5. Two identical bodies are used as heat reservoirs for a heat engine. Their heat capacity at constant pressure is C, which is independent of temperature. The bodies undergo no change of phase and remain at constant pressure. Initially, their temperatures are T and T2, respectively. As a result of the operation of the heat engine, the bodies will reach a common final temperature T. (a) What is the total amount of work done by the engine? (Determine in terms of C, T, T, and Tf.) (b) Derive an inequality that relates T to the initial temperatures T and T. (c) What is the maximum amount of work that can be extracted from the engine?