Equipartition theorem
The classical law that in thermal balance, every way a system can move receives, on average, the same share of energy, proportional to temperature.
For a gas molecule, each way of moving (back and forth, side to side, up and down, rotating, vibrating) gets on average the same amount of energy. Established by Maxwell and Boltzmann in the nineteenth century, the law explained the behaviour of gases widely.
Applied to light, though, it caused trouble. Light in a box can vibrate in countless patterns with ever shorter wavelengths, and giving each the same energy makes the total infinite. Lord Rayleigh set out this calculation in 1900[1]; it later became known as the ultraviolet catastrophe.
The heat needed to warm a solid also falls far below the equipartition prediction at low temperatures. In 1907 Einstein showed that if the vibrations of atoms also come in steps of energy, they "freeze out" at low temperature and can no longer take up energy, explaining the discrepancy[2].
Related terms
- Ultraviolet catastropheThe difficulty that classical physics, applied to blackbody radiation, predicts energy growing without limit at short wavelengths.
- Boltzmann constantThe fundamental constant, written k, that links temperature to the energy per atom.
- EntropyA quantity measuring how many ways a thing can be spread around. In a system that exchanges nothing with its surroundings, entropy can increase but never decrease.