Generalizing thermal resistance and a general thermal engine

Abstract

This article outlines a generalization of the thermal resistance concept used to model and quantify the rates of spontaneous heat transfer. This leads to the natural corollary that a Carnot cycle possesses zero thermal resistance and provides restatements of the Clausius and Kelvin statements of the second law of thermodynamics. Subsequently, basic aspects of a general thermal engine are modeled by the series combination of two non-zero thermal resistances with a Carnot cycle. With constant thermal resistances, the efficiency at maximum power is found to be in agreement with previous literature also concluding that engine power is zero at the Carnot efficiency. An explicit form limiting maximum power output to system thermal resistance and reservoir temperatures is given. Minimizing the thermal resistance maximizes power output, congruent with maximizing heat flow and entropy production. Implications of this model towards practical power generation are presented.