Dulong–Petit law

In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid elements is about 3R, where R is the universal gas constant.

The value of 3R is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of certain solid elements per mole of atoms they contained.

[1] In 1877, Ludwig Boltzmann showed that the constant value of Dulong–Petit law could be explained in terms of independent classical harmonic oscillators.

This model explained why conductors and insulators have roughly the same heat capacity at large temperatures as it depends mostly on the lattice and not on the electronic properties.

Despite its simplicity, Dulong–Petit law offers a fairly good prediction for the heat capacity of many elementary solids with relatively simple crystal structure at high temperatures.

This agreement is because in the classical statistical theory of Ludwig Boltzmann, the heat capacity of solids approaches a maximum of 3R per mole of atoms because full vibrational-mode degrees of freedom amount to 3 degrees of freedom per atom, each corresponding to a quadratic kinetic energy term and a quadratic potential energy term.

Here, it predicts higher heat capacities than are actually found, with the difference due to higher-energy vibrational modes not being populated at room temperatures in these substances.