Molecular kinetic analysis of a finite-time Carnot cycle

Abstract

We study the efficiency at the maximal power $η_\mathrm{max}$ 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 $η_\mathrm{max}=1-\sqrt{T_\mathrm{c}/T_\mathrm{h}}$ which is often called the Curzon-Ahlborn (CA) efficiency $η_\mathrm{CA}$. For the first time numerical experiments to verify the validity of $η_\mathrm{CA}$ are performed by means of molecular dynamics simulations and reveal that our $η_\mathrm{max}$ does not always agree with $η_\mathrm{CA}$, but approaches $η_\mathrm{CA}$ 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.