An ideal reversible refrigerator keeps its inside compartment at 9.0°C.What is the high temperature,T_h,needed to give this refrigerator a coefficient of performance of 3.7? A) 85°C B) 1052°C C) 11°C D) 42°C

Question

Quizplus · Accepted Answer

The coefficient of performance of a refrigerator is given by the ratio of the heat removed from the cold reservoir to the work done. In this case, the coefficient of performance is 3.7, so the heat removed from the cold reservoir is 3.7 times the work done. The heat removed from the cold reservoir is equal to the heat absorbed by the refrigerant, which is equal to the difference in temperature between the high and low temperatures multiplied by the specific heat of the refrigerant. The work done is equal to the difference in temperature between the high and low temperatures multiplied by the Carnot efficiency. Therefore, the coefficient of performance is equal to the ratio of the specific heat of the refrigerant to the Carnot efficiency. In this case, the specific heat of the refrigerant is 1, so the Carnot efficiency is 1/3.7 = 0.27. The Carnot efficiency is equal to 1 - T_c/T_h, where T_c is the low temperature and T_h is the high temperature. Therefore, T_h = T_c/(1 - Carnot efficiency) = 9°C/(1 - 0.27) = 85°C.

An Ideal Reversible Refrigerator Keeps Its Inside Compartment at 9