Onsager coefficients of a finite-time Carnot cycle

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 $T_{\text{h}}-T_{\text{c}}\to 0$ where $T_{\text{h}}$ and $T_{\text{c}}$ 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 ${\eta }_{\text{max}}$ of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.