where is the Liouville operator. It was shown by Kirkwood [1] that this equation could be converted into the Boltzmann equation for species :

(1.3)

where is a very complex term that contains information regarding the dynamics of a binary encounter between two monatomic molecules, and is the force per unit mass acting on a molecules of species .

1b. The general equation of change

Equation 1.3 may be multiplied by a property B and integrated over all momenta to get the general equation of change forB:

(1.4)

It can be shown that if B is conserved in a collision, then the last term on the right side vanishes.

1c. Special equations of change

We may now write down the equations of change by setting B successively equal to mass , momentum , and energy (keeping in mind that the only energy for monatomic molecules is the kinetic energy—for diatomic molecules, see BSL-2e,