CHAPTER 6
1. An open air refrigeration system carries a load of 35 kW with a suction pressure
of 103 kPa and a discharge pressure of 690 kPa. The temperature leaving the
refrigerator is 5 C and that leaving the cooler is 30 C. The compression is
polytropic with n = 1.33 and the expansion is also polytropic but with n = 1.35 .
Determine the power required and the COP .
Solution:
T1 = 5 + 273 = 278 K
T3 = 30 + 273 = 303 K
p 
T4 = T3  s 
 p4 
n 2 −1
n2
0.35
 103  1.35
= (303)
 = 185 K
 690 
Q& A = m& c p (T1 − T4 )
35 = m& (1.0 )(278 − 185)
m& = 0.376 kg s
CHAPTER 6
W&
W&
W&
n1 −1
n 2 −1




n2


&
n1m& RT1  pd  n1
n
m
RT
p

2
3 
s
 
 
=
−1 +
− 1


n1 − 1  ps 
n2 − 1  pd 




0.33
0.35




(
1.33)(0.376 )(0.287 )(278)  690  1.33  (1.35)(0.376 )(0.287 )(303)  103  1.35 
=

 −1 +

 −1
 103 

 690 

0.33
0.35




= 23.82 kW
Q&
35
COP = &A =
= 1.47
W 23.82
2. An air refrigeration system is required to produce 52.5 kW of refrigeration with a
cooler pressure of 1448 kPa and a refrigerator pressure of 207 kPa. Leaving air
temperatures are 29 C for cooler and 5 C for refrigerator. Expansion is isentropic
and compression is polytropic with n = 1.34 . Determine the COP .
Solution:
T1 = 5 + 273 = 278 K
T3 = 29 + 273 = 302 K
ps = 207 kPa
pd = 1448 kPa
p 
T4 = T3  s 
 p4 
n 2 −1
n2
0.4
 207  1.4
= (302 )
 = 173 K
 1448 
Q& A = m& c p (T1 − T4 )
52.5 = m& (1.0 )(278 − 173)
m& = 0.50 kg s
CHAPTER 6
W&
W&
W&
n1 −1
n 2 −1




n2


&
n1m& RT1  pd  n1
n
m
RT
p

2
3 
s
 
 
=
−1 +
− 1


n1 − 1  ps 
n2 − 1  pd 




0.34
0.4




(
1.34 )(0.50)(0.287 )(278)  1448  1.34  (1.4 )(0.50 )(0.287 )(302 )  207  1.4 
=

 −1 +

 −1
 207 

 1448 

0.34
0.4




= 35.66 kW
Q&
52.5
COP = &A =
= 1.47
W 35.66