VII. On stresses in rarified gases arising from inequalities of temperature

TLDR

The study builds on the method developed in the author's earlier work on the dynamical theory of gases. Stress is defined through temperature gradients, with the first and second spatial derivatives of temperature along a direction determining directional pressure differences. Temperature gradients in a rarefied gas produce anisotropic pressure, with the maximum and minimum pressures at a point differing markedly when the gas density is low and temperature disparities arise from nearby solid bodies. This work cites the author's earlier paper, “On the Dynamical Theory of Gases” (Phil.

Abstract

1. In this paper I have followed the method given in my paper “On the Dynamical Theory of Gases” (Phil. Trans., 1867, p. 49). I have shown that when inequalities of temperature exist in a gas, the pressure at a given point is not the same in all directions, and that the difference between the maximum and the minimum pressure at a point may be of considerable magnitude when the density of the gas is small enough, and when the inequalities of temperature are produced by small solid bodies at a higher or lower temperature than the vessel containing the gas. 2. The nature of this stress may be thus defined:— Let the distance from a given point, measured in a given direction, be denoted by h ; then the space-variation of the temperature for a point moving along this line will be denoted by d θ/ dh , and the spaced variation of this quantity along the same line by d 2 θ/ dh 2 .