Kinetic theory of gases
The picture of a gas as countless tiny molecules in ceaseless motion, from which pressure and temperature emerge as statistical averages.
Definition
The kinetic theory of gases explains the macroscopic properties of a gas — pressure, temperature, the gas laws — as statistical consequences of the motion of its molecules. A gas is modelled as a large number of small particles moving in straight lines between brief elastic collisions, filling their container uniformly and exerting pressure by drumming on its walls.
Two results are central. Pressure is the average rate at which molecular momentum is delivered to the walls per unit area, which yields PV = (1/3)Nm⟨v²⟩. Matching this to the ideal gas law identifies absolute temperature with mean molecular kinetic energy: (1/2)m⟨v²⟩ = (3/2)k_BT. Temperature, in this view, simply measures how fast the molecules move on average.
First sketched by Daniel Bernoulli in 1738 and ignored for over a century, the theory was revived by Krönig (1856) and Clausius (1857), extended by Maxwell's distribution of speeds (1859) and Boltzmann's statistical mechanics, and finally placed beyond doubt by Einstein and Perrin's work on Brownian motion.
History
Anticipated by Daniel Bernoulli (1738); re-derived by August Krönig (1856) and Rudolf Clausius (1857); developed into a statistical theory by Maxwell and Boltzmann; vindicated experimentally by Perrin (1908).