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Consider a two-stage cascade refrigeration cycle with a flash chamber as shown in the figure with refrigerant-134a as the working fluid. The evaporator temperature is −10°C and the condenser pressure is 1600 kPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.45 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure and cools the refrigerated space as it vaporizes in the evaporator. The mass flow rate of the refrigerant through the low-pressure compressor is 0.11 kg/s. Assuming the refrigerant leaves the evaporator as a saturated vapor and the isentropic efficiency is 86 percent for both compressors, determine (a) the mass flow rate of the refrigerant through the high-pressure compressor, (b) the rate of refrigeration supplied by the system, and (c) the COP of this refrigerator. Also, determine (d) the rate of refrigeration and the COP if this refrigerator operated on a single-stage vapor-compression cycle between the same evaporating temperature and condenser pressure with the same compressor efficiency and the same flow rate as calculated in part a.
FIGURE P11–65
(a)
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The mass flow rate of the refrigerant through the high-pressure compressor.
Answer to Problem 65P
The mass flow rate of the refrigerant through the high-pressure compressor is
Explanation of Solution
Show the T-s diagram as in Figure (1).
From Figure (1), write the specific enthalpy at state 6 is equal to state 5 due to throttling process.
Here, specific enthalpy at state 6 and 5 is
From Figure (1), write the specific enthalpy at state 8 is equal to state 7 due to throttling process.
Here, specific enthalpy at state 8 and 7 is
Express enthalpy at state 1.
Here, enthalpy saturation vapor at temperature of
Express entropy at state 1.
Here, entropy saturation vapor at temperature of
Express the specific enthalpy at state 2.
Here, specific enthalpy at state 2s is
Express enthalpy at state 3.
Here, enthalpy saturation vapor at pressure of
Express enthalpy at state 5.
Here, enthalpy saturation liquid at pressure of
Express enthalpy at state 7.
Here, enthalpy saturation liquid at pressure of
Express the quality at state 6.
Express the mass flow rate of the refrigerant.
Here, mass flow rate at state 7 is
Conclusion:
Refer Table A-11, “saturated refrigerant-134a-temperature table”, and write enthalpy saturation vapor at temperature of
Substitute
Refer Table A-11, “saturated refrigerant-134a-temperature table”, and write entropy saturation vapor at temperature of
Substitute
Perform the unit conversion of pressure at state 2 from
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 2s corresponding to pressure at state 2 of
Here, enthalpy at state 2s is
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the enthalpy saturation vapor at pressure of
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the enthalpy saturation liquid at pressure of
Substitute
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the enthalpy saturation liquid at pressure of
Substitute
Substitute
Substitute
Substitute
Hence, the mass flow rate of the refrigerant through the high-pressure compressor is
(b)
![Check Mark](/static/check-mark.png)
The rate of refrigeration supplied by the system.
Answer to Problem 65P
The rate of refrigeration supplied by the system is
Explanation of Solution
Express the mass flow rate at state 3.
Express the enthalpy at state 9.
Express the enthalpy at state 4.
Here, specific enthalpy at state 4s is
Express the rate of heat removal from the refrigerated space.
Conclusion:
Substitute
Substitute
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 9 corresponding to pressure at state 9 of
Here, entropy at state 9 is
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 4s corresponding to pressure at state 4 of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is specific entropy at state 9 and specific enthalpy at state 4s respectively.
Show the specific enthalpy at state 4s corresponding to specific entropy as in Table (1).
Specific entropy at state 9 |
Specific enthalpy at state 4s |
0.9164 | 280.71 |
0.9399 | |
0.9536 | 293.27 |
Substitute
Thus, the specific enthalpy at state 4s is,
Substitute
Substitute
Hence, the rate of refrigeration supplied by the system is
(c)
![Check Mark](/static/check-mark.png)
The COP of the refrigerator.
Answer to Problem 65P
The COP of the refrigerator is
Explanation of Solution
Express the power input.
Express the coefficient of performance.
Conclusion:
Substitute
Substitute
Hence, the coefficient of performance of the refrigerator is
(d)
![Check Mark](/static/check-mark.png)
The rate of refrigeration and the COP of the refrigerator.
Answer to Problem 65P
The rate of refrigeration is
Explanation of Solution
Show the T-s diagram as in Figure (1).
From Figure (1), write the specific enthalpy at state 4 is equal to state 3 due to throttling process.
Here, specific enthalpy at state 4 and 3 is
Express the enthalpy at state 2.
Here, specific enthalpy at state 2s is
Express enthalpy at state 3.
Here, enthalpy saturation vapor at pressure of
Express the rate of refrigeration.
Express the rate of work input.
Express the coefficient of performance.
Conclusion:
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 2s corresponding to pressure at state 2 of
Show the specific enthalpy at state 2s corresponding to specific entropy as in Table (2).
Specific entropy at state 2 |
Specific enthalpy at state 2s |
0.9164 | 280.71 |
0.9378 | |
0.9536 | 293.27 |
Use excels and tabulates the values from Table (2) in Equation (XV) to get,
Thus, the specific enthalpy at state 2s is,
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the enthalpy saturation liquid at pressure of
Substitute
Substitute
Substitute
Hence, the rate of refrigeration is
Substitute
Substitute
Hence, the coefficient of performance of the refrigerator is
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Chapter 11 Solutions
THERMODYNAMICS (LL)-W/ACCESS >CUSTOM<
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- Refrigeration and Air Conditioning Technology (Mi...Mechanical EngineeringISBN:9781305578296Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill JohnsonPublisher:Cengage Learning
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