The kinetic theory of gases

The controversy between the caloric and the kinetic, or dynamic, theories of heat was resolved in favour of the latter by James Joule's experiments of the 1840s and by the establishment of first and second laws of thermodynamics by Rudolph Clausius in the early 1850s. Before 1850, various kinetic theories of gases had been proposed, in particular, by John Herapath and John James Waterston, to whom we will return later. Joule had noted that the equivalence of heat and work could be interpreted in terms of the kinetic theory and, in his initial formulation of the first and second laws, Clausius described how they could also be interpreted within this framework, although he emphasised that the laws are quite independent of the particular microscopic theory.

The first systematic account of the kinetic theory was published by Clausius in 1857 in a classic paper entitled ‘The nature of the motion which we call heat.’ This contained a simple derivation of the perfect gas law, assuming that the molecules of a gas can be considered to be elastic spheres which exert a pressure on the walls of the containing vessel by bouncing off them. Let us repeat Clausius's derivation, in a simple form.

Assumptions underlying the kinetic theory of gases

The objective of the kinetic theory is to apply Newtonian physics to large assemblies of atoms or molecules.