A system of physical chemistry - Index of

CHAPTER III.

(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

reaction.

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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