13.1 Introduction

Boyle discovered the law named after him in 1661. Boyle, Newton, and several others tried to explain the behaviour of gases by considering that gases are made up of tiny atomic particles. Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. This is possible as the inter-atomic forces, which are short-range forces that are important for solids and liquids, can be neglected for gases.

The kinetic theory was developed in the nineteenth century by Maxwell, Boltzmann, and others. It has been remarkably successful. It gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. It correctly explains the specific heat capacities of many gases. It also relates measurable properties of gases such as viscosity, conduction, and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.

The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, viscosity, thermal conductivity, and volume, by considering their molecular composition and motion. The theory posits that gas pressure is due to the impacts, on the walls of a container, of molecules or atoms moving at different velocities.

We know that the pressure \(P\), the volume \(V\) and the temperature \(T\) of any gas at low densities obey the equation
\(
P V=n R T = \mu R T
\)
where \(n(\mu)\) is the number of moles in the gas and \(R\) is the gas constant having value \(8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\). The temperature \(T\) is defined on the absolute scale. We define the term ideal gas to mean a gas which always obeys this equation. The real gases available to us are a good approximations of an ideal gas at low density but deviate from it when the density is increased.