The Third Law of Thermodynamics states:

The entropy of a perfect crystal at zero kelvin is zero.

There are two things we need to talk about here. The first is the notion of a perfect crystal. A perfect crystal is a crystal which has no point, linear or planar imperfections. However, this definition is a bit difficult to get around, so a perfect crystal can simply be said to be a perfect regular lattice structure without any imperfections whatsoever.

The second is the notion of entropy. Entropy, as you should already know, has the symbol S, and is defined by the following equation:

S = k_B ln(W)

where

• k_B is the Boltzmann constant (seen in the Ideal Gas Equation pV = Nk_BT), and
• W is the number of ways of arranging the molecules of the system, accounting (this is like a combinatorial multiplication) for the number of possible energy states of the system.

At absolute zero, all molecules are at their lowest energy state, also known as the ground state. Also, in a perfect crystal, there is only one way to arrange the molecules. Therefore, W = 1. So at absolute zero,

S = k_B ln(1) = 0

as claimed by the Third Law.