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.
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)dν | 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)dλ | 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 | \(\frac{hc}{{k}_{B}\mathrm{(5.984901}\ldots )}\) | \(\frac{hc}{{k}_{B}\mathrm{(5.838126229}\ldots )}\) |
