Consider a reversible heat engine operating between two reservoirs, R1 and R2, initially at temperatures TH and TC, respectively, where TH > TC. Assume that the cold reservoir, R2, has an infinite heat capacity (i.e. TC = constant) but that the hot reservoir, R1, is finite with a constant heat capacity C1. Accordingly the temperature of R1 decreases with time from its initial value of TH. In each cycle, the heat engine absorbs an infinitesimal amount of heat dq from R1, converts part of it into work dw, and rejects the remaining heat into R2. The engine stops working when the temperature of the hot reservoir has been lowered to TC. Show that the amount of work done by the engine is W = C1(TH-TC) - C1TC ln (TH/TC).