ICAMET-D-XXX
THERMODYNAMIC PROPERTY FORMULATION OF
HALOGENATED HYDROCARBON REFRIGERANTS
USING VIRIAL COEFFICIENT TYPE EQUATION OF
STATE
A. Author, B. Author, C. Author
Department of Mechanical Engineering
Bengal Engineering and Science University, Shibpur, Howrah, West Bengal- 711103, INDIA
E-mail: ranendraroy2009@gmail.com
FORMULATION
•Formulation of different thermodynamic properties
of halogenated hydrocarbon refrigerants using four
basic equations, namely liquid density, vapour
pressure at saturation, equation of state and
constant volume specific heat given by Downing.
These equations are combined by exact
thermodynamic relationships.
•The virial coefficient type of equation of state is
solved using binary search method. Other equations
are solved and coded in FORTRAN.
•The program accepts temperature as input and
calculates different thermodynamic properties in the
temperature range of –80°C to + 80°C. It can also
generate the thermodynamic properties of the
refrigerants at sub-cooled and superheated state if,
in addition to saturation temperature, degree of
subcool or degree of superheat is supplied.
•The code and hence the formulation is tested for
refrigerant R-12. It is observed that the data
predicted from the present formulation are within the
acceptable limit for all practical purposes.
The expression for liquid density

  RL(3)1  T TC   RL( 4)1  T
43
5/ 3
2
TC 
 RL( 6)1  T TC 
 RL( 7 )1  T TC 
ρ L  RL(1)  RL( 2) 1  T TC

 RL(5) 1  T
13
2/3
TC

Saturated vapour pressure
Log10P  AVP (1) AVP (2)/T AVP (3)Log10T  AVP (4)T
AVP (6) T Log  AVP (6) T   AVP (7)/T2  AVP (8)T2

 AVP (5).
10

T


Equation of state


A(2)  B(2)T C( 2) μ exp(  KT /TC)  ν/T3
A(3)  B(3)T C(3) exp(  KT /TC )
RT
P


2
V b
(V b)
(V b) 3


A(4)  B(4)T C( 4) μ exp(  KT /TC )  ν/T3 A(5)  B(5)T C(5) exp(  KT /TC )


4
(V b)
(V b) 5
A(6)  B(6)T C(6) exp(  KT /TC )

exp(aV)1 C' exp(aV)




Constant volume specific heat of vapour at zero pressure
0
CV
2
3
 ACV(1)  ACV(2)T  ACV(3)T  ACV(4)T  ACV(5) / T
Derivation of enthalpy
PRIMARY FOCUS OF THE STUDY:
To develop a computer code for the
thermodynamic
properties
of
halogenated
hydrocarbon refrigerants based on the basic
refrigerant equations of Downing.
Percentage errors calculation for different
saturated properties in comparison to ASHRAE
handbook data.
Validation of code by comparing the properties
of refrigerant R-12 obtained in this work with
ASHRAE handbook and other standard sources.
dH 
0
CV dT  d(PV) 
Derivation of entropy

 P  
P  T  T   dV
 V 

T
dS 
0
CV
T
Latent heat of vapourization
H fg
 dP 

 
 dT  sat T  Vg  Vf 
 P 
dT  
 dV
 T V
PV
H(T ,P )  C 0V dT 
Tref
2
 d(P V)
T C0
V
V
S(T,P)  
dT  
Tref T
Vref
Pref Vref
  P  T (P /T )V dV  H ref
V
 P 
  dV  Sref
 T V
Vref
Saturated liquid enthalpy and entropy
Hf  Hg  Hfg
Sf  Sg  Hfg /T
RESULTS
300
1.70
R-12
280
1.3
380
R-12
R-12
R-12
260
370
1.2
240
360
1.1
R-12
Saturated vapour entropy,sg(kJ/kg-K)
2.0
1.6
Present computation
0.8
220
200
180
Present Computation
ASHRAE Data
140
-60
-40
-20
0
20
40
60
80
-80
100
-60
-40
20
40
60
80
100
-80
hf (kJ/kg)
Present ASHRAE % Error
data
data
-60
-40
Present
data
129.301
137.766
146.486
155.173
163.969
172.813
181.774
190.823
200.000
209.322
218.817
228.530
238.520
248.861
259.659
271.059
283.282
315
319.655
324.301
328.965
333.607
338.212
342.751
347.206
351.551
355.762
359.808
363.650
367.234
370.491
373.313
375.542
376.911
-20
0
314.99
319.69
324.44
329.23
334.03
338.81
343.53
348.176
352.68
357.05
361.23
365.16
368.81
372.07
374.86
377.01
378.26
+ 0.01
- 0.01
- 0.04
- 0.08
- 0.12
- 0.17
- 0.22
- 0.27
- 0.32
-0.36
-0.39
- 0.41
-0.42
-0.42
- 0.41
-0.38
-0.35
Tsat (0C)
Psat
(bar)
0.639
1.500
2.178
3.069
4.212
5.646
9.567
40
60
80
100
Variation of saturated vapour specific
enthalpy of R-12 with temperature
h(S/H), kJ/kg
Present
values
- 40.00
- 20.00
-10.00
0.00
10.00
20.00
40.00
20
0
Superheated Table of R12 (20K)
hg (kJ/kg)
ASHRAE % Error
data
344.845
354.789
359.684
364.502
369.221
373.821
382.551
*Values
from
Heyhood
34.7
354.7
359.6
364.4
369.1
373.7
382.4
0.9
s(S/H), kJ/kg-K
Present *Values
values
from
Heyhood
1.630 1.6317
1.610 1.6126
1.604 1.6057
1.598 1.6003
1.594 1.5961
1.590 1.5928
1.585 1.5880
* Heywood, R.W., 1968. Thermodynamics Tables in
S.I.Units, Cambridge University Press
Present Computation
ASHRAE Data
0.7
Temperature ( C)
Variation of saturated liquid specific
enthalpy of R-12 with temperature
Saturated Table of R12
- 0.32
- 0.30
- 0.15
- 0.09
- 0.02
0.00
+ 0.02
+ 0.02
0.00
- 0.04
- 0.09
- 0.15
- 0.21
-0.26
- 0.27
-0.24
-0.16
0
0
Variation of saturated vapour specific
volume of R-12 with temperature
129.72
138.19
146.72
155.32
164.01
172.81
181.72
190.78
200.00
209.41
219.03
228.89
239.03
249.51
260.37
271.73
283.75
Present Computation
ASHRAE Data
Temperature ( C)
Temperature ( C)
(00C)
- 80
- 70
- 60
- 50
- 40
- 30
- 20
- 10
0
10
20
30
40
50
60
70
80
-20
1.0
0.8
310
0
Temperature
340
320
120
0.0
-80
350
330
160
0.4
sf(kJ/kg-K)
3
1.2
hg(kJ/kg)
hf, (kJ/kg)
ASHRAE Data
vg (m /kg)
International Conference on Advanced Materials & Energy Technology-Symposia A, IIEST Shibpur, December 17-19, 2014
ABSTRACT
0.6
-80
-60
-40
-20
0
20
40
60
80
100
O
Temperature ( C)
Variation of saturated liquid specific
entropy of R-12 with temperature
1.65
1.60
1.55
1.50
Present Computation
ASHRAE Data
1.45
1.40
-80
-60
-40
-20
0
20
40
60
80
100
0
Temperature( C)
Variation of saturated vapour specific
entropy of R-12 with temperature
CONCLUSION
 A Computer code has been developed for the thermodynamic properties of halogenated
hydrocarbon refrigerants based on the basic refrigerant equations of Downing and some
exact thermodynamic relationships.
 The code is also validated by comparing the different properties of refrigerant R-12
obtained in the present work with the data available in ASHRAE handbook and other
standard sources.
 Percentage errors for different saturated properties in comparison to ASHRAE handbook
data are calculated and some of them are presented in tabular form. The properties of
superheated vapour are also compared with standard values.
 The variations of all the relevant saturated properties of refrigerant R-12 with temperature
are also presented graphically. The agreement is excellent except a few cases.
 The present code can be directly extended to find the thermodynamic properties of other
commonly used halogenated refrigerants by changing the values of different constants
used in different equations.