An ideal gas is heated to a temperature T_in and allowed to expand a small amount against an external ambient pressure, where the external gas has temperature T_out. We found that the fraction of thermal energy dU used to do useful work dW precisely realized the Carnot efficiency. Show that the expansion process described there can be completed to a closed loop giving a heat engine with Carnot efficiency by using reversible processes to bring the fluid back to the initial volume so that addition of thermal energy dU restores the initial temperature T_in.