Consider two identical bodies of heat capacity C, and with negligi- ble thermal expansion coefficients. Show that when they are placed in thermal contact in an adiabatic enclosure their final tempera- ture is (T₁ + T2)/2 where T₁ and T2 are their initial temperatures. Now consider these two bodies being brought to thermal equilib- rium by a Carnot engine operating between them. The size of the cycle is small, so that the temperatures of the bodies do not change appreciably during one cycle; thus the bodies behave as reservoirs during one cycle. Show that the final temperature is (T₁ T2)¹/². (Hint: What is the entropy change of the universe for this second process?)

Consider two identical bodies of heat capacity C, and with negligi- ble thermal expansion coefficients. Show that when they are placed in thermal contact in an adiabatic enclosure their final tempera- ture is (T₁ + T2)/2 where T₁ and T2 are their initial temperatures. Now consider these two bodies being brought to thermal equilib- rium by a Carnot engine operating between them. The size of the cycle is small, so that the temperatures of the bodies do not change appreciably during one cycle; thus the bodies behave as reservoirs during one cycle. Show that the final temperature is (T₁ T2)¹/². (Hint: What is the entropy change of the universe for this second process?)