Thermal efficiency at maximum work output: New results for old heat engines

What is the thermal efficiency of a heat engine producing the maximum possible work per cycle consistent with its operating-temperature range? This question is answered here for four model reversible heat engine cycles. In each case, the work is maximized with respect to two characteristic temperatures that are intermediate between the maximum and minimum cycle temperatures T+ and T−. The maximum-work efficiencies are found to equal or be well approximated by η*=1−(T−/T+)1/2. Because this efficiency is a function solely of the extreme cycle temperatures, it can be compared easily with the corresponding reversible Carnot cycle efficiency ηc =1−T−/T+. Here, η*, which is a much better guide to the performance of actual heat engines than ηc, is the same efficiency found by Curzon and Ahlborn [Am. J. Phys. 43, 22 (1975)] for a model irreversible heat engine operating at maximum power output. The present results show that η* is more ‘‘universal’’ than had been realized previously. If the work output per cycle is kept fixed, the thermal efficiency η of each cycle considered here can be increased by enlarging the heat engine and operating it at less-than-maximum work output per cycle. Formally, for such a fixed work output, η can approach the Carnot efficiency ηc in the limit of infinite engine size.