Molecular kinetic analysis of a finite-time Carnot cycle

Abstract

We study the efficiency at the maximal power ${\eta }_{\max }$ 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 ${\eta }_{\max }=1-\sqrt{T_{\mathrm{c}}/T_{\mathrm{h}}}$ 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 ${\eta }_{\max }$ 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.

arXiv comment6 pages, 4 figures

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