Analytical calculation of the parameters of a molecular gas on a surface in the Smoluchowski problem

An analytical solution of the classical Smoluchowski problem on the temperature jump in molecular (monatomic, diatomic, and polyatomic) gases is presented. The gas occupies a half–space above a flat wall, with a constant temperature gradient and evaporation rate from the “gas–condensed phase” interface set far from this wall. The distribution function is explicitly constructed both in the half–space and at its boundary. Formulas for the concentration and temperature at the interface are derived; in the case of diatomic and polyatomic gases, formulas for temperatures determined by translational and rotational degrees of freedom of molecules are obtained. Numerical calculations are performed.