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(C) The efficiency of a Carnot heat engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1}$.The coefficient of performance of a Carnot

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$\frac{(T_1 - T_2)^2}{T_1 T_2}$

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(C) The efficiency of a Carnot heat engine is given by $\eta = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1}$.The coefficient of performance of a Carnot refrigerator is given by $\beta = \frac{T_2}{T_1 - T_2}$.We need to find the ratio of the efficiency of the heat engine to the coefficient of performance of the refrigerator:Ratio $= \frac{\eta}{\beta} = \frac{\frac{T_1 - T_2}{T_1}}{\frac{T_2}{T_1 - T_2}}$.Simplifying the expression:Ratio $= \frac{T_1 - T_2}{T_1} 	imes \frac{T_1 - T_2}{T_2} = \frac{(T_1 - T_2)^2}{T_1 T_2}$.Thus,the correct option is $C$.

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$,then the ratio of the efficiency of the heat engine to the coefficient of performance of the refrigerator is:

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