Question

The efficiency of a reversible heat engine working between two temperatures is 50\%. The coefficient of performance of a refrigerator working between the same two temperatures but in reverse direction is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

COP of a refrigerator is the inverse of the efficiency difference of a heat engine operating between the same temperatures.

Answer 1

The Correct Option is A

The efficiency of a heat engine is: \[ \eta = \frac{T_H - T_C}{T_H} = 0.5 \] \[ \frac{T_H - T_C}{T_H} = \frac{1}{2} \] \[ T_H - T_C = \frac{T_H}{2} \] \[ T_H = 2T_C \] The coefficient of performance (COP) of a refrigerator is given by: \[ COP = \frac{T_C}{T_H - T_C} \] \[ COP = \frac{T_C}{T_H - T_C} = \frac{T_C}{T_C} = 1 \]