A system of physical chemistry - Index of

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A system of physical chemistry - Index of

- A SYSTEM OF PHYSICAL CHEMISTRY

temperature bears out the Nernst-Lindemann view equally. As a

corollary it follows that the atomic energy content at low temperatures is

proportional to the fourth powtr of the absolute temperature [cf. Stefan's

Law for total radiation). Debye's expression for the energy U of a

solid of volume V which contains N atoms is—

the energy not being ascribed to a single harmonic vibration v, but to

a spectrum of such extending from o to v,„. If we now define the

temperature 6 (the characteristic constant of the substance) by the

expression—

B = —f^ = /3v„, (2)

and introduce into equation (i) as a new dimensionless variable— the

magnitude—

5 = ^Y ..... (3)

we can write—

or, substituting 6 for -^,

we obtain—

U =

9N*T(-)j^ _^ .

. . (5)

Dulong and Petit's Law, if true, would require the relation—

U = sN/^T.

6

Now if we write „ = .v, and differentiate equation (5) with respect to

temperature, we obtain finally—

The magnitude ^Nk has the value 5 955 cals. and may be denoted

by C^ since this numerical limit is reach^-d at high temperatures. Equation

(6) may therefore be rewritten in the form—

Q, _ 12 (•'

o J

fV^ _ 3^

Equation (6) or (7) is Debye's atomic heat formula.

(-)

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