Page:Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt.pdf/12

Comparing this with the general formula that expresses Boltzmann's principle

$S-S_{0}={\frac {R}{N}}\lg W,$

we arrive at the following conclusion:

If monochromatic radiation of frequency ν and energy E is enclosed (by reflecting walls) in the volume v₀, then the probability that at an arbitrary point in time all of the radiation energy located in a part v of the volume v₀ is:

$W={\left({\tfrac {v}{v_{0}}}\right)}^{{\tfrac {N}{R}}{\tfrac {E}{\beta \nu }}}\ .$

Subsequently we conclude:

In terms of heat theory monochromatic radiation of low density (within the realm of validity of Wien's radiation formula) behaves as if it consisted of independent energy quanta of the magnitude Rβν/N.

We also want to compare the average magnitude of the energy quanta of the "black body radiation" with the mean average energy of the center-of-mass-motion of a molecule at the same temperature. The latter is ³/₂(R/N)T, and for the average energy of the Energy quanta Wien's formula gives:

${\frac {\int \limits _{0}^{\infty }\alpha \nu ^{3}e^{-{\frac {\beta \nu }{T}}}d\nu }{\int \limits _{0}^{\infty }{\frac {N}{R\beta \nu }}\alpha \nu ^{3}e^{-{\tfrac {\beta \nu }{T}}}d\nu }}=3{\frac {R}{N}}T.$

The fact that monochromatic radiation (of sufficiently low density) behaves as regards to dependency of entropy on volume like a discontinuous medium that consists of energy quanta of magnitude Rβν/N suggests we should investigate whether the laws of