Two bodies have heat capacities (at constant volume) c, = a and c2 = bT and are thermally isolated from the rest of the universe. Initial temperatures of the bodies are T_10 and T_20, with T_20, > T_10. The two bodies are brought into thermal equilibrium (keeping the volume constant) while delivering as much work as possible to a reversible work source.
(a) What is the final temperature T_f of the two bodies? (In case you are unable to solve for an explicit value of T_i, you will still get full credit if you explain in detail how to obtain the value).
(b) What is the maximum work delivered to the reversible work source? (You may express the answer in terms of T_e without having to explicitly solve for it).