A general property of endoreversible thermal engines

In this work we propose that endoreversible Carnot-type heat engines have a general property independent of the heat transfer law used to describe heat exchanges between the working fluid and its thermal reservoirs. This property has to do with the so-called ecological function [F. Angulo-Brown, J. Appl. Phys. 69, 7465 (1991)]. According to this property, the efficiency at the maximum of the ecological function is the semisum of the Carnot and the maximum power efficiencies for any heat transfer law. This result is obtained by using the quasiparabolic behavior of power versus efficiency. From this property, we obtain a corollary over a general quantitative relation between the power (and also the entropy production) of both maximum power and maximum ecological regimes. We also discuss a criterion to find the best ecological function.