The third law of thermodynamics states that the entropy of a system in a perfect crystalline state is zero, as the temperature approaches zero Kelvin.
Molecular motion decreases with temperature, and a pure substance may form a crystal with an uninterrupted lattice structure as ; that is, a crystal with a unique configuration. If this configuration is such that every atom, ion or molecule is arranged in an orderly and repeating pattern with no defects, distortions or irregularities, it is called a perfect crystal.
The equation for statistical entropy is:
where is the number of ways to achieve the configuration of the system.
Since there is only one way to arrange the configuration of a perfect crystal, and
While the scenario above involves a perfect crystalline state, the law still holds even when the structure at very low temperatures is not flawless, provided the system reaches a unique ground state configuration, meaning .