Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

Abstract

Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.

Thermodynamic quantities of the low-density gas in the weakly nonequilibrium heat-conduction steady state in the linear temperature profile approximation

“…As before [33,34], it is assumed that the fact of mechanical equilibrium of the gas means that the pressure takes the same value everywhere in the vessel:…”

“…, m is particle's mass and h is Planck's constant. These expressions are derived from the equilibrium counterparts, when the equilibrium temperature and number density are substituted by the local ones [33,34].…”