A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25°C by absorbing heat from geothermal water that enters the evaporator at 60°C at a rate of 0.065 kg/s and leaves at 40°C. Refrigerant enters the evaporator at 12°C with a quality of 15 percent and leaves at the same pressure as saturated vapor. If the compressor consumes 1.6 kW of power, determine (a) the mass flow rate of the refrigerant, (b) the rate of heat supply, (c) the COP, and (d) the minimum power input to the compressor for the same rate of heat supply.
FIGURE P6–152
(a)
The mass flow rate of the refrigerant.
Answer to Problem 152RP
The mass flow rate of the refrigerant is
Explanation of Solution
Determine the rate of heat absorbed from the water.
Here, the mass flow rate of the water is
Determine the mass flow rate of a refrigerant.
Conclusion:
From the Table A-11, “Saturated refrigerant R-134a”, obtain the value of saturated pressure of the refrigerant at the inlet temperature of
Here, the pressure of refrigerant is constant in evaporation.
From the Table A-11, “Saturated refrigerant R-134a” to obtain the value of specific enthalpy of the refrigerant at the outlet pressure of
From the Table A-11, “Saturated refrigerant R-134a” to obtain the value of specific enthalpy of saturated liquid and specific enthalpy change upon vaporization of the refrigerant at the inlet temperature of
Calculate the specific enthalpy of refrigerant at evaporator inlet.
Here, the specific enthalpy of saturated liquid is
Substitute
From the Table A-4, “Saturated water-temperature” to obtain the value of specific enthalpy of saturated liquid of water at the inlet temperature of
From the Table A-4, “Saturated water-temperature” to obtain the value of specific enthalpy of saturated liquid of water at the outlet temperature of
Substitute
Substitute
Thus, the mass flow rate of the refrigerant is
(b)
The heating load of the heat pump.
Answer to Problem 152RP
The heating load of the heat pump is
Explanation of Solution
Determine the heating load of the heat pump.
Here, the power input consumed by compressor is
Conclusion:
Substitute
Thus, the heating load of the heat pump is
(c)
The COP of a heat pump operating between the same temperature limits.
Answer to Problem 152RP
The COP of a heat pump operating between the same temperature limits is
Explanation of Solution
Determine the coefficient of performance of the heat pump.
Conclusion:
Substitute
Thus, the COP of a heat pump operating between the same temperature limits is
(d)
The minimum power input to the compressor.
Answer to Problem 152RP
The minimum power input to the compressor is
Explanation of Solution
Determine the maximum coefficient of performance of the heat pump operating between the same temperature limits.
Here, the temperature of higher temperature body is
Determine the minimum power input to the condenser for the same heat pump load.
Conclusion:
Substitute
Substitute
Thus, the minimum power input to the compressor is
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Chapter 6 Solutions
Thermodynamics: An Engineering Approach
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