10 - Gas Kinetic Theory. The Molecular Theory of Dilute Gases at Equilibrium

Abstract

This chapter discusses the gas kinetic theory, which explicitly averages over molecular states of a system of particles obeying classical mechanics in order to gain information about the macroscopic behavior of the gas. Gas kinetic theory is similar in spirit to statistical mechanics. The first model system that represents a dilute gas is a system of noninteracting molecules without internal structure. The first part of the kinetic theory of gases is the mathematical analysis of the behavior of this model system, and includes averages over microscopic states of the molecules of the system, using probability distributions including the Maxwell-Boltzmann probability distribution for the probability distribution for molecular velocities and the probability distribution for molecular speeds. Gas kinetic theory of noninteracting molecules predicts the ideal gas equation of state. It also predicts the rate of wall collisions and the rate of effusion of a dilute gas. The molecules of real gases and liquids are fairly accurately described by a pair potential function that corresponds to intermolecular attractions at moderate distances and repulsions at short distances. The second model of a dilute gas is the hard-sphere gas, which allows analysis of molecular collisions.