Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 50°C at a rate of 0.022 kg/s and leaves at 750 kPa subcooled by 3°C. The refrigerant enters the compressor at 200 kPa superheated by 4°C. Determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the COP of the heat pump. Also, determine (d) the COP and the rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kPa.
FIGURE P11–42
(a)
The isentropic efficiency of the compressor.
Answer to Problem 42P
The isentropic efficiency of the compressor is
Explanation of Solution
Show the T-s diagram for process as in Figure (1).
From Figure (1), write the specific enthalpy at state 3 is equal to state 4 due to throttling process.
Here, specific enthalpy at state 3 and 4 is
Express isentropic efficiency of the compressor.
Here, specific enthalpy at state 1, 2 and 2s is
Express the temperature at state 3.
Here, saturated temperature at pressure of
Express the temperature at state 1.
Here, saturated temperature at pressure of
Express quality at state 2s.
Here, specific entropy at saturated liquid and evaporation and
Express specific enthalpy at state 2s.
Here, specific enthalpy at saturated liquid and evaporation and
Conclusion:
Perform unit conversion of pressure at state 2 from
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 2 corresponding to pressure at state 2 of
Refer Table A-12, “saturated refrigerant-134a-pressure table” and write saturated temperature at pressure of
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table” and write specific enthalpy at state 3 corresponding to pressure at state 3 of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is temperature at state 3 and specific enthalpy at state 3 respectively.
Show the specific enthalpy at state 3 corresponding to temperature as in Table (1).
Temperature at state 3 |
Specific enthalpy at state 3 |
26.69 | 88.82 |
26.06 | |
29.06 | 92.22 |
Substitute
Since the specific enthalpy at state 3 is equal to state 4 due to throttling process.
Refer Table A-12, “saturated refrigerant-134a-pressure table” and write saturated temperature at pressure of
Substitute
Refer Table A-12, “saturated refrigerant-134a-pressure table” and write specific enthalpy and entropy at state 1 corresponding to pressure at state 1 of
Here, specific entropy at state 1 is
The specific entropy at state 1 is equal to specific entropy at state 1.
Here, specific entropy at state 2 is
Refer Table A-12, “saturated refrigerant-134a-pressure table” and write the properties corresponding to pressure at state 2 of
Substitute
Substitute
Substitute
Hence, the isentropic efficiency of the compressor is
(b)
The rate of heat supplied to the heated room.
Answer to Problem 42P
The rate of heat supplied to the heated room is
Explanation of Solution
Express the rate of heat supplied to the heated room.
Here, mass flow rate is
Conclusion:
Substitute
Hence, the rate of heat supplied to the heated room is
(c)
The COP of the heat pump.
Answer to Problem 42P
The COP of the heat pump is
Explanation of Solution
Express the rate of work input.
Express coefficient of performance of heat pump.
Conclusion:
Substitute
Substitute
Hence, the COP of the heat pump is
(d)
The COP and the rate of heat supplied to the heated room.
Answer to Problem 42P
The COP and the rate of heat supplied to the heated room is
Explanation of Solution
Show the T-s diagram for ideal vapor compression cycle as in Figure (2).
From Figure (2), write the specific enthalpy at state 3 is equal to state 4 due to throttling process.
Express the coefficient of performance.
Express the rate of heat supplied to the heated room.
Conclusion:
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the properties corresponding to initial pressure of
Here, specific entropy at state 1 is
Refer Table A-13, “superheated refrigerant 134a”, and write the specific enthalpy at state 2 corresponding to pressure at state 2 of
Show the specific enthalpy at state 2 corresponding to specific entropy as in Table (2).
Specific entropy at state 2 |
Specific enthalpy at state 2 |
0.9185 | 267.34 |
0.9379 | |
0.9481 | 276.46 |
Use Excels and substitute the values from Table (2) in Equation (VI) to get,
Refer Table A-12, “saturated refrigerant-134a-pressure table”, and write the specific enthalpy at state 3 corresponding to pressure at state 3
Here, specific enthalpy at saturated liquid is
Since the specific enthalpy at state 3 is equal to state 4 due to throttling process.
Substitute
Substitute
Hence, the COP and the rate of heat supplied to the heated room is
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