Molecular kinetic analysis of a local equilibrium Carnot cycle

TL;DR

This paper develops a molecular kinetic model for a local equilibrium Carnot cycle, deriving efficiency expressions and validating results with molecular dynamics simulations.

Contribution

It introduces a compatible velocity distribution function for local equilibrium and constructs a Carnot cycle based on it, providing new insights into efficiency at maximum power.

Findings

Efficiency matches endoreversible Carnot efficiency.

Derived an analytic expression for efficiency at maximum power.

Validated theory with molecular dynamics simulations.

Abstract

We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a Maxwell--Boltzmann distribution with a spatially uniform temperature and a spatially varying local center-of-mass velocity. We construct the local equilibrium Carnot cycle of an ideal gas, based on this distribution, and show that the efficiency of the present cycle is given by the endoreversible Carnot efficiency using the molecular kinetic temperatures of the gas. We also obtain an analytic expression of the efficiency at maximum power of our cycle under a small temperature difference. Our theory is also confirmed by a molecular dynamics simulation.