# The Third Law of Thermodynamics

At T = 0, there is no energy corresponding to thermal motion. Further, for a perfect crystal all the atoms or ions which make up the crystal are arranged in a regular, uniform fashion. The absence of spatial disorder and thermal motion may be used to argue that such a material, under these conditions, has zeroentropy. (This idea would be consistent with the molecular interpretation of entropy, which considers the entropy to be proportional to the natural logarithm of the number of ways of arranging the molecules. If there is only one way of arranging the molecules, as in the case outlined above, then the logarithm and by implication the entropy are both zero.)

The idea that the entropy of a regular array of molecules is zero at T = 0 is consistent with a thermodynamic observation (for which there is experimental evidence) known as the Nernst Heat Theorem, which states:

The entropy change accompanying any process of chemical or physical change tends towards zero as the absolute temperature approaches zero.

It follows from this that, if we assign the value zero to the entropies of elements in perfect crystalline form at  T = 0 , then all perfect crystalline compounds also have zero entropy at 0K (because the entropy change accompanying the formation of the compound has, like all entropy changes at this temperature, tended to zero). Thus all perfect crystals may be taken to have zero entropy at T  = 0 . This conclusion is summarised in the Third Law of Thermodynamics:

If the entropy of every element  in its most stable state at T = 0 is taken as zero, then every substance has a positive entropy which at T = 0 may become zero, and does become zero for all perfect crystalline substances.

Note that it is NOT stated as part of the Third Law that entropies are zero at T = 0. It is not necessary for this to be the case for the law to be valid. The law implies that all perfect substances have the same entropy at Absolute Zero, and as far as thermodynamic calculations are concerned it is assigned the value zero purely as a matter of convenience. (The molecular interpretation of entropy outlined above does, however, imply that S = 0 at T = 0.)

Entropies are normally reported on the basis that S(0) = 0 for a perfect crystal. Such entropies are formally called Third-Law Entropies, but are commonly known as standard entropies. When a substance is in its standard state at a temperature T, the standard entropy is denoted Sº(T).

We also define the standard reaction entropy, Δr , as the difference between the molar entropies of the pure separated products and the pure separated reactants, all substances being in their standard states at the specified temperature, and each molar entropy being weighted by the appropriate stoichiometric coefficient: