PreprintCC BY 4.0arXiv
Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond
Abstract
Given a particular heat engine cycle, what is the optimal working medium that results in the highest efficiency? While one might jump to the conclusion that it must surely be the ideal gas, the situation is actually more intricate. Starting with a general Helmholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that for the thermodynamic systems described by our ansatz for the Helmholtz potential the maximal efficiency is achieved, if the working medium is described by a fundamental relation linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and phenomenological models of the rubber band.
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BibTeX
@misc{behrendt2026ideal,
title = {{Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond}},
author = {Gregory Behrendt and Sebastian Deffner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.11966},
eprint = {2608.11966},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11966},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond
AU - Gregory Behrendt
AU - Sebastian Deffner
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2608.11966
UR - https://arxiv.org/abs/2608.11966
AB - Given a particular heat engine cycle, what is the optimal working medium that results in the highest efficiency? While one might jump to the conclusion that it must surely be the ideal gas, the situation is actually more intricate. Starting with a general Helmholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that for the thermodynamic systems described by our ansatz for the Helmholtz potential the maximal efficiency is achieved, if the working medium is described by a fundamental relation linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and phenomenological models of the rubber band.
ER -