ABSTRACT
Since the temperature of a chemical system is proportional to its kinetic energy, it follows that as the temperature approaches absolute zero, the kinetic energy also approaches zero. In other words, all molecular motion stops at T = 0. For a perfectly crystalline solid, at T = 0 every atom is frozen into a well-defined location in the lattice; under these conditions, we may state that there is zero disorder in the crystal, that is, its entropy is zero. This is a statement of the Third Law of Thermodynamics:
The entropy of a perfectly crystalline solid is zero at
. . . [1]
It also is observed experimentally that for all solids, cP A 0 as T A 0. We showed earlier that if we heat a substance from T1 to T2 at constant pressure,
6SP = S ST T2 1< = C dT
0 . . . [2]
In Eqn [2], if we substitute zero kelvin for T1 and any general temperature T for T2 , we get
6SP = S ST T2 1< = ST – S0
= C dT
0 . . . [3]
But the Third Law states that S = 0 at T = 0; therefore Eqn [3] becomes
6SP = ST – 0 = C dT
That is, ST = C dT
0 . . . [4]
Since we can measure heat capacities at any temperature1
it can be seen that, unlike other state functions such as U and H, we can calculate absolute values of S at the temperature T. All we have to do is plot (CP / T ) vs. T and take the area under the curve from T = 0 to T = T, as shown in Fig. 1. This is why tables of thermodynamic data are able to list absolute values so of standard entropies for the elements2 and compounds, in contrast to the standard values for other state properites such as internal energy or enthalpy, which must be reported versus some reference state where the values are arbitrarily defined as zero.
