1) Consider two identical bodies, each with a temperature-independent heat capacity Cy. One is at a higher temperature TH than the other, which is at temperature Tc. a) If these bodies were placed in thermal contact and allowed to come to thermal equilibrium, what would be their common final temperature TЛ? Now consider the case where, instead, these two bodies are in contact with an ideal Carnot heat engine. The heat engine removes heat from the hotter body and deposits some of the heat into the colder body, while doing work. Since these bodies are of finite extent (they are not infinite heat reservoirs), the hot body will become colder and the cold body will becomes hotter until the process stops when they reach the common final temperature T. b) c) d) e) Which final temperature (T or T2) will be lower and why? Calculate the entropy change for the hot body. Calculate the entropy change for the cold body. What is the entropy change for the system (hot body + cold body + heat engine)? [Hint: The process is reversible. Also, the heat engine is ideal so no "extra" entropy is generated in the heat engine; therefore, the entropy change is just that due to the hot and cold bodies.] Hence find T2 in terms of Ty and Tc. f) g) Find the total work done by the heat engine.