Onsager coefficients of a finite-time Carnot cycle

TL;DR

This paper analytically derives the Onsager coefficients for a finite-time Carnot cycle operating near equilibrium, explaining its efficiency at maximum power aligns with the Curzon-Ahlborn limit through tight coupling.

Contribution

It provides an analytical calculation of Onsager coefficients for a finite-time Carnot cycle in the linear-response regime, linking tight coupling to efficiency at maximum power.

Findings

Onsager coefficients satisfy tight-coupling condition

Efficiency at maximum power reaches Curzon-Ahlborn efficiency

Cycle operates in the linear-response regime near equilibrium

Abstract

We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of $T_\mathrm{h}-T_\mathrm{c}\to 0$ where $T_\mathrm{h}$ and $T_\mathrm{c}$ are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power $\eta_\mathrm{max}$ of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.