A system of physical chemistry - Index of

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A system of physical chemistry - Index of

x88 A SYSTEM OF PHYSICAL CHEMISTRY

vibrations constitute waves of " sound "

travelling through the body

with definite speeds. There are, for instance, "distortional" transverse

waves travelling with a velocity v^, and " compressional "

longitudinal

waves travelling with a velocity v«. v^ can be calculated if one

knows the density p and modulus of rigidity fi of the material ; it is in

fact z\ = //f ; V.2 can be calculated if one knows in addition the bulkmodulus

K—

IT a. 4/*

/ 3.

V p

Now, the number of degrees of freedom for vibrations having frequen-

cies between v and v + 8v is, as previously, — jv'^Sv per unit volume for

the transverse waves, and ^v^Sv for the longitudinal. (N.B.—The

factor Stt occurs because the transverse waves are polarisable in two

rectangular planes, the longitudinal are not.) Consequently the

whole modes of vibration per unit volume between v and v + 8v are

( —^-^ :, )v^Bv. We saw above that the similar formula developed foi

the ether by Rayleigh and Jeans suffered from the drawback that, in in-

tegrating it, no finite upper limit could be assigned on account of the

assumed continuity of the ethereal medium. In this case, however,

there must be a finite upper limit to v, because the number of degrees

of freedom cannot exceed 3N for a gram-atom of the substance.

Hence if v,„ is the —

highest frequency possible

.^ /Sttt 47rT\

(where t is the volume of a gram-atom)

v^dv

o

where F is a constant calculable from the elastic constants and density

of the body.

/3N\i

Smce v,„ = (

-p- ) ) v,n IS also calculable. For Al, Cu, Zn, Ag, Pb,

Diamond it is of the order 10^- to lo^^. Now by ascribing, according

to the extension of Planck's work, the energy—

hv

ghvlkt _ J

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