11-42
11-58 A two-stage compression refrigeration system with refrigerant-134a as the working fluid is considered. The fraction
of the refrigerant that evaporates as it is throttled to the flash chamber, the rate of heat removed from the refrigerated space,
and the COP are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. 3 The flash
chamber is adiabatic.
Analysis (a) The enthalpies of the refrigerant at several states are determined from the refrigerant tables (Tables A-11, A12, and A-13) to be
h1  234.44 kJ/kg,
h2  271.40 kJ/kg
h3  262.40 kJ/kg,
T
h5  127.22 kJ/kg,
h6  127.22 kJ/kg
h7  81.51 kJ/kg,
h8  81.51 kJ/kg
The fraction of the refrigerant that evaporates as it is
throttled to the flash chamber is simply the quality at
state 6,
x6 
h6  h f
h fg

1.4 MPa
4
0.6 MPa
5
2
A
7
127.22  81.51
 0.2527
180.90
6
B
8
(b) The enthalpy at state 9 is determined from an energy
balance on the mixing chamber:
0.10 MPa
3 9
·
QL
1
s
E in  E out  E system 0 (steady)  0
E in  E out
 m h   m h
e e
i i
1h9  x 6 h3  1  x6 h2
h9  0.2527 262.40   1  0.2527 271.40   269.13 kJ/kg
P9  0.6 MPa

 s 9  0.9443 kJ/kg  K
h9  269.13 kJ/kg 
also,
P4  1.4 MPa

 h4  287.28 kJ/kg
s 4  s 9  0.9443 kJ/kg  K 
Then the rate of heat removed from the refrigerated space and the compressor work input per unit mass of refrigerant
flowing through the condenser are
m B  1  x 6 m A  1  0.2527 0.25 kg/s   0.1868 kg/s
Q L  m B h1  h8   0.1868 kg/s 234.44  81.51 kJ/kg  28.57 kW
W in  W compI,in  W compII,in  m A h4  h9   m B h2  h1 
 0.25 kg/s 287.28  269.13 kJ/kg  0.1868 kg/s 271.40  234.44  kJ/kg
 11.44 kW
(c) The coefficient of performance is determined from
COPR 
Q L
W
net,in

28.57 kW
 2.50
11.44 kW
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