Maximum temperature of an ideal gas in thermal equilibrium

Hyeong-Chan Kim

Published 2023-11-13Version 1

We explore thermodynamics of an ideal gas system with heat conduction, incorporating a model that accommodates heat dependence. Our model is constructed based on i) the first law of thermodynamics from action formulation and ii) the existence condition of a (local) Lorentz boost between an Eckart observer and a Landau-Lifschitz observer--a condition that extends the stability criterion of thermal equilibrium. The implications of these conditions include: 1) Heat contributes to the energy density through the combination $q/n\Theta^2$ where $q$, $n$, and $\Theta$ represent heat, number density, and temperature, respectively. 2) The energy density exhibits a unique minumum at $q=0$ with respect to the contribution. 3) Our findings indicate an upper limit on the temperature of the ideal gas in thermal equilibrium. The upper limit is governed by the coefficient of the first non-vanishing contribution of heat around equilibrium to the energy density.