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(A) The coefficient of performance $(COP)$ of a refrigerator is defined as the ratio of the heat extracted from the cold reservoir $(Q_2)$ to the work

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When the work done on the system is zero.

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(A) The coefficient of performance $(COP)$ of a refrigerator is defined as the ratio of the heat extracted from the cold reservoir $(Q_2)$ to the work done on the system $(W)$.Mathematically,$COP = \frac{Q_2}{W}$.According to the first law of thermodynamics,$W = Q_1 - Q_2$,where $Q_1$ is the heat rejected to the hot reservoir.If the work done on the system $(W)$ is zero,the denominator becomes zero.As $W 	o 0$,the $COP = \frac{Q_2}{W} 	o \infty$.Therefore,the coefficient of performance becomes infinity when the work done on the refrigerator is zero.

Why does the coefficient of performance of a refrigerator become infinity?

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