Consider two bodies of identical mass m and specific heat c used as thermal reservoirs (source and sink) for a heat engine. The first body is initially at an absolute temperature T1 while the second one is at a lower absolute temperature T2. Heat is transferred from the first body to the heat engine, which rejects the waste heat to the second body. The process continues until the final temperatures of the two bodies Tf become equal. Show that Tf = √T1T2 when the heat engine produces the maximum possible work.

m, c Ti QH HE 2L m, c T2