[QUE/TH-06001] TH-PROBLEM

Two heat reservoirs, each of fixed volume $V$ are at temperatures $T_1$ and $T_2$ ( $T_1\,>\,T_2$) initially. An engine operates between the two till both of them reach the same temperature $T_3$. The specific heat $c_V$ of the reservoirs can be assumed to constant through out. The engine is back to its inital state.

• Show that $$ T_3^2\,\geq\,T_1T_2 $$
• Calculate the maximum work that can be extracted from the two reservoirs. ( Answer in terms of $T_1$ and $T_2$)