Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

622 | Thermodynamics

(In practice, the working fluid of the lower cycle is at a higher pressure and

temperature in the heat exchanger for effective heat transfer.) If the mass flow

rate of the refrigerant through the upper cycle is 0.05 kg/s, determine (a) the

mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat

removal from the refrigerated space and the power input to the compressor,

and (c) the coefficient of performance of this cascade refrigerator.

Solution A cascade refrigeration system operating between the specified

pressure limits is considered. The mass flow rate of the refrigerant through

the lower cycle, the rate of refrigeration, the power input, and the COP are to

be determined.

Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential

energy changes are negligible. 3 The heat exchanger is adiabatic.

Properties The enthalpies of the refrigerant at all eight states are deter-

mined from the refrigerant tables and are indicated on the T-sdiagram.

Analysis The T-sdiagram of the refrigeration cycle is shown in Fig. 11–11.

The topping cycle is labeled cycle Aand the bottoming one, cycle B. For

both cycles, the refrigerant leaves the condenser as a saturated liquid and

enters the compressor as saturated vapor.

(a) The mass flow rate of the refrigerant through the lower cycle is deter-

mined from the steady-flow energy balance on the adiabatic heat exchanger,

(b) The rate of heat removal by a cascade cycle is the rate of heat absorption

in the evaporator of the lowest stage. The power input to a cascade cycle is

the sum of the power inputs to all of the compressors:

W

#

in
W

#

comp I,inW

#

comp II,in
m

#

A^1 h 6 h 52 m

#

B^1 h 2 h 12

Q

#

L
m

#

B^1 h 1 h 42 
^1 0.0390 kg>s^231 239.1655.16^2 kJ>kg^4 
7.18 kW

m#B
0.0390 kg/s

1 0.05 kg>s 231 251.8895.47 2 kJ>kg 4 
m

#

B^31 255.9355.16^2 kJ>kg^4

m#A 1 h 5 h 82 
m#B 1 h 2 h 32

E

#

out
E

#

in^ ¡^ m

#

Ah 5 m

#

Bh 3 
m

#

Ah 8 m

#

Bh 2

4

3

2

1

T

s

6

7

8 5

h 3 = 55.16

h 7 = 95.47

h 6 = 270.92 kJ/kg

h 2 = 255.93

h 5 = 251.88

h 1 = 239.16

h 4 = 55.16

h 8 = 95.47

0.8 MPa

0.32 MPa

0.14 MPa

A

B

FIGURE 11–11

T-sdiagram of the cascade
refrigeration cycle described in
Example 11–3.