A system of physical chemistry - Index of

CHAPTER YII.

(Systems in chemical equilibrium) — Relation between Nernst's heat theorem and

the quantum theory —Mass action equilibrium and heat **of** reaction in terms **of**

the quantum theory.

Nernst's Heat Theorem and the Quantum Theory.

We have already seen (Chap. III.) that the quantum theory appUed

to atomic heat ol solids leads us to expect that at very low temperatures

the atomic heat will become practically zero. If we think **of** two solids

A and B we can state that at low temperatures —

dUJdT = dUjdT = o

or 4U^ - Ub)/^T = o.

If the solid substances A and B are the reactant and resultant respectively

**of** a chemical reaction, the -

expression (Ua Ub) represents the

change in internal energy, U accompanying the reaction. Hence the

quantum theory leads to the conclusion that in a chemical reaction

between solids at very low temperatures—

d\J/dT = o.

This, as far as it goes, is in complete agreement

theorem which states {cf. Chap. XIII., Vol. II.) that—

= o

1- -^ -p (dAidT

^''^''' T =

°\d\JldT = o.

with Nernst's heat

To show that the relation dA/dT = o is likewise in agreement with

the Planck-Einstein hypothesis regarding the energy distribution in

solids, we may proceed as follows : As the molecules or atoms **of** a

soHd at very low temperatures do not possess any sensible kinetic energy

**of** vibration, their mutual distance apart will change very little with

temperature over a limited range in this region. Consequently, the

mutual potential energy **of** the atoms or molecules will remain practically

unchanged, and hence their free or available energy, which depends

upon the potential energy, will also remain unchanged. That is, in the

limit, when T = o, dA/dT = o. The same conclusion may be arrived

at in a slightly different way. We know that the intensity **of** radiation,

and therefore the amplitude **of** the resonators the {i.e. atoms), increases

with the temperature according to a power law considerably greater than

the first. Hence, as temperature falls the amplitude will decrease much

more rapidly, finally becoming exceedingly small. Again, the potential

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