A system of physical chemistry - Index of

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A system of physical chemistry - Index of

176

A SYSTEM OF PHYSICAL CHEMISTRY

to waves of frequencies in the range v, v + 8i'. This number is in fact the

number of independent co-ordinates or degrees of freedom for such quali-

ties of radiation. Ascribing the usual kY units of kinetic and potential

energy to each degree, we obtain for the energy of radiation in the range

Q

V, r -H 8i', the amount -^kHv"- . 8v ergs, or for the energy-density,

Stt

-j-/^Ti'- . 8v ergs per c.c. In terms of wave-lengths we obtain by put-

ting V = r- and 8v = - -,8A, that the energy-density of radiation

A A'

whose wave-lengths he in the range A, A -f- 6A is — rpoA ergs per

A^

c.c.^

It is an obvious drawback to the Rayleigh-Jeans expression

that it

does not approach a finite limit, as A decreases to zero. In fact, the

ether would appear to contain an infinite amount of energy per c.c.

since—

is certamly infinite.

We might evade this objection by observing that exchange of energy

from one type to another must be effected by the material of the enclosure

(as was pointed out above), and that we might reasonably suppose

the radiating mechanisms in the atoms to be of such a nature that

they could not emit radiation of a quality higher than a certain limiting

frequency, and so the upper limit of the integral would be a finite

quantity and not zero. But this would not meet the difficulty that for

the same amount of range in wave-lengths 8A, there is a greater contribution

to the energy density from high-grade qualities than from low-

grade, according to the Rayleigh-Jeans formula ; whereas experiment

shows that the factor of 8A exhibits a maximum value for a certain wavelength

A,„ (dependent on temperature), and approaches zero as a limit

as A approaches zero or infinity.

It has been suggested that the tendency, expressed in the Rayleigh-

Jeans Law, of the radiation energy to pass more and more into the higher

qualities, is in reality a true phenomenon of nature, and that we fail to

appreciate it in our experimental tests because all temperature enclosures

fail to confine the energy of the highest frequencies ; such energy leaks

out, as it were, through the walls and through the small opening facing

the radiometer, almost as fast as it is supplied from low-frequency radiation

by the agency of the walls and so the condition we ; actually observe

is a compromise— a stage on the way to the final consummation

expressed in the ideal formula, but unattainable except after an enormous II

'

Phil. Mair., 49, 539, igoo ; lo, gi, 1905; 17, 229, igog. Nature, ^2, p. 94 and

p. 243, 1905.

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