The effect of the reference frame on the thermophysical properties of an ideal gas

Abstract

The effect that the frame of reference has on the thermophysical properties of an ideal gas is examined from a fundamental theoretical standpoint based on the Boltzmann equation. In continuum mechanics, the principle of material frame-indifference forbids the thermophysical properties of a fluid or solid to depend in any way on the motion of the reference frame. It is demonstrated that the Boltzmann equation is only consistent with material frame-indifference in a strong approximate sense provided that the gas is not highly rarefied and, thus, well within the limits of classical continuum mechanics. Estimates of the mean free times for which material frame-indifference can be invoked in the modeling of gas flows are provided from an analysis of the problem of heat conduction in a rigidly rotating gas. Applications of these results in obtaining asymptotic solutions of the Boltzmann equation for the continuum description of an ideal gas are discussed briefly.