Introduction

12.1 Introduction

The story of kinetic theory begins with a puzzle: what is a gas, really? In 1661, Robert Boyle discovered the law that bears his name, describing how the pressure and volume of a gas are related. But why does a gas behave that way? Boyle himself, along with Newton and several others, tried to explain the behaviour of gases by supposing that they are made up of tiny atomic particles. That hunch was remarkably prescient, but the actual atomic theory would not be firmly established for more than 150 years.

The core idea

Kinetic theory explains the behaviour of gases based on a single, powerful idea: a gas consists of a huge number of atoms or molecules in rapid, ceaseless motion. This picture works because the interatomic forces — the same short-range forces that matter so much for solids and liquids — can be neglected for gases, where molecules spend almost all their time far apart from one another.

Historical development

The kinetic theory was developed in the nineteenth century, primarily by James Clerk Maxwell and Ludwig Boltzmann, and others. It has been remarkably successful — it does not merely describe gases; it explains their behaviour from the ground up, in terms of molecular motion.

What the theory achieves

The kinetic theory gives a molecular interpretation of two of the most fundamental quantities in thermodynamics: pressure and temperature. It is consistent with the classical gas laws and with Avogadro's hypothesis. It correctly explains the specific heat capacities of many gases. And it relates measurable properties of gases — such as viscosity, thermal conduction, and diffusion — to molecular parameters, giving us a way to estimate the sizes and masses of molecules.

What this chapter covers

This chapter gives an introduction to kinetic theory — building the molecular picture step by step and using it to explain the behaviour of gases (and, to a limited extent, solids).

---

These two equations are the heart of the kinetic theory. The first relates pressure $P$ to the number of molecules $N$, their mass $m$, the mean square speed $\overline{v^2}$, and the volume $V$. The second relates the average translational kinetic energy $\overline{K}$ of a molecule to the absolute temperature $T$, with Boltzmann's constant $k_B = 1.38 \times 10^{-23}\ \text{J K}^{-1}$ as the conversion factor. Everything else — the gas laws, the specific heats, the transport phenomena — follows from these two results.