Stefan-Boltzmann Law

#Physics
Hyperphysics Article

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

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

$\displaystyle j^{\star}=\frac{U}{V}=\sigma_{B} T^{4}=s_{B}\tau^{4}$

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

$\displaystyle P=aA\sigma_{B} T^{4}$

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