Remarks

1. Note that ironically, quantum mechanics was discovered via the classical limit of a radiation law! In fact, the Rayleigh-Jeans-law contains no Planck constant $h$, whereas the parameters $a$ and $b$ in the 19th-century `thermodynamic' Wien law contain $h$ and $k_B$, both fundamental constants in microscopic theories (although at that time, the deep physical meaning of $a$ and $b$ was of course not understood).

2. Nowadays, instead of $h$ one often uses $\hbar = h/2\pi$. Instead of the frequency $\nu$ one often uses the angular frequency $\omega=2\pi\nu$. If $\omega$ is used instead of $\nu$, the spectral energy density $w(\omega,T)$ is defined as $w(\omega,T)d\omega = u(\nu,T)d\nu$. Since $d\omega = 2\pi d\nu$, this gives $w(\omega,T)= {\omega^2}/(\pi^2 c^3)\times \hbar\omega /(\exp(\hbar\omega/kT)-1)$. Therefore, be careful when comparing different definitions and doing calculations because a wrong factor $2\pi$ gives a result that is wrong by nearly one order of magnitude!

3. Cosmic black body radiation is a consequence of the `Big Bang Model'. Measurements of the cosmic background radiation corresponding to a temperature $T\approx 2.7$K were performed by R. H. Dicke and co-workers.