Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 35°C at a rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid. If the compressor consumes 1.2 kW of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption from the outside air.
FIGURE P6–57
(a)
The COP of the heat pump.
Answer to Problem 57P
The COP of the heat pump is
Explanation of Solution
Write the expression for the energy balance equation.
Here, the total energy entering the system is
Simplify Equation (II) and write energy balance relation of refrigrent-134a.
Here, the rate of work to be done into the system is
Substitute
Write the expression for the rate of coefficient performance of a heat pump.
Here the rate of required input of the heat pump is
Conclusion:
Convert the unit of pressure from kPa to MPa.
Refer to Table A-13, “Superheated refrigerant-134a”, obtain the below properties at the superheated pressure and temperature of 800 kPa (0.80 MPa) and 35 C using interpolation method of two variables.
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y are superheated temperature and specific enthalpy.
Show the temperature at 31.31 C and 40 C as in Table (1).
Temperature, C | Specific enthaply, |
Saturated liquid, | |
31.31 C | 267.34 |
35 C | ? |
40 C | 276.46 |
Calculate superheated pressure and temperature of 800 kPa (0.80 MPa) and 35 C for liquid phase using interpolation method.
Substitute 31.31 C for
From above calculation the initial enthalpy of condenser is
Refer to Table A-12, “Saturated pressure table” obtain properties at the superheated pressure and quality of final state of 800 kPa and 0.
Write the expression of final specific enthalpy of a two-phase system for condenser.
Here, the specific enthalpy of condenser is
Substitute
Substitute
Substitute
Thus, the COP of the heat pump is
(b)
The rate of heat absorbed from the outside air.
Answer to Problem 57P
The rate of heat absorbed from the outside air is
Explanation of Solution
Write the expression for the rate of conversation of energy principle for refrigerant 134a.
Here, the rate of heat rejected in the condenser is
Conclusion:
Substitute
Thus, the rate of heat absorbed from the outside air is
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Chapter 6 Solutions
EBK THERMODYNAMICS: AN ENGINEERING APPR
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