Molecular Kinetic Analysis of a Finite-Time Carnot Heat Engine

We show the first derivation of the efficiency at the maximum power for a finite-time Carnot heat engine of a weakly interacting gas which we can regard as a nearly ideal gas. Using this simple model, we check the celebrated Curzon-Ahlborn (CA) efficiency by performing the event-driven MD simulation as a numerical experiment for the first time[1,2]. This numerical experiment reveals that the CA efficiency is realized only in the limit of the small temperature difference $T_{\mathrm{c}}$ $\rightarrow$ $T_{\mathrm{h}}$ where $T_{\mathrm{h}}$ and $T_{\mathrm{c}}$ are the temperatures of the hot and cold heat reservoirs, respectively. Our molecular kinetic analysis can explain the numerical results theoretically. \newline[1] F. Curzon and B. Ahlborn, Am. J. Phys. \textbf{43}, 22 (1975). \newline[2] Y. Izumida and K. Okuda, Europhys. Lett. \textbf{83}, 60003 (2008).