## Abstract

*Photon Laws for Black Body Radiation:* Starting with a relation showing the temperature volume changes for black body radiation which is undergoing an adiabatic change, it is shown how photon laws which correspond one by one with known radiant energy laws may be derived. In all instances, excepting two, namely λ_{m}′*T*=const and *ν*_{m}′*T*=const, the photon relations differ from the corresponding radiant energy relations chiefly by having a power of *T* decreased by one, a power of λ increased by one, or a power of *ν* decreased by one. The entropy of black body radiation is strictly proportional to the number of photons involved. *Table of Black Body Radiation Constants*: A table includes values in common units for the collective groups of constants entering the various photon and radiant energy equations mentioned in the paper.

© 1939 Optical Society of America

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### Equations (13)

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(1)
$$\u03f5=h\nu =hc/\mathrm{\lambda},$$
(2)
$$\frac{{u}_{\mathrm{\lambda}}d\mathrm{\lambda}}{{u}_{{\mathrm{\lambda}}_{0}}d{\mathrm{\lambda}}_{0}}=\frac{{u}_{\nu}d\nu}{{u}_{{\nu}_{0}}d{\nu}_{0}}={\left(\frac{{r}_{0}}{r}\right)}^{4}={\left(\frac{T}{{T}_{0}}\right)}^{4}$$
(3)
$$C={a}^{\prime}{T}^{3},$$
(4)
$$N={\sigma}^{\prime}{T}^{3}.$$
(5)
$$\frac{{C}_{\mathrm{\lambda}}d\mathrm{\lambda}/\mathrm{\lambda}}{{C}_{{\mathrm{\lambda}}_{0}}d{\mathrm{\lambda}}_{0}/{\mathrm{\lambda}}_{0}}=\frac{{C}_{\nu}\nu d\nu}{{C}_{{\nu}_{0}}{\nu}_{0}d{\nu}_{0}}={\left(\frac{{r}_{0}}{r}\right)}^{4}={\left(\frac{T}{{T}_{0}}\right)}^{4}.$$
(6)
$${C}_{\mathrm{\lambda}}={T}^{4}{{f}_{1}}^{\prime}(\mathrm{\lambda}T),$$
(7)
$${C}_{\nu}={T}^{2}{{f}_{2}}^{\prime}(\nu /T),$$
(8)
$${{\mathrm{\lambda}}_{m}}^{\prime}T=\text{const.,}$$
(9)
$${{\nu}_{m}}^{\prime}/T=\text{const.}$$
(10)
$${N}_{\mathrm{\lambda}}=(\mathrm{\lambda}/hc){\mathcal{R}}_{\mathrm{\lambda}}$$
(11)
$$\text{or}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{N}_{\nu}=(1/h\nu ){\mathcal{R}}_{\nu}.$$
(12)
$$\mathrm{\lambda}=({T}_{0}/T){\mathrm{\lambda}}_{0},$$
(13)
$$\frac{{C}_{\mathrm{\lambda}}}{{C}_{{\mathrm{\lambda}}_{0}}}=\frac{{N}_{\mathrm{\lambda}}}{{N}_{{\mathrm{\lambda}}_{0}}}={\left(\frac{T}{{T}_{0}}\right)}^{4}.$$