Question

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at $T_1$ =800 K and rejects to sink at $T_2$ K. The second engine B receives heat rejected by the first engine and rejects to another sink at $T_3$ =300 K If the work outputs of two engines are equal, then the value of $T_2$ is

• A. 100K
• B. 300K
• C. 550K
• D. 700K

Answer 1

The correct option is C 550K

${\eta }_A=\frac{T_1-T_2}{T_1}=\frac{W_A}{Q_1}\Rightarrow {\eta }_B=\frac{T_2-T_3}{T_2}=\frac{W_B}{Q_2}$
$\therefore \frac{Q_1}{Q_2}=\frac{T_1}{T_2}\times \frac{T_2-T_3}{T_1-T_2}=\frac{T_1}{T_2}$ $\therefore W_A=W_B$
$\therefore T_2=\frac{T_1+T_3}{2}=\frac{800+300}{2}=550K$