r e f r i g e r a t i o n produced in
kg / s
h2 =183.19; // kJ / kg
h3 =209.41; // kJ / kg
h4 =74.59; // kJ / kg
h1 = h4 ;
disp ( ” ( i ) The r e f r i g e r a n t f l o w r a t e ” )
RE_net = h2 - h1 ; // Net r e f r i g e r a t i n g e f f e c t p r o d u c e d
p e r kg
372
10 m = RE / RE_net ;
11 disp ( ” R e f r i g e r a n t f l o w r a t e =” )
12 disp ( m )
13 disp ( ” kg / s ” )
14
15
16 disp ( ” ( i i ) The C .O . P . =” )
17 COP =( h2 - h1 ) /( h3 - h2 ) ;
18 disp ( COP )
19
20
21 disp ( ” ( i i i ) The power r e q u i r e d t o d r i v e t h e
c o m p r e s s o r =” )
22 P = m *( h3 - h2 ) ;
23 disp ( P )
24 disp ( ”kW” )
25
26
27
disp ( ” ( i v ) The r a t e o f h e a t r e j e c t i o n t o t h e
c o n d e n s e r =” )
28 rate = m *( h3 - h4 ) ;
29 disp ( rate )
30 disp ( ”kW” )
Scilab code Exa 14.16 16
1 clc
2
3 disp ( ” ( i )
I f an e x p a n s i o n c y l i n d e r i s u s e d i n a
v a p o u r c o m p r e s s i o n system , t h e work r e c o v e r e d
would be e x t r e m e l y s m a l l , i n f a c t n o t e v e n
s u f f i c i e n t to overcome the mechanical f r i c t i o n .
I t w i l l n o t be p o s s i b l e t o g a i n any work . F u r t h e r
, t h e e x p a n s i o n c y l i n d e r i s b u l k y . On t h e o t h e r
hand t h e e x p a n s i o n v a l v e i s a v e r y s i m p l e and
373
handy d e v i c e , much c h e a p e r t h a n t h e e x p a n s i o n
c y l i n d e r . I t does not need i n s t a l l a t i o n ,
l u b r i c a t i o n or maintenance . ”)
4 disp ( ” The e x p a n s i o n v a l v e a l s o c o n t r o l s t h e
r e f r i g e r a n t flow rate according to the
requirement , in addition to s e r v i n g the f u n c t i o n
of r e d u c t i n g the p r e s s u r e of the r e f r i g e r a n t . ”)
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disp ( ” ( i i ) The c o m p a r i s o n b e t w e e n c e n t r i f u g a l and
r e c i p r o c a t i n g compressors ”)
disp ( ” 1 . S u i t a b i l i t y ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” S u i t a b l e f o r h a n d l i n g l a r g e v o l u m e s o f a i r a t
low p r e s s u r e s ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” S u i t a b l e f o r low d i s c h a r g e s o f a i r a t h i g h
p r e s s u r e . ”)
disp ( ” 2 . O p e r a t i o n a l s p e e d s ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” U s u a l l y h i g h ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ”Low” )
disp ( ” 3 . A i r s u p p l y ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” C o n t i n u o u s ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
374
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disp ( ” P u l s a t i n g ” )
disp ( ” 4 . B a l a n c i n g ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” L e s s V i b r a t i o n s ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” C y c l i c v i b r a t i o n s o c c u r ” )
disp ( ” 5 . L u b r i c a t i o n s y s t e m ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” G e n e r a l l y s i m p l e l u b r i c a t i o n s y s t e m s a r e
r e q u i r e d . ”)
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” G e n e r a l l y c o m p l i c a t e d ” )
disp ( ” 6 . Q u a l i t y o f a i r d e l i v e r e d ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” A i r d e l i v e r e d i s r e l a t i v e l y more c l e a n ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” G e n e r a l l y c o n t a m i n a t e d w i t h o i l . ” )
disp ( ” 7 . A i r c o m p r e s s o r s i z e ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” S m a l l f o r g i v e n d i s c h a r g e ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” L a r g e f o r same d i s c h a r g e ” )
375
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disp ( ” 8 . F r e e a i r h a n d l e d ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” 2000 −3000 m3/ min ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” 250 −300 m3/ min ” )
disp ( ” 9 . D e l i v e r y p r e s s u r e ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” N o r m a l l y b e l o w 10 b a r ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” 500 t o 800 b a r ” )
disp ( ” 1 0 . U s u a l s t a n d a r d o f c o m p r e s s i o n ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” I s e n t r o p i c c o m p r e s s i o n ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” I s o t h e r m a l c o m p r e s s i o n ” )
disp ( ” 1 1 . A c t i o n o f c o m p r e s s o r ” )
disp ( ” C e n t r i f u g a l c o m p r e s s o r ” )
disp ( ” Dynamic a c t i o n ” )
disp ( ” R e c i p r o c a t i n g c o m p r e s s o r ” )
disp ( ” P o s i t i v e d i s p l a c e m e n t ” )
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disp ( ” ( i i i ) ” )
h2 =344.927; // kJ / kg
h4 =228.538; // kJ / kg
h1 = h4 ;
cpv =0.611; // / kJ / kg0C
// s 2=s 3
t3 =39.995; // 0C
h3 =363.575+ cpv *( t3 -30) ;
Rn = h2 - h1 ;
W = h3 - h2 ;
COP = Rn / W ;
disp ( ”COP =” )
disp ( COP )
cp =2.0935; // kJ / kg 0C
Q =2400/24/3600*[4.187*(15 -0) +335+ cp *(0 -( -5) ) ];
W = Q / COP ;
disp ( ”Work r e q u i r e d =” )
disp ( W )
disp ( ”kW” )
Scilab code Exa 14.17 17
1 clc
2 disp ( ” ( i i ) Mass o f
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9
r e f r i g e r a n t c i r c u l a t e d per minute
”)
h2 =352; // kJ / kg
h3 =374; // kJ / kg
h4 =221; // kJ / kg
h1 = h4 ;
v2 =0.08; //mˆ3/ kg
rpm =500;
D =0.2;
377
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21
L =0.15;
n_vol =0.85;
RE = h2 - h1 ;
V = %pi /4* D ^2* L * rpm *2* n_vol ;
m = V / v2 ;
disp ( ” Mass o f r e f r i g e r a n t c i r c u l a t e d p e r m i n u t e = ” )
disp ( m )
disp ( ” kg / min ” )
disp ( ” ( i i i ) C o o l i n g c a p a c i t y i n t o n n e s o f
r e f r i g e r a t i o n =” )
22 cc =50*( h2 - h1 ) *60/14000;
23 disp ( cc )
24 disp ( ”TR” )
25
26 disp ( ” ( i v )COP =” )
27 COP =( h2 - h1 ) /( h3 - h2 ) ;
28 disp ( COP )
Scilab code Exa 14.18 18
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12
clc
te = -10; // 0C
tc =40; // 0C
h3 =220; // kJ / kg
h2 =183.1; // kJ / kg
h1 =74.53; // kJ / kg
h_f4 =26.85; // kJ / kg
m =1; // kg
disp ( ” ( i ) The C . O. P . t h e c y c l e =” )
COP =( h2 - h1 ) /( h3 - h2 ) ;
disp ( COP )
378
13
14 disp ( ” ( i i ) R e f r i g e r a t i n g c a p a c i t y =” )
15 RC = m *( h2 - h1 ) ;
16 disp ( RC )
17 disp ( ” kJ / min ” )
18
19 disp ( ” C o m p r e s s o r power =” )
20 CP = m *( h3 - h2 ) /60;
21 disp ( CP )
22 disp ( ” kJ / s ” )
Scilab code Exa 14.19 19
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22
clc
h2 =178.61; // kJ / kg
h3a =203.05; // kJ / kg
h_f4 =74.53; // kJ / kg
h1 = h_f4 ;
s3a =0.682; // kJ / kg K
s2 =0.7082; // kJ / kg K
cp =0.747; // kJ / kg K
T3a =313; //K
CE =20; // C o o l i n g e f f e c t
C =0.03;
v_g =0.1088;
p_d =9.607;
p_s =1.509;
n =1.13;
m = CE /( h2 - h1 ) ;
T3 = T3a * %e ^(( s2 - s3a ) / cp )
h3 = h3a + cp *( T3 - T3a ) ;
P = m *( h3 - h2 ) ;
disp ( ” Power r e q u i r e d by t h e machine =” )
379
23 disp ( P )
24 disp ( ”kW” )
25
26 n_vol =1+ C - C *( p_d / p_s ) ^(1/ n ) ; // V o l u m e t r i c e f f i c i e n c y
27 V1 = m * v_g ; // volume o f r e f r i g e r a n t a t t h e i n t a k e
conditions
28 V_swept = V1 / n_vol ;
29
30 V = V_swept *60/300;
31 disp ( ” P i s t o n d i s p l a c e m e n t =” )
32 disp ( V )
33 disp ( ”mˆ3 ” )
Scilab code Exa 14.20 20
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clc
h2 =1450.22; // kJ / kg
h3a =1488.57; // kJ / kg
h_f4 =366.072; // kJ / kg
cpl2 =4.556; // kJ / kg K
cpv1 =2.492; // kJ / kg K
cpv2 =2.903; // kJ / kg K
T1 =303; //K
T2 =308; //K
s3a =5.2086; // kJ / kg K
s2 =5.755; // kJ / kg K
T3a =308; //K
N =1000;
h_f4a = h_f4 - cpl2 *( T2 - T1 ) ;
h1 = h_f4a ;
T3 = T3a * %e ^(( s2 - s3a ) / cpv2 ) ;
h3 = h3a + cpv2 *( T3 - T3a ) ;
m =50/( h2 - h1 ) ;
380
21
22 disp ( ” ( i ) Power r e q u i r e d =” )
23 P = m *( h3 - h2 ) ;
24 disp ( P )
25 disp ( ”kW” )
26
27
28 disp ( ” ( i i ) C y l i n d e r d i m e n s i o n s ” )
29 D =( m *4*60/ %pi /1.2/ N /0.417477) ^(1/3) ;
30 disp ( ” D i a m e t e r o f c y l i n d e r =” )
31 disp ( D )
32 disp ( ”m” )
33
34 L =1.2* D ;
35 disp ( ” Length o f t h e c y l i n d e r=” )
36 disp ( L )
37 disp ( ”m” )
Scilab code Exa 14.21 21
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clc
cooling_load =150; //W
n_vol =0.8;
N =720; // rpm
h2 =183; // kJ / kg
h1 =74.5; // kJ / kg
v2 =0.08; //mˆ3/ kg
m = cooling_load /(108.5*1000) ;
disp ( ” Mass f l o w r a t e o f t h e r e f r i g e r a n t =” )
disp ( m )
disp ( ” kJ / s ” )
d = m * v2 / n_vol ;
disp ( ” D i s p l a c e m e n t volume o f t h e c o m p r e s s o r =” )
381
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17
disp ( d )
disp ( ”mˆ3/ s ” )
Scilab code Exa 14.22 22
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clc
h2 =183.2; // kJ / kg
h3 =222.6; // kJ / kg
h4 =84.9; // kJ / kg
v2 =0.0767; //mˆ3/ kg
v3 =0.0164; //mˆ3/ kg
v4 =0.00083; //mˆ3/ kg
V =1.5*1000*10^( -6) ; // P i s t o n d i s p l a c e m e n t volume m
ˆ3/ r e v o l u t i o n
11 n_vol =0.80;
12
13 disp ( ” ( i ) Power r a t i n g o f t h e c o m p r e s s o r (kW) ” )
14 discharge = V *1600* n_vol ; // C o m p r e s s o r d i s c h a r g e
15 m = discharge / v2 ;
16
17 P = m /60*( h3 - h2 ) ; //kW
18 disp ( ” Power =” )
19 disp ( P )
20 disp ( ”kW” )
21
22
23 disp ( ” ( i i ) R e f r i g e r a t i n g e f f e c t =” )
24 RE = m /60*( h2 - h4 ) ;
25 disp ( RE )
26 disp ( ”kW” )
382
Scilab code Exa 14.23 23
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clc
COP =6.5;
W =50; //kW
h3a =201.45; // kJ / kg
h_f4 =69.55; // kJ / kg
h1 = h_f4 ;
h2 =187.53; // kJ / kg
cp =0.6155; // kJ / kg
t3a =35; // 0C
RC = W * COP ; // R e f r i g e r a t i n g c a p a c i t y
Q1 = h2 - h_f4 ; // Heat e x t r a c t e d p e r kg o f r e f r i g e r a n t
rate = RC / Q1 ; // R e f r i g e r a n t f l o w r a t e
Q2 = W / rate ; // Heat i n p u t p e r kg
h = h2 + Q2 ; // E n t h a l p y o f v a p o u r a f t e r c o m p r e s s i o n
Q =h - h3a ; // S u p e r h e a t
t3 = Q / cp + t3a ;
disp ( ” t 3=” )
disp ( t3 )
disp ( ” C ” )
Scilab code Exa 14.24 24
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clc
Q1 =500; // t o t a l h e a t i n g r e q u i r e m e n t o f 500 kJ / min
n_compressor =0.8;
s1 =0.7035; // kJ / kg K
s2 =0.6799; // kJ / kg K
T2 =322.31; //K
cp =0.7; // kJ / kg K
h_v2 =206.24; // kJ / kg
h_l2 =84.21; // kJ / kg
383
10 h_v1 =182.07 // kJ / kg
11
12 Q2 = Q1 / n_compressor ; // Heat r e j e c t e d by t h e c y c l e
13
14 // Entropy o f d r y s a t u r a t e d v a p o u r a t 2 b a r= Entr opy
o f s u p e r h e a t e d v a p o u r a t 12 b a r
15 T = T2 * %e ^(( s1 - s2 ) / cp ) ;
16
17 H = h_v2 + cp *( T - T2 ) ; // E n t h a l p y o f s u p e r h e a t e d v a p o u r
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24
a t 12 b a r
Q3 =H - h_l2 ; // Heat r e j e c t e d p e r c y c l e
m = Q2 / Q3 ; // kg / min
W = m *( H - h_v1 ) /60; //kW
W_actual = W / n_compressor ;
disp ( ” Power =” )
disp ( W_actual )
disp ( ”kW” )
Scilab code Exa 14.25 25
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clc
h2a =183.2; // kJ / kg K
cpv =0.733; // Vapour s p e c i f i c h e a t i n kJ / kg K
cpl =1.235; // L i q u i d s p e c i f i c h e a t i n kJ / kg K
s2a =0.7020; // Entropy o f v a p o u r i n kJ / kg K
s3a =0.6854; // Entropy o f v a p o u r i n kJ / kg K
T2 =270; //K
T2a =263; //K
T3a =303; //K
h3a =199.6; // kJ / kg
h_f4 =64.6; // kJ / kg
dT4 =6; // dT4=T4−T4a
v2a =0.0767;
n =2; // number o f c y l i n d e r
384
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h2 = h2a + cpv *( T2 - T2a ) ;
s2 = s2a + cpv * log ( T2 / T2a ) ;
T3 = T3a * %e ^(( s2 - s3a ) / cpv ) ;
h3 = h3a + cpv *( T3 - T3a ) ;
h_f4a = h_f4 - cpl * dT4 ;
h1 = h_f4a ;
v2 = v2a / T2a * T2 ;
disp ( ” ( i ) R e f r i g e r a t i n g e f f e c t p e r kg =” )
RE = h2 - h1 ;
disp ( RE )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Mass o f r e f r i g e r a n t t o be c i r c u l a t e d p e r
m i n u t e =” )
32 m =2400/ RE ;
33 disp ( m )
34 disp ( ” kg / min ” )
35
36
disp ( ” ( i i i ) T h e o r e t i c a l p i s t o n d i s p l a c e m e n t p e r
m i n u t e =” )
37 v = m * v2 ;
38 disp ( v )
39 disp ( ”mˆ3/ min ” )
40
41
disp ( ” ( i v ) T h e o r e t i c a l power r e q u i r e d t o run t h e
compressor = ”)
42 P = m /60*( h3 - h2 ) ;
43 disp ( P )
44 disp ( ”kW” )
45
46
disp ( ” ( v ) Heat removed t h r o u g h t h e c o n d e n s e r p e r min
=” )
47 Q = m *( h3 - h_f4a ) ;
48 disp ( Q )
49 disp ( ” kJ / min ” )
385
50
51 disp ( ” ( v i ) T h e o r e t i c a l b o r e ( d ) and s t r o k e ( l ) ” )
52 d =( v / n / %pi *4/1.25/1000) ^(1/3) *1000;
53 disp ( ” T h e r o r i t i c a l b o r e =” )
54 disp ( d )
55 disp ( ”mm” )
56
57 disp ( ” s t r o k e =” )
58 l =1.25* d ;
59 disp ( l )
60 disp ( ”mm” )
Scilab code Exa 14.26 26
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clc
h2 =1597; // kJ / kg
h3 =1790; // kJ / kg
h4 =513; // kJ / kg
h1 = h4 ;
t3 =58; // 0C
x1 =0.13;
tc =27; // 0C
capacity =10.5; // t o n n e s
disp ( ” ( i ) C o n d i t i o n o f t h e v a p o u r a t t h e o u t l e t o f
t h e c o m p r e s s o r =” )
12 t = t3 - tc ;
13 disp ( t )
14 disp ( ” C ” )
15
16
disp ( ” ( i i ) C o n d i t i o n o f v a p o u r a t e n t r a n c e t o
e v a p o r a t o r =” )
17 disp ( x1 )
18
19
disp ( ”COP =” )
386
20 COP =( h2 - h1 ) /( h3 - h2 ) ;
21 disp ( COP )
22
23 disp ( ” ( i v ) Power r e q u i r e d =” )
24 P = capacity *14000/ COP /3600;
25 disp ( P )
26 disp ( ”kW” )
Scilab code Exa 14.27 27
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clc
h2 =615; // kJ / kg
h3 =664; // kJ / kg
h4 =446; // kJ / kg
h1 = h4 ;
v2 =0.14; //mˆ3/ kg
capacity =20; // t o n n e s
n =6; // number o f c y l i n d e r
disp ( ” ( i ) R e f r i g e r a t i n g e f f e c t p e r kg =” )
RE = h2 - h1 ;
disp ( RE )
disp ( ” kJ / kg ” )
disp ( ” ( i i ) Mass o f r e f r i g e r a n t t o be c i r c u l a t e d p e r
m i n u t e =” )
16 m = capacity *14000/ RE /60;
17 disp ( m )
18 disp ( ” kg / min ” )
19
20 disp ( ” ( i i i ) T h e o r e t i c a l
21 v = v2 * m ;
22 disp ( v )
23 disp ( ”mˆ3/ min ” )
24
p i s t o n d i s p l a c e m e n t =” )
387
25 disp ( ” ( i v ) T h e o r e t i c a l power =” )
26 P = m /60*( h3 - h2 ) ;
27 disp ( P )
28 disp ( ”kW” )
29
30 disp ( ” ( v )COP =” )
31 COP =( h2 - h1 ) /( h3 - h2 ) ;
32 disp ( COP )
33
34 disp ( ” ( v i ) Heat removed t h r o u g h t h e c o n d e n s e r =” )
35 Q = m *( h3 - h4 ) ;
36 disp ( Q )
37 disp ( ” kJ / min ” )
38
39 disp ( ” ( v i i ) T h e o r e t i c a l d i s p l a c e m e n t p e r m i n u t e p e r
c y l i n d e r ”)
40
41 d =( v / n *4/ %pi /950) ^(1/3) *1000;
42 disp ( ” D i a m e t e r o f c y l i n d e r =” )
43 disp ( d )
44 disp ( ”mm” )
45
46 l = d ;
47 disp ( ” S t r o k e l e n g t h =” )
48 disp ( l )
49 disp ( ”mm” )
388
Chapter 15
Heat Transfer
Scilab code Exa 15.1 1
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clc
t1 =60; // 0C
t2 =35; // 0C
L =0.22; //m
k =0.51; //W/m 0C
q = k *( t1 - t2 ) / L ;
disp ( ” Rate o f h e a t t r a n s f e r p e r mˆ2 =” )
disp ( q )
disp ( ”W/mˆ2 ” )
Scilab code Exa 15.2 2
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clc
t1 =1325; // 0C
t2 =1200; // 0C
t3 =25; // 0C
L =0.32; //m
389
6 k_A =0.84; //W/m 0C
7 k_B =0.16; //W/m 0C
8
9 // L B =0.32 −L A
10 // ( t1 −t 2 ) / ( L A / k A ) =( t1 −t 3 ) / ( ( L A / k A + L B / k B )
11
12 L_A =( t1 - t2 ) * k_A / k_B * L /(( t1 - t3 ) -( t1 - t2 ) * k_A / k_A +( t1 -
t2 ) * k_A / k_B ) ; //m
13 disp ( ” L A=” )
14 disp ( L_A *1000)
15 disp ( ”mm” )
16
17 L_B =0.32 - L_A ; //m
18 disp ( ” L B ” )
19 disp ( L_B *1000)
20 disp ( ”mm” )
21
22
23 disp ( ” ( i i ) Heat l o s s p e r u n i t a r e a =” )
24 q =( t1 - t2 ) / L_A * k_A ;
25 disp ( q )
26 disp ( ”W/mˆ2 ” )
27
28
29 disp ( ” I f a n o t h e r l a y e r o f i n s u l a t i n g m a t e r i a l
is
added , t h e h e a t l o s s from t h e w a l l w i l l r e d u c e ;
c o n s e q u e n t l y the temperature drop a c r o s s the f i r e
b r i c k l i n i n g w i l l d r o p and t h e i n t e r f a c e
t e m p e r a t u r e t 2 w i l l r i s e . As t h e i n t e r f a c e
temperature i s already f i x e d . Therefore , a
s a t i s f a c t o r y s o l u t i o n w i l l n o t be a v a i l a b l e by
adding l a y e r of i n s u l a t i o n . ”)
Scilab code Exa 15.3 3
390
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clc
L_A =0.1; //m
L_B =0.04; //m
k_A =0.7; //W/m 0C
k_B =0.48; //W/m 0C
k_C =0.065; //W/m 0C
//Q2=0.2∗Q1
L_C =0.8*[( L_A / k_A ) + ( L_B / k_B ) ]* k_C /0.2;
disp ( ” t h i c k n e s s o f r o c k w o o l i n s u l a t i o n =” )
disp ( L_C *1000)
disp ( ”mm” )
Scilab code Exa 15.4 4
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clc
L_A =0.2; //m
L_C =0.006; //m
L_D =0.1; //m
t1 =1150; // 0C
t2 =40; // 0C
dt = t1 - t2 ;
k_A =1.52; //W/m 0C
k_B =0.138; //W/m 0C
k_D =0.138; //W/m 0C
k_C =45; //W/m 0C
q =400; //W/mˆ2
disp ( ” ( i ) The v a l u e o f x = ( L C ) ” )
L_B =(( t1 - t2 ) / q - ( L_A / k_A + L_C / k_C + L_D / k_D ) ) * k_B
*1000;
16 disp ( ” L B =” )
17 disp ( L_B )
18 disp ( ”mm” )
19
391
20
21
disp ( ” ( i i ) T e m p e r a t u r e o f t h e o u t e r s u r f a c e o f t h e
s t e e l p l a t e t s o =” )
22 t_so = q * L_D / k_D + t2 ;
23 disp ( t_so )
24 disp ( ” 0C” )
Scilab code Exa 15.5 5
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clc
k_A =150; //W/m 0C
k_B =30; //W/m 0C
k_C =65; //W/m 0C
k_D =50; //W/m 0C
L_A =0.03; //m
L_B =0.08; //m
L_C = L_B ;
L_D =0.05; //m
A_A =0.01; //mˆ2
A_B =0.003; //mˆ2
A_C =0.007; //mˆ2
A_D =0.01; //mˆ2
t1 =400; // 0C
t4 =60; // 0C
R_thA = L_A / k_A / A_A ;
R_thB = L_B / k_B / A_B ;
R_thC = L_C / k_C / A_C ;
R_thD = L_D / k_D / A_D ;
R_th_eq = R_thB * R_thC /( R_thB + R_thC ) ;
R_th_total = R_thA + R_th_eq + R_thD ;
392
27
28 Q =( t1 - t4 ) / R_th_total ;
29 disp ( ”Q=” )
30 disp ( Q )
31 disp ( ”W” )
Scilab code Exa 15.6 6
1 clc
2 L =0.012; //m
3 t_hf =95; // 0C
4 t_cf =15; // 0C
5 k =50; //W/m 0C
6 h_hf =2850; //W/mˆ2 0C
7 h_cf =10; //W/mˆ2 0C
8
9 disp ( ” ( i ) Rate o f h e a t
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18
l o s s p e r mˆ2 o f t h e t a n k
s u r f a c e area ”)
U =1/(1/ h_hf + L / k + 1/ h_cf ) ;
A =1; //mˆ2
q = U * A *( t_hf - t_cf ) ;
disp ( ” q=” )
disp ( q )
disp ( ”W/mˆ2 ” )
disp ( ” ( i i ) T e m p e r a t u r e o f t h e o u t s i d e s u r f a c e o f t h e
t a n k =” )
19 t2 = q / h_cf + t_cf ;
20 disp ( t2 )
21 disp ( ” 0C” )
Scilab code Exa 15.7 7
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clc
L_A =0.003; //m
L_B =0.05; //m
L_C = L_A ;
k_A =46.5; //W/m 0C
k_B =0.046; //W/m 0C
k_C = k_A ;
h0 =11.6; //W/mˆ2 0C
hi =14.5; //W/mˆ2 0C
t0 =25; // 0C
ti =6; // 0C
A =0.5*0.5*2+0.5*1*4; //mˆ2
disp ( ” ( i ) The r a t e o f r e m o v a l o f h e a t =” )
Q = A *( t0 - ti ) /(1/ h0 + L_A / k_A + L_B / k_B + L_C / k_C + 1/
hi ) ;
18 disp ( Q )
19 disp ( ”W” )
20
21
22
disp ( ” ( i i ) The t e m p e r a t u r e a t t h e o u t e r s u r f a c e o f
t h e m e t a l s h e e t =” )
23 t1 = t0 - Q / h0 / A ;
24 disp ( t1 )
25 disp ( ” 0C” )
Scilab code Exa 15.8 8
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clc
L_A =0.25; //m
L_B =0.1; //m
L_C =0.15; //m
k_A =1.65; //W/m
C
394
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k_C =9.2; //W/m C
t_hf =1250; // C
t1 =1100; // C
t_cf =25; // C
h_hf =25; //W/mˆ2 C
h_cf =12; //W/mˆ2 C
disp ( ” ( i ) Thermal c o n d u c t i v i t y =” )
q = h_hf *( t_hf - t1 ) ;
k_B = L_B /(( t_hf - t_cf ) /q -1/ h_hf - L_A / k_A - L_C / k_C -1/ h_cf
);
17 disp ( ” Thermal c o n d u c t i v i t y , k=” )
18 disp ( k_B )
19 disp ( ”W/mˆ2 C ” )
20
21
22 disp ( ” ( i i ) The o v e r a l l t r a n s f e r c o e f f i c i e n t =” )
23 R_th_total =1/ h_hf + L_A / k_A + L_B / k_B + L_C / k_C +1/ h_cf ;
24 U =1/ R_th_total ;
25 disp ( U )
26 disp ( ”W/mˆ2 C ” )
27
28
29 disp ( ” ( i i i ) A l l s u r f a c e t e m p e r a t u r e ” )
30
31 disp ( ” t 1=” )
32 disp ( t1 )
33 disp ( ” C ” )
34
35 t2 = t1 - q * L_A / k_A ;
36 disp ( ” t 2=” )
37 disp ( t2 )
38 disp ( ” C ” )
39
40 t3 = t2 - q * L_B / k_B ;
41 disp ( ” t 3=” )
42 disp ( t3 )
395
43 disp ( ” C ” )
44
45 t4 = t3 - q * L_C / k_C ;
46 disp ( ” t 4=” )
47 disp ( t4 )
48 disp ( ” C ” )
Scilab code Exa 15.9 9
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clc
r1 =0.01; //m
r2 =0.02; //m
r3 =0.05; //m
t1 =600; // 0C
t3 =1000; // 0C
k_B =0.2; //W/m 0C
q =2* %pi *( t1 - t3 ) /( log ( r3 / r2 ) / k_B ) ;
disp ( ” Heat t r a n s f e r p e r m e t r e o f l e n g t h =” )
disp ( q )
disp ( ”W/m” )
Scilab code Exa 15.10 10
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clc
r1 =0.06; //m
r2 =0.12; //m
r3 =0.16; //m
k_A =0.24; //W/m 0C
k_B =0.4; //W/m 0C
h_hf =60; //W/mˆ2 0C
h_cf =12; //W/mˆ2 0C
t_hf =65; // 0C
396
10 t_cf =20; // 0C
11 L =60; //m
12
13 Q =2* %pi * L *( t_hf - t_cf ) /(1/ h_hf / r1 + log ( r2 / r1 ) / k_A +
log ( r3 / r2 ) / k_B + 1/ h_cf / r3 ) ;
14 disp ( ” Rate o f h e a t l o s s =” )
15 disp ( Q )
16 disp ( ”W” )
Scilab code Exa 15.11 11
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clc
r1 =0.06; //m
r2 =0.08; //m
k_A =42; //W/m 0C
k_B =0.8; //W/m 0C
t_hf =150; // 0C
t_cf =20; // 0C
h_hf =100; //W/mˆ2 0C
h_cf =30; //W/mˆ2 0C
//Q= 2 . 1 ∗ 2 ∗ %pi ∗ r ∗L kW
//Q= 0 . 9 8 9 ∗ L ∗ 1 0 ˆ 3 W
//Q=2∗%pi ∗L ∗ ( t h f − t c f ) / ( 1 / h h f / r 1 + l o g ( r 2 / r 1 ) / k A
+ l o g ( r 3 / r 2 ) / k B + 1/ h c f / r 3 )
//By s o l v i n g a b o v e e q u a t i o n , u s i n g h i t and t r i a l
method we g e t
r3 =0.105; //m
thickness =( r3 - r2 ) *1000; //mm
disp ( ” T h i c k n e s s o f i n s u l a t i o n =” )
disp ( thickness )
disp ( ”mm” )
397
Scilab code Exa 15.12 12
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clc
r2 =0.7; //m
r1 =0.61; //m
dt =220; // d t=t1 −t 2 ; 0C
k =0.083; //W/m 0C
Q = dt /(( r2 - r1 ) /(4* %pi * k * r1 * r2 ) ) ;
disp ( ” Rate o f h e a t l e a k a g e =” )
disp ( Q )
disp ( ”W” )
Scilab code Exa 15.13 13
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r1 =0.001; //m
r2 =0.0018; //m
k =0.12; //W/m 0C
h0 =35; //W/mˆ2 0C
rc = k / h0 ;
thickness =( rc - r1 ) *10^3; //mm
disp ( ” C r i t i c a l t h i c k n e s s o f i n s u l a t i o n =” )
disp ( thickness )
disp ( ”mm” )
// P e r c e n t a g e c h a n g e i n h e a t t r a n s f e r r a t e :
// Case I : The h e a t f l o w t h r o u g h an i n s u l a t e d w i r e
//Q1=2∗%pi ∗L ∗ ( t1 − t a i r ) / ( l o g ( r 2 / r 1 ) / k + 1/ h0 / r 2 )
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// Case I I : The h e a t f l o w t h r o u g h an i n s u l a t e d w i r e
when c r i t i c a l t h i c k n e s s i s u s e d i s g i v e n
//Q2=2∗%pi ∗L ∗ ( t1 − t a i r ) / ( l o g ( r c / r 1 ) / k + 1/ h0 / r c )
// % i n c r e a s e =(Q2−Q1 ) /Q1∗ 10 0
%increase =(1/( log ( rc / r1 ) / k + 1/ h0 / rc ) -1/( log ( r2 / r1 ) /
k + 1/ h0 / r2 ) ) /(1/( log ( r2 / r1 ) / k + 1/ h0 / r2 ) ) *100;
25 disp ( ” P e r c e n t a g e c h a n g e i n h e a t t r a n s f e r r a t e =” )
26 disp ( %increase )
27 disp ( ”%” )
Scilab code Exa 15.14 14
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clc
A =1*1.5; //mˆ2
ts =300; // 0C
tf =20; // 0C
h =20; //W/mˆ2 0C
Q = h * A *( ts - tf ) /10^3; //kW
disp ( ” Rate o f h e a t t r a n s f e r =” )
disp ( Q )
disp ( ”kW” )
Scilab code Exa 15.15 15
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d =0.0015; //m
l =0.15; //m
A = %pi * d * l ;
ts =120; // 0C
tf =100; // 0C
399
7 h =4500; //W/mˆ2 0C
8
9 Q = h * A *( ts - tf ) ;
10 disp ( ” E l e c t r i c power t o be s u p p l i e d =” )
11 disp ( Q )
12 disp ( ”W” )
Scilab code Exa 15.16 16
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D =0.045; //m
l =3.2; //m
u =0.78; //m/ s
k =0.66; //W/m K
v =0.478*10^( -6) ; //mˆ2/ s
Pr =2.98;
tw =70; // 0C
tf =50; // 0C
A = %pi * D * l ;
Re = D * u / v ;
h =0.023*( Re ) ^0.8*( Pr ) ^0.4/ D * k ;
disp ( ” Heat t r a n s f e r co− e f f i c i e n t =” )
disp ( h )
disp ( ”W/mˆ2 K” )
Q = h * A *( tw - tf ) /10^3;
disp ( ” Rate o f h e a t t r a n s f e r =” )
disp ( Q )
disp ( ”kW” )
Scilab code Exa 15.17 17
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rho =983.2; // kg /mˆ2
cp =4.187; // kJ / kg K
k =0.659; //W/m 0C
v =0.478*10^( -6) ; //mˆ2/ s
m =0.5/60; // kg / s
D =0.02; //m
ti =20; // 0C
t0 =50; // 0C
ts =85; // s u r f a c e t e m p e r a t u r e i n 0C
tf =1/2*( ts +( ti + t0 ) /2) ;
A = %pi /4* D ^2;
u = m / rho / A ;
Re = D * u / v ;
// S i n c e Re < 2 0 0 0 , h e n c e t h e f l o w i s l a m i n a r .
Nu =3.65;
h = Nu * k / D ;
tb =( t0 + ti ) /2;
L = m * cp *10^3*( t0 - ti ) /( ts - tb ) / h / D / %pi ;
disp ( ” Length o f t h e t u b e r e q u i r e d f o r f u l l y
d e v e l o p e d f l o w =” )
24 disp ( L )
25 disp ( ”m” )
Scilab code Exa 15.18 18
1 clc
2 m_h =0.2; // kg / s
3 m_c =0.5; // kg / s
4 t_h1 =75; // 0C
5 t_h2 =45; // 0C
6 t_c1 =20; // 0C
401
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hi =650; //W/mˆ2 0C
h0 = hi ;
cph =4.187;
cpc = cph ;
Q = m_h * cph *( t_h1 - t_h2 ) ;
t_c2 = m_h * cph / cpc *( t_h1 - t_h2 ) / m_c + t_c1 ;
theta =(( t_h1 - t_c1 ) - ( t_h2 - t_c2 ) ) / log (( t_h1 - t_c1 ) /(
t_h2 - t_c2 ) ) ; // L o g a r i t h m i c mean t e m p e r a t u r e
difference
16
17 U = hi * h0 /( hi + h0 ) ;
18 A = Q *10^3/ U / theta ;
19 disp ( ” The a r e a o f h e a t e x c h a n g e r =” )
20 disp ( A )
21 disp ( ”mˆ2 ” )
Scilab code Exa 15.19 19
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clc
t_c1 =25; // 0C
t_c2 =65; // 0C
cph =1.45; // kJ / kg K
m_h =0.9; // kg / s
t_h1 =230; // 0C
t_h2 =160; // 0C
U =420; //W/mˆ2 0C
cpc =4.187; // kJ / kg K
disp ( ” ( i ) The r a t e o f h e a t t r a n s f e r =” )
Q = m_h * cph *( t_h1 - t_h2 ) ;
disp ( Q )
disp ( ” kJ / s ” )
402
16
17 disp ( ” ( i i ) The mass f l o w r a t e o f w a t e r =” )
18 m_c = Q / cpc /( t_c2 - t_c1 ) ;
19 disp ( m_c )
20 disp ( ” kg / s ” )
21
22
23 disp ( ” ( i i i ) The s u r f a c e a r e a o f h e a t e x c h a n g e r =” )
24 LMTD =(( t_h1 - t_c2 ) - ( t_h2 - t_c1 ) ) / log (( t_h1 - t_c2 ) /(
25
26
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t_h2 - t_c1 ) ) ; // l o g a r i t h m i c mean t e m p e r a t u r e
difference
A = Q *10^3/ U / LMTD ;
disp ( ”A=” )
disp ( A )
disp ( ”mˆ2 ” )
Scilab code Exa 15.20 20
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m_s =800/60; // kg / s
m_c = m_s ;
m_g =1350/60; // kg / s
m_h = m_g ;
t_h1 =650; // 0C
t_c1 =180; // 0C
t_c2 =350; // 0C
d =0.03; //m
L =3; //m
cph =1; // kJ / kg K
cpc =2.71; // kJ / kg K
h_g =250;
h_s =600;
t_h2 = t_h1 -( m_c * cpc *( t_c2 - t_c1 ) / cph / m_h ) ;
U = h_g * h_s /( h_g + h_s ) ;
403
18 Q = m_h * cph *10^3*( t_h1 - t_h2 ) ;
19 theta =(( t_h1 - t_c2 ) - ( t_h2 - t_c1 ) ) / log (( t_h1 - t_c2 ) /(
t_h2 - t_c1 ) ) ; // l o g a r i t h m i c mean t e m p e r a t u r e
difference
20 //A=N∗ %pi ∗d∗L
21
22 N = Q / U / theta /( %pi * d * L ) ;
23 disp ( ” number o f t u b e s r e q u i r e d =” )
24 disp ( N )
25 disp ( ” t u b e s ” )
Scilab code Exa 15.21 21
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di =0.0296; //m
d0 =0.0384; //m
U =4000; //W/mˆ2 0C
V =3; //m/ s
t_c1 =24; // 0C
x =0.9;
ps =(760 -660) /760*1.0133; // b a r
t_h1 =51; // 0C
t_h2 =51; // 0C
h_fg =2592; // kJ / kg
t_c2 =47; // 0C
P =15; //MW
ssc =5; // s p e c i f i c steam c o n s u m p t i o n i n kg /kWh
cpc =4.187; // kJ ? kg K
rho =1000;
m_s = P *10^3* ssc /60; // kg / min
disp ( ” ( i ) Mass o f c o o l i n g w a t e r c i r c u l a t e d p e r
m i n u t e =” )
21 m_w = m_s * x * h_fg / cpc /( t_c2 - t_c1 ) ;
404
22 disp ( m_w )
23 disp ( ” kg / min ” )
24
25
26 disp ( ” ( i i ) C o n d e n s e r s u r f a c e a r e a ” )
27 Q = m_s * x * h_fg *10^3/60;
28
29 theta =(( t_h1 - t_c1 ) - ( t_h2 - t_c2 ) ) / log (( t_h1 - t_c1 ) /(
t_h2 - t_c2 ) ) ; // L o g a r i t h m i c mean t e m p e r a t u r e
difference
30 A = Q / U / theta ;
31 disp ( A )
32 disp ( ”mˆ2 ” )
33
34
35 disp ( ” ( i i i ) Number o f t u b e s r e q u i r e d p e r p a s s =” )
36 Np = m_w /60*4/ %pi / di ^2/ V / rho ;
37 disp ( Np )
38
39
40 disp ( ” ( i v ) Tube l e n g t h =” )
41 L = A / %pi / d0 /(2* Np ) ;
42 disp ( L )
43 disp ( ”m” )
Scilab code Exa 15.22 22
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cp =4.187; // kJ / kg C
u =0.596*10^( -3) ; // Ns /mˆ2
k =0.635; //W/m C
Pr =3.93;
d =0.020; //m
l =2; //m
m_c =10; // kg / s
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t_c1 =17; // / C
t_h1 =100; // C
t_h2 =100; // C
rho =1000;
N =200;
Np = N / l ;
h0 =10*10^3;
V = m_c *4/ %pi / d ^2/ rho / Np ;
Re = rho * V * d / u ;
hi = k / d *0.023*( Re ) ^0.8*( Pr ) ^0.33;
U = hi * h0 /( hi + h0 ) ;
// t h e t a 1=t h 1 −t c 1 ;
// t h e t a 2=t h 2 −t c 2 ;
//AMTD=( t h e t a 1+t h e t a 2 ) /2
//AMTD=91.5 − 0 . 5 ∗ t c 2
t_c2 =( U * %pi * d * l * N *91.5 + m_c * cp *10^3* t_c1 ) /( m_c * cp
*10^3 + U * %pi * d * l * N *0.5) ;
28 disp ( ” w a t e r e x i t t e m p e r a t u r e =” )
29 disp ( t_c2 )
30 disp ( ” C ” )
Scilab code Exa 15.23 23
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A =0.12; //mˆ2
T =800; //K
a =5.67*10^( -8) ;
disp ( ” ( i ) The t o t a l r a t e o f e n e r g y e m i s s i o n =” )
Eb = a * A * T ^4;
disp ( Eb )
disp ( ”W” )
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12 disp ( ” ( i i ) The i n t e n s i t y o f n o r m a l r a d i a t i o n =” )
13 Ibn = a * T ^4/ %pi ;
14 disp ( Ibn )
15 disp ( ”W/mˆ 2 . s r ” )
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18 disp ( ” ( i i i ) The w a v e l e n g t h o f maximum m o n o c h r o m a t i c
e m i s s i v e power =” )
19 wavelength =2898/ T ;
20 disp ( wavelength )
21 disp ( ” m ” )
Scilab code Exa 15.24 24
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2 wavelength =0.49; // m
3 a =5.67*10^( -8) ;
4
5 disp ( ” ( i ) The s u r f a c e t e m p e r a t u r e o f t h e sun ” )
6 T =2898/ wavelength ;
7 disp ( T )
8 disp ( ”K” )
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11 disp ( ” ( i i ) The h e a t f l u x a t t h e s u r f a c e o f t h e sun =
”)
12 E_sun = a * T ^4;
13 disp ( E_sun )
14 disp ( ”W/mˆ2 ” )
Scilab code Exa 15.25 25
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T =2773; //K
lambda =1.2*10^( -6) ; //m
e =0.9;
a =5.67*10^( -8) ;
disp ( ” ( i ) Monochromatic e m i s s i v e power a t 1 . 2 m
length ”)
C1 =0.3742*10^( -15) ; //W.mˆ4/mˆ2
C2 =1.4388*10^( -4) ; //mK
E_lambda_b = C1 * lambda ^( -5) /( exp ( C2 / lambda / T ) -1) ;
disp ( ” E la mb da b =” )
disp ( E_lambda_b )
disp ( ”W/mˆ2 ” )
disp ( ” ( i i ) Wavelength a t which t h e e m i s s i o n i s
maximum =” )
17 lambda_max =2898/ T ;
18 disp ( lambda_max )
19 disp ( ” m ” )
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21
22 disp ( ” ( i i i ) Maximum e m i s s i v e power =” )
23 E_lambda_b_max =1.285*10^( -5) * T ^5;
24 disp ( E_lambda_b_max )
25 disp ( ”W/mˆ2 p e r m e t r e l e n g t h ” )
26
27
28 disp ( ” ( i v ) T o t a l e m i s s i v e power =” )
29 Eb = a * T ^4;
30 disp ( Eb )
31 disp ( ”W/mˆ2 ” )
32
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34 disp ( ” ( v ) T o t a l e m i s s i v e power =” )
35 E = e * a * T ^4;
36 disp ( E )
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disp ( ”W/mˆ2 ” )
Scilab code Exa 15.26 26
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T1 =1273; //K
T2 =773; //K
e1 =0.42;
e2 =0.72;
a =5.67*10^( -8) ;
disp ( ” ( i ) When t h e body i s g r e y w i t h 1
q = e1 * a *( T1 ^4 - T2 ^4) /10^3; //kW
disp ( ” Heat l o s s p e r m2 by r a d i a t i o n =” )
disp ( q )
disp ( ”kW” )
disp ( ” ( i i ) When t h e body i s n o t g r e y ” )
E_emitted = e1 * a * T1 ^4;
E_absorbed = e2 * a *( T2 ) ^4;
q =( E_emitted - E_absorbed ) /10^3;
disp ( ” Heat l o s s p e r m2 by r a d i a t i o n =” )
disp ( q )
disp ( ”kW” )
Scilab code Exa 15.27 27
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d =0.022; //m
di =0.18; //m
e1 =0.62;
e2 =0.82;
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= 0.42 ”)
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rho =7845; // kg /mˆ3
T1a =693; //K ; For c a s e I
T1b =813; //K ; For c a s e I I
T2 =1373; //K
l =1; //m
a =5.67*10^( -8) ;
cp =0.67; // kJ / kg K
A1 = %pi * d * l ;
A2 = %pi * di * l ;
Qi = A1 * a *( T1a ^4 - T2 ^4) /(1/ e1 + A1 / A2 *(1/ e2 - 1) ) ;
Qe = A1 * a *( T1b ^4 - T2 ^4) /(1/ e1 + A1 / A2 *(1/ e2 - 1) ) ;
Qav = -( Qi + Qe ) /2;
t_h = %pi /4* d ^2* rho * cp *( T1b - T1a ) *10^3/ Qav ;
disp ( ” Time r e q u i r e d f o r t h e h e a t i n g o p e r a t i o n ” )
disp ( t_h )
disp ( ” s ” )
Scilab code Exa 15.28 28
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r1 =0.05; //m
r2 =0.1; //m
T1 =400; //K
T2 =300; //K
e1 =0.5;
e2 =0.5;
F_12 =1;
a =5.67*10^( -8) ;
//A1/A2=r 1 / r 2
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12 Q = a *( T1 ^4 - T2 ^4) /((1 - e1 ) / e1 +1/ F_12 +(1 - e2 ) / e2 * r1 / r2 ) ;
13 disp ( ” h e a t t r a n s f e r r a t e p e r m2 a r e a by r a d i a t i o n ” )
14 disp ( Q )
15 disp ( ”W/mˆ2 ” )
Scilab code Exa 15.29 29
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r1 =0.05; //m
r2 =0.1; //m
r3 =0.15; //m
T1 =1000; //K
T3 =500; //K
e1 =0.05;
e2 = e1 ;
e3 = e1 ;
a =5.67*10^( -8) ;
F_12 =1;
F_23 =1;
// A1∗ a ∗ ( T1ˆ4−T2 ˆ 4 ) /( ( (1 − e 1 ) / e 1 ) + 1/ F 12 + ((1 − e 2 ) /
e 2 ) ∗A1/A2 ) = A2∗ a ∗ ( T2ˆ4−T3 ˆ 4 ) /( ( (1 − e 2 ) / e 2 ) + 1/
F 23 + ((1 − e 3 ) / e 3 ) ∗A2/A3 )
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17 // A1/A2=r 1 / r 2 =5/10=0.5
18 // A2/A3=r 2 / r 3 =10/15=0.67
19
20 // S o l v i n g t h i s we g e t
21 T2 =770; //K
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23 Q1 = a *( T1 ^4 - T2 ^4) /(((1 - e1 ) / e1 ) + 1/ F_12 + ((1 - e2 ) / e2 )
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* r1 / r2 ) ;
disp ( ” Heat f l o w p e r m2 a r e a o f c y l i n d e r 1 =” )
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disp ( Q1 )
disp ( ”W” )
Scilab code Exa 15.30 30
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r1 =0.105; //m
r2 =0.15; //m
T1 =120; //K
T2 =300; //K
e1 =0.03;
e2 =0.03;
h_fg =209.35; // kJ / kg
a =5.67*10^( -8) ;
F_12 =1;
Q =4* %pi * r1 ^2* a *( T1 ^4 - T2 ^4) /( ((1 - e1 ) / e1 ) + 1/ F_12 +
((1 - e2 ) / e2 ) * r1 ^2/ r2 ^2) ;
rate = - Q *3600/ h_fg /1000;
disp ( ” Rate o f e v a p o r a t i o n = ” )
disp ( rate )
disp ( ” kg /h ” )
Scilab code Exa 15.31 31
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T1 =91; //K
T2 =303; //K
e1 =0.03;
e2 =0.03;
d1 =0.3; //m
d2 =0.45; //m
412
8 a =5.67*10^( -8) ;
9 F_12 =1;
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11 Q =4* %pi *( d1 /2) ^2* a *( T1 ^4 - T2 ^4) /( ((1 - e1 ) / e1 ) + 1/
F_12 + ((1 - e2 ) / e2 ) * d1 ^2/ d2 ^2) ;
12 disp ( ” Rate o f h e a t f l o w =” )
13 disp ( Q )
14 disp ( ”W” )
Scilab code Exa 15.32 32
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e1 =0.3;
e2 =0.8;
e3 =0.04;
A1 =1; //mˆ2
A2 = A1 ;
A3 = A1 ;
// ( E b1 − E b3 ) /[(1 − e 1 ) / e 1 +1+(1− e 3 ) / e 3 ] = ( E b3 −
E b2 ) /[(1 − e 3 ) / e 3 +1+(1− e 2 ) / e 2 ]
// a ∗ ( T1ˆ4−T3 ˆ 4 ) / ( 1 / e 1 +1/ e3 −1)=a ∗ ( T3ˆ4−T2 ˆ 4 ) / ( 1 / e 3
+1/ e2 −1)
// T3 ˆ 4 = 0 . 4 8 ∗ ( T1 ˆ 4 + 1 . 0 8 ∗ T2 ˆ 4 )
// Q12=a ∗ ( T1ˆ4−T2 ˆ 4 ) / ( 1 / e 1 +1/ e2 −1)
// Q13=a ∗ ( T1ˆ4−T3 ˆ 4 ) / ( 1 / e 1 +1/ e3 −1)
// % r e d u c t i o n =(Q 12−Q13 ) /Q12 ;
%reduction =1 -0.131*0.52;
disp ( ” P e r c e n t a g e r e d u c t i o n i n h e a t f l o w due t o
s h i e l d =” )
21 disp ( %reduction )
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22
disp ( ”%” )
414
Chapter 16
Compressible Flow
Scilab code Exa 16.1 1
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V1 =300; //m/ s
p1 =78; //kN/mˆ2
T1 =313; //K
p2 =117; //kN/mˆ2
R =287; // J / kg K
y =1.4;
// L e t r 1=p1 / r h o 1
r1 = R * T1 ;
V2 = sqrt (2*( y /( y -1) * r1 *(1 -( p2 / p1 ) ^(( y -1) / y ) ) + V1
^2/2) ) ;
13 disp ( ” V e l o c i t y o f g a s a t s e c t i o n 2 =” )
14 disp ( V2 )
15 disp ( ”m/ s ” )
Scilab code Exa 16.2 2
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p1 =35; //kN/mˆ2
V1 =30; //m/ s
T1 =423; //K
V2 =150; //m/ s
R =290; // J / kg K
y =1.4;
// L e t r 1=p2 / p1
r1 = R * T1 ;
p2 = p1 *(1 -(( V2 ^2/2 - V1 ^2/2) *( y -1) / y / r1 ) ) ^( y /( y -1) ) ;
disp ( ” p2=” )
disp ( p2 )
disp ( ”kN/mˆ2 ” )
T2 = T1 *( p2 / p1 ) ^(( y -1) / y ) ;
t2 = T2 -273;
disp ( ” t 2 =” )
disp ( t2 )
disp ( ” C ” )
Scilab code Exa 16.3 3
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2 SG =0.8;
3 rho_oil =800; // kg /mˆ3
4 K_oil =1.5*10^9; //N/mˆ 2 ; c r u d e o i l
5 K_Hg =27*10^9; //N/mˆ 2 ; Mercury
6 rho_Hg =13600; // kg /mˆ3
7
8 C_oil = sqrt ( K_oil / rho_oil ) ;
9 disp ( ” S o n i c v e l o c i t y o f c r u d e o i l =” )
10 disp ( C_oil )
11 disp ( ”m/ s ” )
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C_Hg = sqrt ( K_Hg / rho_Hg )
disp ( ” S o n i c v e l o c i t y o f Mercury =” )
disp ( C_Hg )
disp ( ”m/ s ” )
Scilab code Exa 16.4 4
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T =228; //K
M =2;
R =287; // Jkg K
y =1.4;
C = sqrt ( y * R * T ) ;
V = M * C *3600/1000;
disp ( ” V e l o c i t y o f t h e p l a n e =” )
disp ( V )
disp ( ”km/ h ” )
Scilab code Exa 16.5 5
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a =40* %pi /180; // Mach a n g l e i n r a d i a n s
y =1.4;
R =287; // J / kg K
T =288; //K
C = sqrt ( y * R * T ) ;
V = C / sin ( a ) ;
disp ( ” V e l o c i t y o f b u l l e t =” )
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disp ( V )
disp ( ”m/ s ” )
Scilab code Exa 16.6 6
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p =88.3; //kN/mˆ2
T =271; //K
M =40* %pi /180;
y =1.4;
R =287; // J / kg K
C = sqrt ( y * R * T ) ;
V = C / sin ( M ) ;
disp ( ” V e l o c i t y o f t h e p r o j e c t i l e =” )
disp ( V )
disp ( ”m/ s ” )
Scilab code Exa 16.7 7
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h =1800; //m
T =277; //K
t =4; // s
y =1.4;
R =287; // J / kg K
C = sqrt ( y * R * T ) ;
// t a n ( a )=h/ t ∗V
//V=C/ s i n ( a )
// From a b o v e two e q u a t i o n s we g e t
418
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14 a =( acos ( C / h * t ) ) ;
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16 V = C / sin ( a ) *3600/1000;
17 disp ( ” Speed o f t h e a i r c r a f t =” )
18 disp ( V )
19 disp ( ”km/ h ” )
Scilab code Exa 16.8 8
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R =287; // J / kg K
y =1.4;
V0 =1000*1000/3600; //m/ s
p0 =78.5; //kN/mˆ2
T0 =265; //K
C0 = sqrt ( y * R * T0 ) ;
M0 = V0 / C0 ;
disp ( ” ( i ) S t a g n a t i o n p r e s s u r e =” )
ps = p0 *(1+(( y -1) /2* M0 ^2) ) ^( y /( y -1) ) ;
disp ( ps )
disp ( ”kN/mˆ2 ” )
disp ( ” ( i i ) S t a g n a t i o n t e m p e r a t u r e =” )
Ts = T0 *(1+(( y -1) /2* M0 ^2) ) ;
disp ( Ts )
disp ( ”K” )
disp ( ” ( i i i ) S t a g n a t i o n d e n s i t y =” )
rho_s = ps *10^3/ R / Ts ;
disp ( rho_s )
419
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disp ( ” kg /mˆ3 ” )
Scilab code Exa 16.9 9
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V0 =1000*1000/3600; //m/ s
T0 =320; //K
p_atm =98.1; //kN/mˆ2
p =9.81; //kN/mˆ2
p0 =98.1 - p ;
R =287; // J / kg K
y =1.4;
C0 = sqrt ( y * R * T0 ) ;
M0 = V0 / C0 ;
disp ( ” S t a g n a t i o n p r e s s u r e =” )
ps = p0 *(1+(( y -1) /2* M0 ^2) ) ^( y /( y -1) ) ;
disp ( ps )
disp ( ”kN/mˆ2 ” )
disp ( ” S t a g n a t i o n t e m p e r a t u r e =” )
Ts = T0 *(1+(( y -1) /2* M0 ^2) ) ;
disp ( Ts )
disp ( ”K” )
disp ( ” S t a g n a t i o n d e n s i t y =” )
rho_s = ps *10^3/ R / Ts ;
disp ( rho_s )
disp ( ” kg /mˆ3 ” )
M =0.8;
420
32 CF =1+ M0 ^2/4+(2 - y ) /24* M0 ^4;
33 disp ( ” C o m p r e s s i b i l i t y f a c t o r ” )
34 disp ( CF )
Scilab code Exa 16.10 10
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R =287; // J / kg K
y =1.4;
p0 =220*10^3; //N/mˆ2
T0 =300; //K
V0 =200; //m/ s
C0 = sqrt ( y * R * T0 ) ;
rho_0 = p0 / R / T0 ;
disp ( ” S t a g n a t i o n p r e s s u r e =” )
disp ( ” ( i ) C o m p r e s s i b i l i t y i s n e g l e c t e d ” )
ps =( p0 + rho_0 * V0 ^2/2) /10^3;
disp ( ” p s=” )
disp ( ps )
disp ( ”kN/mˆ2 ” )
disp ( ” ( i i ) C o m p r e s s i b i l i t y i s a c c o u n t e d f o r ” )
M0 = V0 / C0 ;
ps =( p0 + rho_0 * V0 ^2/2*(1+ M0 ^2/4+(2 - y ) /24* M0 ^4) ) /10^3;
disp ( ” p s=” )
disp ( ps )
disp ( ”kN/mˆ2 ” )
Scilab code Exa 16.11 11
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p0 =35*10^3; // Pa
T0 =235; //K
ps =65.4*10^3; //N/mˆ2
R0 =8314; //Nm/ mole K
M =28;
R = R0 / M ;
rho_0 = p0 / R / T0 ;
Va = sqrt (2*( ps - p0 ) / rho_0 ) ;
disp ( ” Speed o f t h e a i r c r a f t =” )
disp ( Va )
disp ( ”m/ s ” )
Scilab code Exa 16.12 12
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p0 =30*10^3; //N/mˆ2
V0 =152; //m/ s
y =1.4;
rho_0 =1.224; // kg /mˆ3
ps = p0 + rho_0 * V0 ^2/2;
rho_0 =0.454; // kg /mˆ3
V0 = sqrt (2*( ps - p0 ) / rho_0 ) ;
C0 = sqrt ( y * p0 / rho_0 ) ;
M = V0 / C0 ;
ccf =(1+ M ^2/4) ; // C o m p r e s s i b i l i t y c o r r e c t i o n f a c t o r
V = V0 / sqrt ( ccf ) ; // True s p e e d o f a i r c r a f t
disp ( ” True s p e e d o f a i r c r a f t =” )
disp ( V )
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disp ( ”m/ s ” )
Scilab code Exa 16.13 13
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M =3; // Mach number
d =0.2; //m
p_nozzle =7.85; //kN/mˆ2
T_nozzle =200; //K
y =1.4;
A = %pi /4* d ^2;
disp ( ” R e s e r v o i r p r e s s u r e =” )
p_res = p_nozzle *(1+(( y -1) /2* M ^2) ) ^( y /( y -1) ) ;
disp ( p_res )
disp ( ”kN/mˆ2 ” )
disp ( ” R e s e r v o i r t e m p e r a t u r e =” )
T_res = T_nozzle *(1+(( y -1) /2* M ^2) ) ;
disp ( T_res )
disp ( ”K” )
disp ( ” T h r o a t a r e a ( c r i t i c a l ) =” )
Ac = A * M /((2+( y -1) * M ^2) /( y +1) ) ^(( y +1) /2/( y -1) ) ;
disp ( Ac )
disp ( ”mˆ2 ” )
Scilab code Exa 16.14 14
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2 R =287; // J / kg K
3 y =1.4;
4 p_atm =100; //kN/mˆ2
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p1 =284+ p_atm ; //kN/mˆ2
T1 =297; //K
D =0.02; //m
A2 = %pi /4* D ^2;
rho_1 = p1 *10^3/ R / T1 ;
m_max =0.685* A2 * sqrt ( p1 *10^3* rho_1 ) ;
disp ( ”Maximum f l o w r a t e =” )
disp ( m_max )
disp ( ” kg / s ” )
Scilab code Exa 16.15 15
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clc
R =287; // J / kg K
y =1.4;
p1 =2500*10^3; //N/mˆ2
T1 =293; //K
p2 =1750*10^3; //N/mˆ2
rho_1 = p1 / R / T1 ;
V2 = sqrt (2* y /( y -1) * p1 / rho_1 *(1 -( p2 / p1 ) ^(( y -1) / y ) ) ) ;
disp ( ” V e l o c i t y o f a i r =” )
disp ( V2 )
disp ( ”m/ s ” )
Scilab code Exa 16.16 16
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2 R =287; // J / kg K
3 y =1.4;
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p_atm =10^5; //N/mˆ2
T1 =293; //K
D2 =0.025; //m
p1 =140*10^3; //N/mˆ2
A2 = %pi /4* D2 ^2;
disp ( ” ( i ) Mass r a t e o f f l o w o f a i r when p r e s s u r e i n
t h e t a n k i s 140 kN/m2 ( a b s . ) ” )
12 rho_1 = p1 / R / T1 ;
13 p2 =10^5; //N/mˆ2
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15 m = A2 * sqrt (2* y /( y -1) * p1 * rho_1 *(( p2 / p1 ) ^(2/ y ) - ( p2 / p1
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) ^(( y +1) / y ) ) ) ;
disp ( ”m=” )
disp ( m )
disp ( ” kg / s ” )
disp ( ” ( i i ) Mass r a t e o f f l o w o f a i r when p r e s s u r e i n
t h e t a n k i s 300 kN/m2 ( a b s . ) ” )
22 p1 =300*10^3; //N/mˆ2
23 p2 =10^5; //N/mˆ2
24 rho_1 = p1 / R / T1 ;
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disp ( ” The p r e s s u r e r a t i o p2 / p1 b e i n g l e s s t h a n t h e
c r i t i c a l r a t i o 0.528 , the flow in the nozzle w i l l
be s o n i c ” ) ;
m_max =0.685* A2 * sqrt ( p1 * rho_1 ) ;
disp ( ”m max=” )
disp ( m_max )
disp ( ” kg / s ” )
Scilab code Exa 16.17 17
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clc
p1 =200; //kN/mˆ2
V1 =170; //m/ s
T1 =473; //K
A1 =0.001; //mˆ2
R =287; // J / kg K
cp =1000; // J / kg K
y =1.4;
disp ( ” ( i ) S t a g n a t i o n t e m p e r a t u r e ( Ts ) and s t a g n a t i o n
p r e s s u r e ( ps ) ”)
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12 Ts = T1 + V1 ^2/2/ cp ;
13 disp ( ” Ts=” )
14 disp ( Ts )
15 disp ( ”K” )
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17 ps = p1 *( Ts / T1 ) ^( y /( y -1) ) ;
18 disp ( ” p s=” )
19 disp ( ps )
20 disp ( ”kN/mˆ2 ” )
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23 disp ( ” ( i i ) S o n i c v e l o c i t y and Mach number a t
this
s e c t i o n ”)
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25 C1 = sqrt ( y * R * T1 ) ;
26 disp ( ” S o n i c v e l o c i t y =” )
27 disp ( C1 )
28 disp ( ”m/ s ” )
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30 M1 = V1 / C1 ;
31 disp ( ”Mach number = ” )
32 disp ( M1 )
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35 disp ( ” ( i i i ) V e l o c i t y , Mach number and f l o w a r e a a t
o u t l e t s e c t i o n where p r e s s u r e i s 110 kN/m2” )
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p2 =110; //kN/mˆ2
M2 = sqrt (2/( y -1) *(( ps / p2 ) ^(( y -1) / y ) - 1) ) ;
disp ( ”M2=” )
disp ( M2 )
T2 = Ts *( p2 / ps ) ^(( y -1) / y ) ;
C2 = sqrt ( y * R * T2 ) ;
V2 = M2 * C2 ;
disp ( ”V2=” )
disp ( V2 )
disp ( ”m/ s ” )
A2 =( p1 * A1 * V1 * T2 / T1 / p2 / V2 ) *10^6;
disp ( ”A2=” )
disp ( A2 )
disp ( ”mmˆ2 ” )
disp ( ” ( i v ) P r e s s u r e ( p t ) , t e m p e r a t u r e ( Tt ) , v e l o c i t y
( Vt ) , and f l o w a r e a ( At ) a t t h r o a t o f t h e n o z z l e
”)
Mt =1;
Tt = Ts /(1+( y -1) /2* Mt ^2) ;
disp ( ” Tt =” )
disp ( Tt )
disp ( ”K” )
pt = ps *( Tt / Ts ) ^( y /( y -1) ) ;
disp ( ” p t ” )
disp ( pt )
disp ( ”kN/mˆ2 ” )
Ct = sqrt ( y * R * Tt ) ;
Vt = Mt * Ct ;
At =( p1 * A1 * V1 * Tt / T1 / pt / Vt ) *10^6;
disp ( ” At=” )
disp ( At )
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disp ( ”mmˆ2 ” )
Scilab code Exa 16.18 18
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clc
y =1.4;
p1 =26.5; //kN/mˆ2
rho_1 =0.413; // kg /mˆ3
M1 =2;
R =287;
M2 = sqrt ((( y -1) * M1 ^2 + 2) /(2* y * M1 ^2 - (y -1) ) ) ;
disp ( ”Mach number M2=” )
disp ( M2 )
p2 = p1 *(2* y * M1 ^2 - (y -1) ) /( y +1) ;
disp ( ” p2=” )
disp ( p2 )
disp ( ”kN/mˆ2 ” )
rho_2 = rho_1 *(( y +1) * M1 ^2) /(( y -1) * M1 ^2 + 2) ;
disp ( ” d e n s i t y , r h o 2 =” )
disp ( rho_2 )
disp ( ” kg /mˆ3 ” )
T1 = p1 *10^3/ rho_1 / R ;
disp ( ”T1=” )
disp ( T1 )
disp ( ”K” )
T2 = T1 *(( y -1) * M1 ^2 + 2) *(2* y * M1 ^2 - (y -1) ) /(( y +1) ^2*
M1 ^2) ;
28 disp ( ”T2=” )
29 disp ( T2 )
30 disp ( ”K” )
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C1 = sqrt ( y * R * T1 ) ;
V1 = M1 * C1 ;
disp ( ”V1=” )
disp ( V1 )
disp ( ”m/ s ” )
C2 = sqrt ( y * R * T2 ) ;
V2 = M2 * C2 ;
disp ( ”V2 =” )
disp ( V2 )
disp ( ”m/ s ” )
Scilab code Exa 16.19 19
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M1 =1.5;
p1 =170; //kN/mˆ2
T1 =296; //K
y =1.4;
disp ( ” ( i ) P r e s s u r e , t e m p e r a t u r e and Mach number
downstream o f t h e s h o c k ” )
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9 p2 = p1 *(2* y * M1 ^2 - (y -1) ) /( y +1) ;
10 disp ( ” p2=” )
11 disp ( p2 )
12 disp ( ”kN/mˆ2 ” )
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14 T2 = T1 *(( y -1) * M1 ^2 + 2) *(2* y * M1 ^2 - (y -1) ) /( y +1) ^2/ M1
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^2;
disp ( ”T2=” )
disp ( T2 )
disp ( ”K” )
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19 M2 = sqrt ((( y -1) * M1 ^2 + 2) /(2* y * M1 ^2 - (y -1) ) ) ;
20 disp ( ”M2=” )
21 disp ( M2 )
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23 strength = p2 / p1 - 1;
24 disp ( ” S t r e n g t h o f s t o c k =” )
25 disp ( strength )
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