A system of physical chemistry - Index of


A system of physical chemistry - Index of


(Physical equilibrium in solids) — Theory of atomic heats of solids— Equations

of Einstein, Nernst-Lindemann, and Debye.

Einstein s Exlensioti of Planck's Quantutn Theory to the Calculation of

Specific Heats of Solids [Crystalline Substances) and Supercooled

Liquids (" Amorphous Solids "). [Cf Einstein, Annalen der Fhysik,

[4], 22. 180, 1907.)

The specific heat of a substance at constant volume is defined as the

increase in total energy when the substance rises 1° in temperature.

Let us take as our unit of mass the gram-mole or gram-atom (in the

case of monatomic substances), and we then can write—

^^ ~ dT'

Note.—U here stands for total energy possessed by the substance at

a given temperature. It is not to be confused with the significance

attached to U in the " "

elementary thermodynamical treatment (Chap. I.,

Vol. II.), in which " U " stood for decrease in total energy due to chemical


Let us now restrict our attention to solids (or supercooled liquids),

taking as particular instances the metallic elements. These, as we have

seen, are regarded as monatomic, so that the gram-atom and grammolecule

are identical terms in these cases. Now we want to find out

to what the total or internal energy of a metal is due. It is usual to

regard the solid state as characterised by vibrations of the atoms about

their respective centres of gravity. Such vibrations can, of course, take

place in the three dimensions of space, i.e. each atom possesses three

degrees of freedom. As we have seen, each vibration represents energy,

one-half of which is kinetic, one-half potential, as long as the amplitude

of the vibration is not too great. This vibrational is energy regarded

as representing all the internal energy possessed by the atom, at least

at low temperatures (at high temperatures the energy of vibration of

the electrons inside each atom would have to be considered, but at

ordinary temperature and at lower temperatures the total energy of

the solid may be ascribed to the vibration of the atoms). We have

already discussed this, and we have seen that on applying the principle

of equipartition of energy the atomic heat of metals should be

-R = 5 '9 5 5 cals. per degree, and that this should be independent of

temperature. As already pointed out, this numerical value is certainly


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