Two identically constructed objects, surrounded by thermal insulation, are used as energy reservoirs for a Carnot engine. The finite reservoirs both have mass m and specific heat c. They start out at temperatures Th and Tc, where Th > Tc, (a) Show that the engine will stop working when the final temperature of each object is (Th Tc) 1/2. (b) Show that the total work done by the Carnot engine is