Chapter 2 - Kinetic Theory

Summary

Maxwell's velocity distribution function together with Clausius's mean free path concept were the key elements that made it possible to develop connections between the motions of microscopic molecules (molecules are defined in a very broad sense here, referring to any neutral or charged particle composing the gas) and the macroscopic properties of gases (observable by the methods of classical physics).

In this chapter we introduce some fundamental concepts of kinetic theory. For more details we refer the reader to books on classical kinetic theory (cf. Gombosi 1994).

Collisions

First, we introduce several statistical quantities such as the mean free path, collision frequency, collision rate, collision cross section, and differential cross section. We shall also see that these quantities are closely related to each other and to other fundamental molecular quantities. We will use very simple physical models to emphasize the basic concepts behind these new statistical quantities.

Mean Free Path

The free path is the distance traveled by a molecule between two successive collisions. The mean free path is the average distance between two successive collisions of a single molecule.

Consider a single molecule with velocity v. Assume that this particle suffers a collision with another molecule at a distance of s = 0. Let P_path(s) denote the probability that this molecule survives a distance s without suffering a second collision.