Efficiency at maximum power output for an engine with a passive piston

TL;DR

This paper theoretically investigates the efficiency at maximum power of an engine with a passive piston, revealing conditions under which the efficiency approaches or falls below the CNCA limit, supported by simulations and models.

Contribution

It introduces a theoretical framework for passive piston engines, analyzing efficiency limits for dilute and dense gases, and verifies findings with molecular dynamics and mean-field models.

Findings

Efficiency for dilute gas approaches CNCA efficiency.

Efficiency for dense gas is lower than CNCA even with small temperature differences.

Tight coupling condition holds for dilute gas but not for dense gas due to heat leaks.

Abstract

Efficiency at maximum power (MP) output for an engine with a passive piston without mechanical controls between two reservoirs is theoretically studied. We enclose a hard core gas partitioned by a massive piston in a temperature-controlled container and analyze the efficiency at MP under a heating and cooling protocol without controlling the pressure acting on the piston from outside. We find the following three results: (i) The efficiency at MP for a dilute gas is close to the Chambadal-Novikov-Curzon-Ahlborn (CNCA) efficiency if we can ignore the side wall friction and the loss of energy between a gas particle and the piston, while (ii) the efficiency for a moderately dense gas becomes smaller than the CNCA efficiency even when the temperature difference of reservoirs is small. (iii) Introducing the Onsager matrix for an engine with a passive piston, we verify that the tight coupling condition for the matrix of the dilute gas is satisfied, while that of the moderately dense gas is not satisfied because of the inevitable heat leak. We confirm the validity of these results using the molecular dynamics simulation and introducing an effective mean-field-like model which we call stochastic mean field model.