An ecological optimization criterion for finite-time heat engines

An endoreversible Carnot-type heat engine is studied under the usual restrictions: no friction, working substance in internal equilibrium (endoreversibility), no mechanical inertial effects, and under Newton's cooling law for heat transfer between working fluid and heat reservoirs. A monoparametric family of straight lines which is isoefficient is found; i.e., all points (engine configurations) that belong to same line have the same efficiency. Along each line the power output divided by entropy production is a constant. From these properties and by using some dissipated quantities, relationships are obtained between reversible work and finite-time work and between reversible efficiency and finite-time efficiency. An "ecological" criterion is proposed for the best mode of operation of this heat engine. It consists in maximizing a function representing the best compromise between power and the product of entropy production and the cold reservoir temperature. The corresponding efficiency results almost equal to the average of the Carnot and the Curzon and Ahlborn [Am. J. Phys. 43, 22 (1975)] efficiencies.