A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II i8'

C = sN/^

'

{e-^ - I)-'

where ^ = ^- If -^ is small, i.e. if v is small or T large, this expression.

approaches the value 3Ni, which is known to be 5-95 calories, and is

indeed the Dulong- Petit value of the atomic specific heat. For small

values of T, however, x is large and the above expression grows smaller

and smaller, ultimately approaching the limit zero as T approaches zero

or X approaches infinity. That is, there should be a gradual decrease

to zero of the specific heat of a solid as the temperature approaches

absolute zero. This was known to be true in a general way. Further,

as C is a function of - , the curves connecting specific heat and tem-

perature for various monatomic solids should be similar. In fact, for two

solids whose atomic frequencies are vi and vo, the curve for the second

would be obtained from the curve for the first by maintaining the same

ordinates (representing C) and altering all the abscissae (representing T)

in the ratio vi : v^. A series of now famous researches were undertaken

by Nernst and his pupils ; details of the work will be found in papers

in the Ann. der Phys., p. 395, igii, in the Zeitsch. Jiir Electrochem.,

191 1 and 1 91 2, in the Theorie du Rayonnement, and in Nernst's four

lectures delivered at University College, London, on the solid state.

The similarity of the curves was proved, while Einstein's actual ex-

pression, although following the general course of the change in specific

heat with the temperature, exhibited considerable numerical discrepancies,

especially at low temperatures. Nernst and Lindemann pro-

posed an alternative formula— r-

C = ^N/^

[e^ - if

L

'

2

e

'x\ 2£

This, although in good agreement with results, was a piece of lucky

guesswork, founded on no solid theoretical basis. In a paper in the

Ann. der Phys., 39, p. 789, 191 2, Debye attacked the problem from

a broad standpoint, and his result, from its agreement with experiment

and the soundness of its premises, seems to have approached finality

in this domain.

Debye points out that there can be no single " characteristic "

vibration of the atoms of a monatomic solid. There are an enormous

number of such vibrations; they constitute an "acoustic" spectrum;

they are the fundamental and overtones of the body considered as

emitting a note. A knowledge of the elastic constants of the material

is sufficient to determine them, just as Rayleigh and Jeans determined

the frequencies possible in a cubical "block" of ether. For these

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