A system of physical chemistry - Index of

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A system of physical chemistry - Index of

DEB YES EQUATION 75

Copper gave an equally satisfactory result. On the whole Debye's

equation applies more exactly even than the equation of Nernst and

Lindemann. Debye's equation has of course the further advantage that

it possesses a theoretical basis, whilst that of Nernst and Lindemann is

semi-empirical.

Note on the method of evaluating the summation term of the Debye formula m

the form given by Nernst and Lindemann.

To evaluate—

» = " g^ /

I 3 6 6

n = , 'V«T «%t) n-r) "(t)^

Set — equal to x. Also set ^-^ = a. Then e-nx = anx = -

(a-v)" yn if y be set

equal to ax.

The sum can therefore be written :

or the same expression may be written :

nx

» = I n = I

tanx(±+^_ +_^+ M

\nx n^x'^ n'^x^ n*x*J

n = I

"^"^

First term. Second term.

n = 00

First term = if-^l + Zl + i:! + . . . ad inf7\.

xLi 23 -

J

Second term = IR + ^. + "^ + "^^ + . . . o J

Fourth term = — Z 4.^^ 4. Z^ j.iL + , . , ad inf. .

x\_i*' 2" 3^ 4* J

Each of these series is convergent, so that only the first three or four expressionsin

each need be taken into account.

Characteristic Infra-red Frequencies Obtained from Debye's Formula.

— By means of equation (2) of the preceding section it is possible to

calculate the characteristic infra-red frequency vmax. (which represents

the upper limit of the spectrum of vibrations) from a determination of

the characteristic temperature 6. This temperature can be obtained in

turn from the elastic constants of the substance as has been shown by

Debye. Making use of Debye's values of ^, H. S. Allen {Proc. Roy.

Sac, A, 94, 100 (19 1 7)) has calculated Vmax. for the elements given in

the following table. It will be observed that the frequencies so obtained

agree very well with those calculated by methods previously mentioned :—

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