Effective temperature and performance characteristics of heat engines

Abstract

For a heat engine working between two heat reservoirs, a hot reservoir at high temperature T H and a cold reservoir at low temperature T L , an effective temperature and an effective efficiency are introduced. The effective temperature is defined as the square root of the ratio between the net work output of the heat engine w net and the SOT function (a new function introduced in this article). The SOT function is defined as the negative of the cyclic integral of the heat transfer change divided by the square of the temperature. The effective efficiency of the heat engine is defined (a novel definition) as one minus the ratio between the low temperature and the effective temperature. The effective temperature and the effective efficiency are worked out in details for the Carnot heat engine and the air standard cycles (Otto, Brayton, Stirling, and Ericsson). It was found for the considered cycles that the effective temperature is given by the expression () and the effective efficiency is given by the expression () for all the considered cycles. The importance of these two proposed measures is twofold: educational and they could be used as a quick tool by the designer.