On the inequality of partial temperatures of a homogeneous gas mixture in thermodynamical equilibrium state

A modified definition of the state of thermodynamical equilibrium of a homogeneous multicomponent gas mixture is given. It is based on the discrete character of collisions but not on the smoothed by multiple collisions dynamical structure with the physical determination of the kinetic time $dt$. Application of rigorous mathematical methods which adequately describe the discrete character of collisions leads to a qualitatively new structure of the distribution functions and unexpected physical consequences. It is shown that owing to the inequality of head-on and head-tail collisions of particles, partial temperatures of a homogeneous multicomponent gas mixture in thermodynamical equilibrium cannot be equal to each other. It is found that relations of the partial temperatures to the mixture temperature are dependent on the molecular weights and concentrations of the gas components.