Maximum work from a finite reservoir by sequential Carnot cycles

The production of work from a heat source with finite heat capacity is discussed. We examine the conversion of heat from such a source first by a single Carnot engine and then by a sequence of Carnot engines. The optimum values of the operating temperatures of these engines are calculated. The work production and efficiency of a sequence with an arbitrary number of engines is derived, and it is shown that the maximum available work can be extracted only when the number of cycles in the sequence becomes infinite. The results illustrate the importance of recovery or bottoming processes in the optimization of work-producing systems. In addition, the present model illuminates one practical limitation of the Carnot cycle: The Carnot efficiency is only obtainable from a heat source with infinite heat capacity. However, another cycle, somewhat reminiscent of the Otto and Brayton cycles, is derived which will provide the maximum efficiency for a heat source with a finite heat capacity.