On the efficiency of rate processes. Power and efficiency of heat engines

Abstract

We analyze the power and efficiency of heat engines which operate subject to irreversible heat flow. First, we consider a specific model, with a cycle for an ideal gas similar to that of a reversible Carnot engine (’’isothermal cycle’’), and find the maximum power, and efficiency at the point of maximum power (ηm), for given heat bath temperatures and compression ratio. We prove that the cycle chosen produces more power than any other conceivable cycle in the limit of large compression ratio; the derivation is made for an ideal or van der Waals gas as a working fluid, but this is not restrictive in this limit. We use these results to obtain a general formulation, of upper bounds on power and ηm, valid for isothermal cycles to study the dependence of these quatities on the form of the law of irreversible heat conduction. We find that ηm depends only on the heat bath temperatures and the form of the irreversible rate process, but is independent of the material properties of the system. The dependence of ηm on the form of the rate process suggests the concept of ’’efficiency of rate processes.’’