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Transport properties of gases with rotational states McCourt, Frederick Richard Wayne

Abstract

Theoretical expressions for the transport coefficients of a single component gas with a nonzero but small local angular momentum density are obtained from a modified Boltzmann equation which takes into account the presence of degenerate internal states (specifically, rotational states). As is to be expected, a number of Onsager reciprocal relations are found connecting the transport coefficients. A linearization of the Boltzmann equation is carried out by means of a perturbation expansion about a local equilibrium state which is characterized by a local temperature, stream velocity and angular momentum density. This perturbation is expressed as a linear combination of the macroscopic gradients of the system, whose coefficients, being tensors, are expanded in terms of irreducible Cartesian tensors made up of the angular momentum pseudovector operator J and the reduced velocity vector W. The transport coefficients are then given by combinations of certain scalar expansion coefficients. Expressions for these expansion coefficients in terms of square bracket integrals are obtained with the aid of an iterative variational procedure based on a scalar product which allows for the lack of time reversal symmetry of the Boltzmann collision operator. Finally, the square bracket integrals are reduced to relative and center-of-mass coordinates and expressed in terms of generalized collision cross sections. The techniques developed for the rotating gas with a nonzero local angular momentum density are utilized to obtain an expression for the change in the thermal conductivity of a gas when placed in a magnetic field. It is shown that at saturation the ratio of the changes in the thermal conductivity with the magnetic field (a) parallel to, and (b) perpendicular to, the temperature gradient is 2/3. This value agrees with the experimental result for paramagnetic gases.

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