Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. I

TLDR

Numerical values of viscosity and heat conductivity coefficients, expected from the formal theory with specific molecular force assumptions, have not yet been obtained. The study aims to use the derived results to experimentally test the existence of Einstein‑Bose statistics in real gases. The authors generalize Lorentz–Enskog nonstationary gas theory to quantum statistics, deriving hydrodynamic equations, distribution functions, and formal expressions for viscosity and heat conductivity, and provide exact, statistics‑independent formulas for derivatives of the equilibrium coefficient A and an adiabatically invariant equation‑of‑state function W. The derived expressions for viscosity and heat conductivity coefficients hold for all quantum statistics and degrees of degeneracy.

Abstract

The theory of gases in nonstationary states, given by Lorentz and Enskog, is generalized for the quantum statistics to give the hydrodynamical equations and the distribution function in first and second approximation, and formal expressions for the viscosity and heat conductivity coefficients. These results are valid for all statistics and for all degrees of degeneration. Two essential points contribute to this generality: (a) Exact expressions independent of statistics and degeneration can be given for the coordinate and time derivatives of the coefficient $A$ of the equilibrium distribution function in terms of the pressure and temperature gradients and time derivatives, though a closed expression for this coefficient as a function of $v$ and $T$ is known only in limiting cases; (b) The function $W$ of the general equation of state for ideal gases in all statistics $pv=(\frac{\mathrm{RT}}{M})W({v}^{\frac{2}{3}}T)$ is adiabatically invariant. Numerical values of the viscosity and heat conductivity coefficients, which should come out of the formal theory on the introduction of special assumptions about the molecular forces, have not yet been obtained. It is our hope that these results, when found, may furnish an experimental test of the existence of Einstein-Bose statistics in real gases, as is required by theory.