A system of physical chemistry - Index of

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A system of physical chemistry - Index of

NERNSTS HEAT THEOREM 145

energy, and therefore the free energy, may be regarded as sensibly

independent of the temperature when the temperature is low. It cannot

be said, of course, that the validity of the Planck-Einstein is theory a

proof of the validity of Nernst's heat theorem. They are, however, in

agreement. This point will perhaps be rendered clearer by the following

considerations.

We know that in the case of any process carried out reversibly, the

Gibbs-Helmholtz equation states—

A - U = T . {dAldT)y.

Further, A - U = Q where Q is heat absorbed in the process.

Hence Q/T = S = {dAldT)^, where S is the change in entropy of the

system as a result of the process. Applying Nernst's theorem we conclude

that at very low temperatures the change in entropy due to the

process is zero. In other words, Nernst's theorem is identical with the

statement that at absolute zero the entropy of all substances is the same.

Planck has already pointed out {cf. Chap. I.) that the quantum hypothesis

is equivalent to the assumption that the entropy of all substances at

absolute zero is zero also. This is really a special case of the conclusion

involved in Nernst's heat theorem. The theorem and the quantum

theory are therefore in agreement, but the heat theorem is independent

of the quantum hypothesis.^

Calculation of the Affinity of a Chemical Process from Thermal Data by

the Simultaneous Application of Nernsfs Heat Theorem and the

Quantum Theory of Atomic Heats.

Equations (3) and (4) of Chap. XIII. of Vol. II., which express the

Nernst heat theorem, contain certain coefficients /?, y, etc., which are

calculated from measurements of the molecular or atomic heats of the

reactants and resultants of the reaction considered. These terms are,

in fact, the temperature coefficients of the molecular heats of the react-

ing substances. In principle, the introduction of the quantum theory

(say in the form of the Nernst-Lindemann equation) is simply a matter

of substitution of this equation in the original equations of Nernst for

A and U. To indicate how this is carried out in it practice is necessary

to put the Nernst equations into a more general form than that ex-

pressed by the equations (3) and (4) referred to.

The change, U, in the internal energy of a system as a result of a

chemical reaction is, by definition, the difference of the internal energies

of reactants and resultants, reckoned in terms of the stoicheiometrical

quantities required for the reaction. For any single substance Z we can

write : dU^/dT = c^, where c^ denotes the molecular heat of the sub-

stance Z at constant volume. Hence Uz = constant + c,dT. Hence

^z>

* The relation between the heat theorem and the quantum theory is further

considered by O. Sackur (Annalen der Physik, 34, 455, iQii).

VOL. III. 10

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