Effect of Dissipation on Density Profile of One Dimensional Gas
Abstract
We study the effect of dissipation on the density profile of a one dimensional gas that is subject to gravity. The gas is in thermal equilibrium at temperature T with a heat reservoir at the bottom wall. Perturbative analysis of the Boltzmann equation reveals that the correction due to dissipation resulting from inelastic collisions is positive for 0<z<zc and negative for z>zc with z the vertical coordinate. The numerically determined value for zc is mgzc/kBT≈ 1.1613, where g is the gravitational constant and m is the particle mass.
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