11-52
11-66 A two-stage cascade refrigeration cycle with a flash chamber with refrigerant-134a as the working fluid is
considered. The mass flow rate of the refrigerant through the high-pressure compressor, the rate of refrigeration, the COP
are to be determined. Also, the rate of refrigeration and the COP are to be determined if this refrigerator operated on a
single-stage vapor-compression cycle under similar conditions.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible.
Analysis (a) From the refrigerant-134a tables (Tables A-11 through A-13)
h1  h g @ 10C  244.51 kJ/kg
s1  s g @ 10C  0.9377 kJ/kg.K
P2  450 kPa 
 h2 s  261.07 kJ/kg

s 2  s1
C 
0.86 
h2 s  h1
h2  h1
261.07  244.51

 h2  263.76 kJ/kg
h2  244.51
T
1.6 MPa
4s 4
5
A
7
6
9
B 3
−10C
8
h3  h g @ 450 kPa  257.53 kJ/kg
2s
2
0.45 MPa
1
s
h5  h f @ 1600 kPa  135.93 kJ/kg
h6  h5  135.93 kJ/kg
h7  h f @ 450 kPa  68.81 kJ/kg
h8  h7  68.81 kJ/kg
h6  135.93 kJ/kg 
 x 6  0.3557
P6  450 kPa

The mass flow rate of the refrigerant through the high pressure compressor is determined from a mass balance on the flash
chamber
m 
m 7
0.11 kg/s

 0.1707 kg/s
1  x 6 1  0.3557
Also,
m 3  m  m 7  0.1707  0.11  0.06072 kg/s
(b) The enthalpy at state 9 is determined from an energy balance on the mixing chamber:
m h9  m 7 h2  m 3 h3
(0.1707 kg/s)h9  (0.11 kg/s)(263.76 kJ/kg)  (0.06072 kg/s)(257.53 kJ/kg) 
 h9  261.54 kJ/kg
Then,
P9  450 kPa

s 9  0.9393 kJ/kg
h9  261.54 kJ/kg 
P4  1600 kPa 
 h4 s  288.41 kJ/kg
s 4  s9

C 
0.86 
h4 s  h9
h4  h9
288.41  261.54

 h4  292.78 kJ/kg
h4  261.54
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.
11-53
The rate of heat removal from the refrigerated space is
Q L  m 7 (h1  h8 )  (0.11 kg/s)(244.51  68.81)kJ/kg  19.33 kW
(c) The power input and the COP are
W in  m 7 (h2  h1 )  m (h4  h9 )
 (0.11 kg/s)(263.76  244.51)kJ/kg  (0.1707 kg/s)(292.78  261.54)kJ/kg  7.45 kW
COP 
Q L 19.33

 2.59
7.45
W in
(d) If this refrigerator operated on a single-stage cycle between the same pressure limits, we would have
h1  h g @ 10C  244.51 kJ/kg
s1  s g @ 10C  0.9377 kJ/kg.K
P2  1600 kPa 
 h2 s  287.85 kJ/kg
s 2  s1

h  h1
 C  2s
h2  h1
2
T
·
QH
2s
·
Win
1.6 MPa
3
287.85  244.51
0.86 

 h2  294.90 kJ/kg
h2  244.51
−10C
4
·
QL
1
s
h3  h f @ 1600 kPa  135.93 kJ/kg
h4  h3  135.93 kJ/kg
Q L  m (h1  h4 )  (0.1707 kg/s)(244.51  135.93)kJ/kg  18.54 kW
W in  m (h2  h1 )  (0.1707 kg/s)(294.90  244.51)kJ/kg  8.60 kW
COP 
Q L 18.54

 2.16
8.60
W in
Discussion The cooling load decreases by 4.1% while the COP decreases by 16.6% when the cycle operates on the singlestage vapor-compression cycle.
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.
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