A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at −35°C by rejecting waste heat to cooling water that enters the condenser at 18°C at a rate of 0.25 kg/s and leaves at 26°C. The refrigerant enters the condenser at 1.2 MPa and 50°C and leaves at the same pressure subcooled by 5°C. If the compressor consumes 3.3 kW of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the COP, and (d) the minimum power input to the compressor for the same refrigeration load.
FIGURE P6–107
(a)
The mass flow rate of the refrigerant.
Answer to Problem 107P
The mass flow rate of the refrigerant is
Explanation of Solution
Determine the rate of heat transferred to the water.
Here, the mass flow rate of the water is
Determine the mass flow rate of a refrigerant.
Conclusion:
From the Table A-13, “Superheated refrigerant R-134a” obtain the value of enthalpy of the refrigerant at the inlet of the condenser at the 1.2 MPa of pressure and
From the Table A-13, “Superheated refrigerant R-134a” obtain the value of temperature of the refrigerant at the inlet of the condenser at the 1.2 MPa of pressure as,
Calculate the exit temperature of the refrigerant in the condenser.
Here, the temperature leave from the condenser is
Substitute
Refer to Table A-11, “Saturated refrigerant R-134a”, obtain the below exit enthalpy of the condenser at compressed liquid state on the basis of exit temperature of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y are temperature and enthalpy of vaporization.
Show the temperature at
S. No |
Temperature, |
enthalpy of vaporization |
1 | ||
2 | ||
3 |
Calculate exit enthalpy of the condenser at compressed liquid state on the basis of exit temperature of
Substitute
From above calculation the exit enthalpy of the condenser at compressed liquid state on the basis of exit temperature of
Repeat the above Equation (IV) to obtain the value of enthalpy of saturated liquid that entering the inlet of the condenser at the
Repeat the above Equation (IV) to obtain the value of enthalpy of saturated liquid which is leaving the condenser at the
Substitute
Substitute
Thus, the mass flow rate of the refrigerant is
(b)
The refrigeration load of the refrigerator.
Answer to Problem 107P
The refrigeration load of the refrigerator is
Explanation of Solution
Determine the refrigeration load of the refrigerator.
Here, the power input consumed by compressor is
Conclusion:
Substitute
Thus, the refrigeration load of the refrigerator is
(c)
The COP of a reversible refrigerator operating between the same temperature limits.
Answer to Problem 107P
The COP of a reversible refrigerator operating between the same temperature limits is
Explanation of Solution
Determine the coefficient of performance of the refrigerator.
Conclusion:
Substitute
Thus, the COP of a reversible refrigerator operating between the same temperature limits is
(d)
The minimum power input to the compressor.
Answer to Problem 107P
The minimum power input to the compressor is
Explanation of Solution
Determine the maximum coefficient of performance of the reversible refrigerator 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 refrigerator load.
Conclusion:
Substitute
Substitute
Thus, the minimum power input to the compressor is
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EBK THERMODYNAMICS: AN ENGINEERING APPR
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