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(D) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1 = 500 \ K$ and $T_2 = 400 \ K$.$\eta = 1 - \frac{400}{500} =

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$10$

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(D) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1 = 500 \ K$ and $T_2 = 400 \ K$.$\eta = 1 - \frac{400}{500} = 1 - 0.8 = 0.2$.The efficiency is also defined as $\eta = 1 - \frac{Q_2}{Q_1}$,where $Q_1 = 100 \ J$ is the heat absorbed and $Q_2$ is the heat rejected.For a reversible engine,$\frac{Q_2}{Q_1} = \frac{T_2}{T_1} = 0.8$,so $Q_2 = 0.8 	imes 100 \ J = 80 \ J$.According to the Second Law of Thermodynamics,for any real engine,the efficiency $\eta_{real} \le \eta_{Carnot}$.$1 - \frac{Q_2}{Q_1} \le 0.2 \implies \frac{Q_2}{Q_1} \ge 0.8$.$Q_2 \ge 0.8 	imes 100 \ J = 80 \ J$.Therefore,any value of $Q_2$ less than $80 \ J$ is impossible. Thus,$10 \ J$ is impossible.

$A$ heat engine is operating between $500 \ K$ and $400 \ K$. If the engine absorbs $100 \ J$ of heat,which of the following is an impossible amount of heat rejected by the engine (in $J$)?

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