Molecular kinetic analysis of a local equilibrium Carnot cycle

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.

9 pages, 5 figures

References in corpus (8)

• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• Onsager coefficients in periodically driven systems
• Molecular kinetic analysis of a finite-time Carnot cycle
• H. B. Reitlinger and the origins of the Efficiency at Maximum Power formula for Heat Engines
• Efficiency of Single Particle Engines
• Linear irreversible heat engines based on the local equilibrium assumptions
• Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

Cited by in corpus (2)

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