Two Carnot engines A and B are operated in su | vedclass

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(C) For Carnot engine $A$,the efficiency is $\eta_A = \frac{T_1 - T_2}{T_1} = \frac{W_A}{Q_1}$.For Carnot engine $B$,the efficiency is $\eta_B = \frac

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$550$

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(C) For Carnot engine $A$,the efficiency is $\eta_A = \frac{T_1 - T_2}{T_1} = \frac{W_A}{Q_1}$.For Carnot engine $B$,the efficiency is $\eta_B = \frac{T_2 - T_3}{T_2} = \frac{W_B}{Q_2}$.Since the heat rejected by engine $A$ is the heat received by engine $B$,we have $Q_2 = Q_1(1 - \eta_A) = Q_1 \left( \frac{T_2}{T_1} \right)$.Given that the work outputs are equal,$W_A = W_B$,which implies $Q_1 \eta_A = Q_2 \eta_B$.Substituting the expressions: $Q_1 \left( \frac{T_1 - T_2}{T_1} \right) = Q_1 \left( \frac{T_2}{T_1} \right) \left( \frac{T_2 - T_3}{T_2} \right)$.Simplifying this,we get $T_1 - T_2 = T_2 - T_3$.Therefore,$2T_2 = T_1 + T_3$,which gives $T_2 = \frac{T_1 + T_3}{2}$.Substituting the given values: $T_2 = \frac{800 + 300}{2} = \frac{1100}{2} = 550 \ K$.

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