A reversible refrigerator operates between a low temperature reservoir at T_C and a high temperature reservoir at T_H. Its coefficient of performance is given by: A) (T_H - T_C)/T_C B) T_C/(T_H - T_C) C) (T_H - T_C)/T_H D) T_H/(T_H - T_C) E) T_H(T_H + T_C)

Question

Quizplus · Accepted Answer

The coefficient of performance (COP) of a refrigerator is defined as the ratio of the amount of heat extracted from the low temperature reservoir to the amount of work done by the compressor. Mathematically, COP = QL/W, where QL is the amount of heat extracted from the low temperature reservoir and W is the amount of work done by the compressor. The work done by the compressor is equal to the difference in the amount of heat absorbed by the refrigerator from the low temperature reservoir and the amount of heat rejected to the high temperature reservoir, i.e., W = QH - QL, where QH is the amount of heat rejected to the high temperature reservoir. Therefore, the COP can also be expressed as COP = QL/(QH - QL). In the given options, only option B is in this form, i.e., COP = QL/(QH - QL) = T_C/(T_H - T_C), hence it is the correct answer.

A Reversible Refrigerator Operates Between a Low Temperature Reservoir at TC

A Reversible Refrigerator Operates Between a Low Temperature Reservoir at T_C