A refrigerator freezer compartment is maintained at a temperature of -15°F by re

Question

A refrigerator freezer compartment is maintained at a temperature of -15°F by removing heat at a rate of 4500 Btu/hr. The refrigerator is located in a room with a temperature of 75°F. The power input required to run the refrigerator is 1200 Btu/hr.

(a) Calculate the COP for the refrigeration cycle.
(b) Calculate the rate of heat transfer (Btu/hr) from the refrigerant to the room.
(c) Calculate the power (Btu/hr) to run the cycle and the heat transfer rate (Btu/hr) from the refrigerant to the room if the refrigeration cycle was reversible. Assume that the heat transfer rate from the freezer compartment to the refrigerant is the same 4500 Btu/hr as for the actual cycle.

Explanation / Answer

T1 = 75 F = 296.89 K

T2 = - 15 F = 246.89 K

W in = 1200 Btu hr

heat removed = Q2 = 4500 Btu/hr

COP = Q2/W in = 4500/1200 = 3.75

b) heat given to room = Q1 = Q2 + W in = 4500 + 1200 = 5700 Btu/hr

c) For reversible cycle,

COP' = T2/ (T1 - T2)

= 246.89 / (296.89 - 246.89)

= 4.94

Also Q2 = 4500 Btu/hr

NOW COP' = Q2/ Win

4.94 = 4500/ W in

W in = 910.93 Btu/hr = power required

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