Question

Using Rayleigh-Jeans formula, find the total energy density. Can you explain Stefan-Boltzmann

law from this? Explain your answer.

Answer 1

We know that

Rayleigh-Jeans formula,

$\rho_w=\frac{hw^3}{\pi^2 c^3}\times\frac{1}{e^{\frac{hw}{kT}-1}}$

total energy density Stefan-Boltzmann

$U=\smallint_0^n\rho_wdw$

where n=infinite

$U=\frac{h}{\pi^2c^3}\smallint_0^n\frac{w^3dw}{e^{(\frac{hw}{kT}-1)}}=\frac{\pi ^2k^4}{15c^3h^3}T^4$

$U=\alpha T^4$