Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond

Gregory Behrendt; Sebastian Deffner

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arXiv · 2608.11966

Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond

Gregory Behrendt·Sebastian Deffner

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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 Hemlholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that quite universally the maximal efficiency is achieved for thermodynamics systems, whose working mediums are linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and pheonmenological models of the rubber band.

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Gregory Behrendt, Sebastian Deffner. 2026-08-12. Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond. https://arxiv.org/abs/2608.11966

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