THE CLASSICAL BOLTZMANN-EQUATION OF A MOLECULAR GAS

A classical Boltzmann equation which describes the time evolution of the distribution function in the phase space of a single molecule is developed for a low-density gas made up of nonreacting molecules of arbitrary structure. This development is based on the Liouville equation, the equation describing the time evolution of the distribution function in the phase space of the entire system through the Bogoliubov-Born-Green-Kirkwood-Yvon set of equations, the equations which describe the time evolution of the contracted distribution functions. The set of equations is truncated by use of the molecular chaos assumption, the assumption that the dynamical states of a pair of molecules are uncorrelated before a collision. From the general result the form of the collision integral arising from collisions between two diatomic molecules is considered as a special case. This result is then further reduced to the idealized rigid-rotor, harmonic-oscillator model. This result is then shown to be a generalization of an earlier development.