A system of physical chemistry - Index of

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A system of physical chemistry - Index of

52

A SYSTEM OF PHYSICAL CHEMISTRY

The expression for U then becomes—

It will be observed that this equation differs from the expression

3RT (obtained by applying the ^^z^/partition principle, energy being

regarded as continuous), by the substitution of the term „ vi^ _ — ^'^

place of T.

Differentiating U with respect to T we obtain Einstein's equation

for the atomic (or molecular) heat of a solid at constant volume, viz.—

On the " classical "

view, the factor multiplied by 3R would have been

6

5

4

3

2

I

f:dT

unity. The " correction " term will be seen to contain T and is therefore

a function of temperature. On Einstein's theory one would expect

the atomic heat itself to be a function of temperature, as is experimentally

the case. Qualitatively, therefore, this marks a considerable advance over

the older theory. It still remains to be seen whether the expression

given really reproduces the values of C„ at various temperatures quantita-

dU . . .

—, tively. The shape of the curve for as given by Emstem's formula

is shown in the

represent

accompanying figure (Fig. in

5), which the ordinates

atomic heats and the abscissae the temperature expressed in

T

terms of tt-

. . .

. For any given substance the vibration frequency is taken

to be a constant.

It will be seen from the figure that when ^— >o-y the term

Pov

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