Linear irreversible heat engines based on the local equilibrium assumptions

TL;DR

This paper develops a linear irreversible heat engine model based on local equilibrium assumptions, deriving efficiency at maximum power that aligns with the Curzon-Ahlborn efficiency through thermodynamic flux-force relations and Onsager theory.

Contribution

It introduces a finite-time Carnot cycle model under local equilibrium assumptions and demonstrates its efficiency at maximum power matches the Curzon-Ahlborn limit using linear response and Onsager relations.

Findings

Efficiency at maximum power equals Curzon-Ahlborn efficiency.

Model satisfies tight-coupling condition in Onsager framework.

Derived thermodynamic relations consistent with linear response theory.

Abstract

We formulate an endoreversible finite-time Carnot cycle model based on the assumptions of local equilibrium and constant energy flux, where the efficiency and the power are expressed in terms of the thermodynamic variables of the working substance. By analyzing the entropy production rate caused by the heat transfer in each isothermal process during the cycle, and using an endoreversible condition applied to the linear response regime, we identify the thermodynamic flux and force of the present system and obtain a linear relation that connects them. We calculate the efficiency at maximum power in the linear response regime by using the linear relation, which agrees with the Curzon-Ahlborn efficiency known as the upper bound in this regime. This reason is also elucidated by rewriting our model into the form of the Onsager relations, where our model turns out to satisfy the tight-coupling condition leading to the Curzon-Ahlborn efficiency.