# 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) 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 $$\frac{hc}{{k}_{B}\mathrm{(5.984901}\ldots )}$$ $$\frac{hc}{{k}_{B}\mathrm{(5.838126229}\ldots )}$$