The third law of thermodynamics states that the entropy of a pure perfect crystal is 0 at 0 K: ? S(0K) = 0. At 0K the atoms in a pure perfect crystal are aligned perfectly and do not move. Moreover, there is no entropy of mixing since the crystal is pure. For a mixed crystal containing the atomic or molecular species A and B, there are many possible arrangements of A and B and there is therefore entropy associated with the arrangement of the atoms/molecules.

    As with any good scientific law, there are exceptions. The following are exceptions to the third law of thermodynamics:

• C=O: carbon monoxide molecules can align in various ways in a crystal, so there is entropy associated with C=O crystals at 0K. In this case, A and B are equally probable and the following equation can be used to calculate the entropy (called residual energy): S = nR [ 1/2 ln(1/2) + 1/2 ln (1/2) ] = -nRln2
• Glasses: glass is actually disorded microscopically, so it's not a pure perfect crystal.

    It's useful to know the temperature dependence of S (along with other thermodynamic parameters) so you can do experiments at a few temperatures and calculate the S for any temperature.