Thermodynamics of slow solutions to the Gas-Piston equations

TL;DR

This paper develops power series expansions to describe heat exchange in a gas-piston system under slow, non-quasi-static driving conditions, enhancing understanding of its non-equilibrium thermodynamics.

Contribution

It introduces a novel application of regular perturbation techniques to derive analytic formulas for heat in slowly driven gas-piston systems, addressing a gap in non-equilibrium thermodynamics.

Findings

Power series expansions for heat exchange are derived.

The approach applies to systems with slowly varying external force and temperature.

Results improve understanding of non-quasi-static thermodynamic processes.

Abstract

Despite its historical importance, a perfect gas enclosed by a pistons and in contact with a thermal reservoirs is a system still largely under study. Its thermodynamic properties are not yet well understood when driven under non-equilibrium conditions. In particular, analytic formulas that describe the heat exchanged with the reservoir are rare. In this paper we prove a power series expansions for the heat when both the external force and the reservoir temperature are slowly varying over time but the overall process is not quasi-static. To do so, we use the dynamical equations from [Cerino \emph{et al.}, \textit{Phys. Rev. E}, \textbf{91} 032128] and an uncommon application of the regular perturbation technique.