M. P. Melrose
Universiw o f London King's College London, W.C. 2, England
Textbook Errors, 97
Statistical Mechanics and the Third Law
There appears to he some over-simplification, even in modern textbooks of physical chemistry,' about the way in which statistical mechanics provides theoretical justification for the third law of thermodynamics. What is often implied is that statistical mechanics determines S,, the temperature independent part of the entropy which is unknown in pure thermodynamics. This is not quite true: the statistical expression for S, still contains a term which is undetermined. The real contribution of the statistical treatment lies in the demonstration, which is beyond pure thermodynamics, that the value of S, is of no practical significance. The most familiar argument about the third law arises in statistical treatments whose basic postulate is the Planck-Boltzmann relation. S
=
klnn
(1)
This expression gives a statistical analog for the entropy of an isolated system (i.e., E, V, and N are constant) which can be realized in 0 different dynamical states. The typical argument is then as follows. At the lowest temperatures, the system will tend to adopt its lowest energy state. Since, as far as we know, most systems are non-degenerate in their lowest energy states (i.e., 0, = I), eqn. (1) is taken as confirmation of the "strong" statement of the third law, that S, is zero. This statement is sometimes weakened to "S, may he taken as zero" to allow for the possibility of nuclear degeneracies near OoI
