Inhomogeneity of the Ideal Gas of a Finite Number of Particles with Angular Momentum Conservation

Abstract

We continue to study various aspects of the behavior of a classical ideal gas in a stationary axisymmetric container. The symmetry of the vessel leads to the conservation of the gas’s angular momentum and, hence, the state of gas rotation. We consider the case of a nonrotating two-dimensional gas of a finite number of colliding particles. In this case, the gas statistical distributions differ from the classical ones found in the nineteenth century. We will show that the filling of the axisymmetric vessel with a nonrotating gas is not uniform and provide the exact spatial distribution of gas particles. This previously unknown distribution depends on all the particle masses and is found explicitly. The absence of a rotation in gas layers is shown through the investigation of the distributions of the tangential components of particle momenta. We also show that, for any number of particles in a container, the behavior of a massive enough particle may be unusual. The analytic results are confirmed by simple numerical experiments.