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(A) The initial efficiency of a Carnot engine is given by $\eta_1 = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1}$,where $T_1$ is the source temperature

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(A) The initial efficiency of a Carnot engine is given by $\eta_1 = 1 - \frac{T_2}{T_1} = \frac{T_1 - T_2}{T_1}$,where $T_1$ is the source temperature and $T_2$ is the sink temperature $(T_1 > T_2)$.When both temperatures are decreased by $100 \ K$,the new temperatures are $T_1' = T_1 - 100$ and $T_2' = T_2 - 100$.The new efficiency is $\eta_2 = 1 - \frac{T_2 - 100}{T_1 - 100} = \frac{(T_1 - 100) - (T_2 - 100)}{T_1 - 100} = \frac{T_1 - T_2}{T_1 - 100}$.Since $T_1 - 100 Therefore,$\eta_2 > \eta_1$,which means the efficiency of the engine increases.

In a Carnot engine,if the temperatures of the source and the sink are decreased by $100 \ K$ each,then the efficiency of the engine:

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