Two Carnot engines A and B are operated in series. The first one, A, receives heat at $T_1(=600 \mathrm{~K})$ and rejects to a reservoir at temperature $T_{2 \text { _ }}$. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3(=400 \mathrm{~K})$. Calculate the temperature $T_2$ if the work outputs of the two engines are equal