Molecular kinetic analysis of a finite-time Carnot cycle

TL;DR

This paper investigates the efficiency at maximum power of a finite-time Carnot cycle with a nearly ideal gas, using molecular dynamics simulations and kinetic analysis to compare with the Curzon-Ahlborn efficiency.

Contribution

It provides the first numerical verification of the Curzon-Ahlborn efficiency for a molecular gas system and offers a kinetic theory explanation for its validity.

Findings

Efficiency approaches Curzon-Ahlborn in the limit of small temperature difference.

Numerical experiments show deviations from CA efficiency at larger temperature differences.

Kinetic analysis explains the conditions under which CA efficiency holds.

Abstract

We study the efficiency at the maximal power $\eta_\mathrm{max}$ of a finite-time Carnot cycle of a weakly interacting gas which we can reagard as a nearly ideal gas. In several systems interacting with the hot and cold reservoirs of the temperatures $T_\mathrm{h}$ and $T_\mathrm{c}$, respectively, it is known that $\eta_\mathrm{max}=1-\sqrt{T_\mathrm{c}/T_\mathrm{h}}$ which is often called the Curzon-Ahlborn (CA) efficiency $\eta_\mathrm{CA}$. For the first time numerical experiments to verify the validity of $\eta_\mathrm{CA}$ are performed by means of molecular dynamics simulations and reveal that our $\eta_\mathrm{max}$ does not always agree with $\eta_\mathrm{CA}$, but approaches $\eta_\mathrm{CA}$ in the limit of $T_\mathrm{c} \to T_\mathrm{h}$. Our molecular kinetic analysis explains the above facts theoretically by using only elementary arithmetic.