Equipa

Meet Equipa, who shares energy out fairly: the same average slice for every way a molecule can move.

In a gas in thermal equilibrium, energy is constantly passed around in collisions. The equipartition theorem of classical physics says that each 'quadratic' degree of freedom, meaning each term in the energy that goes as a square of a speed or a position, gets on average ½k_BT of energy.

A helium atom can move in three directions, so its average kinetic energy is 3/2 k_BT. At room temperature, 300 K, that is about 6.2×10⁻²¹ joules. A nitrogen molecule can also rotate about two axes, giving it 5/2 k_BT, which is why the molar heat capacity of air is larger than that of helium.

Equipartition explains measured heat capacities of many gases and the Dulong–Petit value for solids at room temperature.

It also fails, and the failures mattered. Molecular vibrations hold far less energy than equipartition predicts at room temperature, and solids' heat capacities fall at low temperature. Explaining these 'frozen out' modes was one of the clues that led to quantum theory.