Table 1 Wien’s peaks for the energy and the entropy of radiation for different dispersion rules, corresponding to different values of the dispersion coefficient m.

From: Entropy of radiation: the unseen side of light

ϑ B ϑ (T)dϑ Dispersion rule m Energy Entropy
ν 2 \(2\nu {B}_{{\nu }^{2}}(T)d\nu \) frequency-squared 2 \(\frac{hc}{{k}_{B}\mathrm{(1.593624}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(1.178179641}\ldots )}\)
ν B ν (T) linear frequency 3 \(\frac{hc}{{k}_{B}\mathrm{(2.821439}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(2.538231893}\ldots )}\)
\(\sqrt{\nu }\) \(\frac{1}{2\sqrt{\nu }}{B}_{\sqrt{\nu }}(T)d\nu \) square root frequency 7/2 \(\frac{hc}{{k}_{B}\mathrm{(3.380946}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(3.137016422}\ldots )}\)
log ν \(\frac{1}{\nu }{B}_{\mathrm{log}\nu }(T)d\nu \) logarithmic frequency 4 \(\frac{hc}{{k}_{B}\mathrm{(3.920690}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(3.706085183}\ldots )}\)
log λ \(\frac{1}{\lambda }{B}_{\mathrm{log}\lambda }(T)d\lambda \) logarithmic wavelength 4 \(\frac{hc}{{k}_{B}\mathrm{(3.920690}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(3.706085183}\ldots )}\)
\(\sqrt{\lambda }\) \(\frac{1}{2\sqrt{\lambda }}{B}_{\sqrt{\lambda }}(T)d\lambda \) square root wavelength 9/2 \(\frac{hc}{{k}_{B}\mathrm{(4.447304}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(4.255382544}\ldots )}\)
λ B λ (T) linear wavelength 5 \(\frac{hc}{{k}_{B}\mathrm{(4.965114}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(4.791267357}\ldots )}\)
λ 2 \(2\lambda {B}_{{\lambda }^{2}}(T)d\lambda \) wavelength-squared 6 \(\frac{hc}{{k}_{B}\mathrm{(5.984901}\ldots )}\) \(\frac{hc}{{k}_{B}\mathrm{(5.838126229}\ldots )}\)