Thermodynamics and Chemistry

CHAPTER 6

6 The Third Law and Cryogenics

The third law of thermodynamics concerns the entropy of perfectly-ordered crystals at zero
kelvins.
When a chemical reaction or phase transition is studied at low temperatures, and all
substances are pure crystals presumed to be perfectly ordered, the entropy change is found
to approach zero as the temperature approaches zero kelvins:

lim

T! 0

ÅSD 0 (6.0.1)

(pure, perfectly-ordered crystals)

Equation6.0.1is the mathematical statement of theNernst heat theorem^1 orthird law of
thermodynamics. It is true in general only if each reactant and product is a pure crystal
with identical unit cells arranged in perfect spatial order.

6.1 The Zero of Entropy

There is no theoretical relation between the entropies of different chemical elements. We
can arbitrarily choose the entropy of every pure crystalline element to be zero at zero
kelvins. Then the experimental observation expressed by Eq.6.0.1requires that the entropy
of every pure crystallinecompoundalso be zero at zero kelvins, in order that the entropy
change for the formation of a compound from its elements will be zero at this temperature.
A classic statement of the third law principle appears in the 1923 bookThermodynamics
and the Free Energy of Chemical Substancesby G. N. Lewis and M. Randall:^2

“If the entropy of each element in some crystalline state be taken as zero at the

absolute zero of temperature:every substance has a finite positive entropy, but

at the absolute zero of temperature the entropy may become zero, and does so

become in the case of perfect crystalline substances.”

(^1) Nernst preferred to avoid the use of the entropy function and to use in its place the partial
derivative.@A=@T /V (Eq.5.4.9). The original 1906 version of his heat theorem was in the form
limT! 0 .@ÅA=@T /VD 0 (Ref. [ 39 ]).
(^2) Ref. [ 104 ], p. 448.

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