III.

The Kinetic Theory of Gases

The subject of the University of Cambridge’s Adams Prize for 1857 was a study of the motions of Saturn‘s rings, whose structure and stability were in doubt at the time. On winning the prize and revising his essay for publication in 1859, Maxwell concluded that the ring system of Saturn consists of concentric rings of particles.

Alerted to problems of particle motions, Maxwell became interested in a paper by Rudolf Clausius on the kinetic theory of gases—the theory that explains the behaviour of gases in terms of the motions of their molecules, or constituent particles. Clausius had used a probabilistic argument to calculate the motions of the gas molecules, and Maxwell advanced on his procedure by introducing a statistical function (identical in form to the distribution formula in the theory of errors) for the distribution of velocities among the gas molecules. He established results for gaseous diffusion, viscosity, and thermal conductivity.

He turned to an experimental investigation of the viscosity of gases at different temperatures and pressures, observing the decay in the torsional oscillation of discs. He found that gas viscosity was a linear function of the absolute temperature. In his paper “On the Dynamical Theory of Gases” (1867), he suggested that gas molecules should be considered as centres of a force of repulsion that falls off in strength as the fifth power of the separation, a result in agreement with this experimental finding. He also presented a new derivation of the law of distribution of velocities.

Maxwell perceived that the kinetic theory of gases bore on wider problems in the theory of heat, and he expounded the implications of his theory in his “demon” paradox (a term coined by Thomson). According to the second law of thermodynamics, heat flows from hot to cold bodies unless work is done to force it to flow the other way. But Maxwell’s theory that the velocities of gas molecules are widely distributed suggests that individual faster-moving molecules could move from a cold to a hot body transferring heat as they did so. It would require the action of the demon to manipulate molecules in sufficient numbers to produce an observable flow of heat from the cold body to the hotter one, and thus violate the second law of thermodynamics. This law therefore applies only to large groups of molecules; it is a statistical law.

Maxwell’s ideas on gases and thermodynamics were developed by Ludwig Boltzmann in the 1870s, and became the accepted basis for these areas of physics.