The Kinetic Theory of Gases

According to the kinetic theory, molecules in a gas fly about in all directions, frequently colliding with each other and with their containing walls. Conceptually simple though it may be, this picture is not something suggested directly by any of our experience with matter in bulk. However, it does account at once for the tendency of a gas to expand without limit. Daniel Bernoulli, a Swiss mathematician, worked out the consequences of the kinetic theory in 1738. His work apparently had no impact whatever on the course of science, being noticed only after James Joule in England, and two German physicists, August Kronig and Rudolph Clausius, had developed the same theory independently in the 1840's and 1850s. In the intervening century Charles and Gay-Lussac had clarified the macroscopic laws of gas behavior, the gas thermometer had been perfected, chemical evidence for the existence of atoms and molecules had become overwhelmingly convincing, the steam engine was utilizing heat energy for mechanical work, thermo-dynamics was well launched as a quantitative theory, caloric had been abandoned, and the general law of energy conservation had been formulated. By the time these strides in the science of temperature and heal had caught up with the forward leap of Bernoulli, he was long dead and this part of his work forgotten. Yet, when the time was ripe the same ideas were regenerated by several scientists in different places at nearly the same time in a more typical pattern of scientific development.

It might seem surprising that any mathematical derivation based on the kinetic theory could be simple. At the submicroscopic level, a gas appears to be an incalculable chaos of flying molecules, no two moving in exactly the same way, and none moving far between vigorous collisions with its neighbors. Yet from this chaos flows a beautifully simple derivation of the ideal-gas law which illuminates the content of the kinetic theory and, even more important, which establishes the connection between temperature and molecular energy.