Two carnot engines $A$ and $B$ are operated in series. The first one, $A,$ receives heat at $T_1\left(=600K\right)$ and rejects to a reservoir at temperature $T_2.$ The second engine $B$ receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3\left(=400K\right).$ Calculate the temperature $T_2$ if the work outputs of the two engines are equal:

• Correct answer
  A

  $500 K$
• B

  $400 K$
• C

  $300 K$
• D

  $600 K$

Solution

$W=Q_1-Q_2=Q_2-Q_3$

$\Rightarrow \frac{Q_1}{Q_2}+\frac{Q_3}{Q_2}=2$

$\frac{T_1}{T_2}+\frac{T_3}{T_2}=2$

$T_2=\frac{T_1+T_3}{2}=500K$

Hence, the correct answer is option: 'A'.