A system of physical chemistry - Index of

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A system of physical chemistry - Index of

AFFENDIX II 173

another without any change in the energy or quality of the trains). For

this reason, if the walls are perfectly reflecting, any arbitrary condition

of radiation supposed existing at one moment would remain permanently

unaffected in the energy and quality of its constituents, and only by the

introduction of a piece of non-reflecting matter into the enclosure could

the radiation be gradually brought to the condition of " full " or " complete

" radiation for the temperature, the condition considered by Balfour

Stewart and Kirchhoff.

Wien, himself, had made an attempt to determine the form of the

function in the numerator of his so-called displacement formula.^ He

considered the enclosure to contain a perfectly absorbing or "black"

body, which he assumed to be a gas with its molecules distributed according

to the Maxwell Law, and its temperature therefore proportional

to the mean-squared velocity. A further hypothesis (a very doubtful

one) was the assumption that those molecules whose velocities lie within

certain narrow limits at a definite instant are at that instant emitting

light within narrow frequency limits, with an intensity proportional to

the number of those molecules. By these means Wien arrived at the

c

form e ~at for his function /(^T), c being a constant. Measurements^

carried out shortly after by Lummer and Pringsheim, Beckmann, and

Rubens verified the formula as a good representation of the facts for

short wave-lengths, but found it completely at variance with the facts

for long wave-lengths.

It was by the application of statistical principles in another direction

that the next advance towards a correct radiation formula was made.

Wien had considered the molecules of the black body. Lord Rayleigh,

and afterwards Jeans, considered the radiation itself, assigned co-ordinates

to it and "degrees of freedom," and applied the results of Max-

well's distribution law directly to these concepts. Such applications

are certainly rather easier to apprehend " physically " in the case of gas

molecules than in that of constituent wave-trains of radiation ; there is

more " substantiality " about a molecule than a wave-train. The repre-

sentation of a molecule as a small, hard sphere with perfect resilience,

which is quite adequate for many purposes, and analogies with billiardballs,

discs, etc., put one on fairly familiar terms with molecular motion

and exchange of energy. The degrees of freedom of such simple systems

are easily calculable, being in fact six for a " "

rigid molecule of any

shape. Even if we introduce atomic structure into the molecules, the

degrees can still be computed if one knows the parts and their connections.

The energy of the system at a is given temperature then obtained

by the principle of equipartition, which is derived from the law of distribution,

and asserts that the kinetic energy can be calculated by assigning

to each degree of freedom an amount \kT ergs, where k is the

molecular gas constant (i "35 x lo^i^ ergs/degrees), an equal amount

of potential energy being also assigned to any degree of freedom, if thero

are " elastic " forces of the usual simple harmonic type.

' Wied. Ann., 58, p. 662, 1896.

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