For which combination of working temperatures | vedclass

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(D) The efficiency of a Carnot engine is given by the formula $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the temperature of the source and $T_2$ is t

Vedclass · Accepted Answer

$40 K, 20 K$

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(D) The efficiency of a Carnot engine is given by the formula $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the temperature of the source and $T_2$ is the temperature of the sink.To maximize the efficiency $\eta$,the ratio $\frac{T_2}{T_1}$ must be minimized.Let us calculate the ratio for each option:$(a)$ $\frac{60}{80} = 0.75$$(b)$ $\frac{80}{100} = 0.80$$(c)$ $\frac{40}{60} \approx 0.667$$(d)$ $\frac{20}{40} = 0.50$Comparing these values,the ratio is minimum for option $(d)$. Therefore,the efficiency is highest for the combination $40 K$ and $20 K$.

For which combination of working temperatures is the efficiency of a Carnot engine the highest?

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