Chapter 22, Problem 1OQ

To determine

The coefficient of performance of refrigerator from second law of thermodynamics.

Answer to Problem 1OQ

Option (d), finite.

Explanation of Solution

Second law of thermodynamics states that external work is necessary to pump heat from lower temperature to higher temperature. A refrigerator takes energy from cold reservoir and expels at hot reservoir. Refrigerator has to do work to convert heat from cold reservoir to hot reservoir. Coefficient of performance is the ratio of heat extracted from cold reservoir to work done on the refrigerant.

The maximum efficiency of a refrigerator is possible if it is working in Carnot cycle. The expression for efficiency is $\frac{T_c}{T_h-T_c}$, where $T_c$ is the temperature of cold reservoir and $T_h$ is the temperature of cold reservoir. For a refrigerator hot reservoir is the environment. The difference cannot exceed a particular limit. Temperature difference will be finite always. This causes efficiency to remain in a finite value.

Conclusion:

Therefore, according to second law of thermodynamics the coefficient of performance of a refrigerator must be finite. Thus, option (d) is correct.

Since coefficient of performance of refrigerator can be greater than 1, option (a) is incorrect.

Since coefficient of performance of refrigerator can be greater than 1, option (b) is incorrect.

Since coefficient of performance of refrigerator can be greater than or less than 1, option (c) is correct.

Since coefficient of performance of refrigerator can be zero, option (e) is incorrect.