Two identical objects, A and B, are thermally and mechanicallyisolated from the rest of the world. Their initial temperatures areTA > TB. Each object has heat capacity C (the same for bothobjects) which is independent of temperature. (a) Suppose theobjects are placed in thermal contact and allowed to come tothermal equilibrium. What is their final temperature? How muchentropy is created in this process? How much work is done on theoutside world in this process? (b) Instead, suppose objects A(temperature TA) and B (temperature TB < TA) are used as thehigh and low temperature heat reservoirs of a heat engine. Theengine extracts energy from object A (lowering its temperature),does work on the outside world, and dumps waste heat to object B(raising its temperature). When the temperatures of A and B are thesame, the heat engine is in the same state as it started and theprocess is finished. Suppose this heat engine is the most efficientheat engine possible. In other words, it performs the maximum workpossible. What is the final temperature of the objects? How muchentropy is created in this process? How much work is done on theoutside world in this process?
