The efficiency of a Carnot engine operating w | vedclass

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(D) For the Carnot engine:Efficiency $\eta = 0.4$,$T_1 = 1000 K$,$Q_1 = 150 J$.Work done $W = \eta 	imes Q_1 = 0.4 	imes 150 = 60 J$. (Statement $A$

Vedclass · Accepted Answer

$(A, B, C)$

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(D) For the Carnot engine:Efficiency $\eta = 0.4$,$T_1 = 1000 K$,$Q_1 = 150 J$.Work done $W = \eta 	imes Q_1 = 0.4 	imes 150 = 60 J$. (Statement $A$ is correct)Efficiency $\eta = 1 - \frac{T_2}{T_1} \implies 0.4 = 1 - \frac{T_2}{1000} \implies \frac{T_2}{1000} = 0.6 \implies T_2 = 600 K$. (Statement $B$ is correct)For the heat pump:Coefficient of performance $COP = 10$,$T_3 = 300 K$,Work input $W = 60 J$.$COP = \frac{Q_3}{W} \implies 10 = \frac{Q_3}{60} \implies Q_3 = 600 J$ (Heat extracted from cold reservoir).Heat supplied to hot reservoir $Q_4 = Q_3 + W = 600 + 60 = 660 J$. (Statement $D$ is incorrect)$COP = \frac{T_3}{T_3 - T_4} \implies 10 = \frac{300}{300 - T_4} \implies 300 - T_4 = 30 \implies T_4 = 270 K$. (Statement $C$ is correct)Thus,statements $A, B,$ and $C$ are correct.

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