The kinetic theory of a special type of rigid molecule

Abstract

1. The present paper is an exercise in the classical kinetic theory, with no admixture of quantum theory, or of the modern theory of atomic structure. The researches of Chapman and Enskog suggest an attempt to see how far exact methods can be used when the molecule has rotational as well as translational energy. It is now well established that if λ is the thermal conductivity, μ the viscosity, and c v the specific heat at constant volume of a monatomic gas, λ/μ c v is nearly equal to 2·5. No exhaustive theory is yet in sight for polyatomic gases, but the views of Eucken are of great interest, and his formula λ/μ c v = ¼ (9γ - 5) agrees with many experiments. The present paper discusses the effect of energy of rotation on viscosity and thermal conductivity in a special case, and may help to elucidate certain points, notwithstanding the crudeness of the adopted model. The need of a molecular model which shall lend itself to calculation has often been felt. In his first paper on the kinetic theory, Maxwell considered the collision of perfectly elastic bodies of any form, and enunciated the theorem about energy of rotation which was afterwards included in the general doctrine of equipartition in the steady state. Of recent years more attention has been paid to slight departures from the steady state, with a view to obtaining a rigorous theory of thermal conductivity, diffusion, and viscosity. Jeans considered the perfectly elastic collisions of smooth spheres whose centres of mass and figure are different. Approximations were made by neglecting powers of r /σ higher than the second, where r is the eccentricity and σ the diameter of the molecule, so that we have rather an unfortunate limiting case in which energy of rotation only adjusts itself infinitely slowly in comparison with that of translation; while the free path phenomena were not treated in detail. It appeared to the writer that there would be less trouble with the molecular model suggested by Bryan. Imagine two spheres to collide and grip each other, so as to bring the points of contact to relative rest. A small elastic deformation is produced, which we suppose to be released immediately afterwards, the force during release being equal to that at the corresponding stage of compression. Thus the relative velocity of the points of contact is reversed by collision.