Q. Two Carrnot engines A and B are operated in series. The first one, A, receives heat at $T_1(= 600 \; K)$ 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 $T_3(= 400 \; K)$. Calculate the temperature $T_2$ if the work outputs of the two engines are equal :

Solution:

$w_1 = w_2$
$\Delta u_1 = \Delta u_2$
$T_3 - T_2 = T_2 - T_1$
$2T_2 = T_1 + T_3$
$T_2 = 500 \; K$

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