Stefan-Boltzmann Law

Hyperphysics Article

$\frac{U}{V}=\frac{{\pi }^2}{15(\hslash c{)}^3}{\tau }^4$

• $U$ is the energy of the energy of a blackbody in 3D
• $V$ is the volume of the gas
• $\tau$ is the fundamental temperature of the blackbody

$j^{\star }=\frac{U}{V}={\sigma }_B{T}^4=s_B{\tau }^4$

• Check if it’s the same as $\frac{U}{V}$
• $j^{\star }$ is the blackbody radiant emittance or flux density of radiant energy
• ${\sigma }_B$ is the Stefan-Boltzmann Constant
• $s_B$ is also the Stefan-Boltzmann Constant
• Same as intensity with units of $\frac{\mathrm{W}}{{\mathrm{m}}^2}$

$P=aA{\sigma }_B{T}^4$

• $P$ is the power of blackbody radiant emittance
• $A$ is the surface area of the blackbody
• $a$ is the graybody emissivity