# What is Stefan Boltzmann law used for?

May 9, 2018

The Stefan-Boltzmann law is $L = A \sigma {T}^{4}$, where:

• $A$ = surface area (${m}^{2}$)
• $\sigma$ = Stefan-Boltzmann (~5.67*10^-8Wm^-2K^-4)
• $T$ = surface temperature ($K$)

Assuming the object acts as a black-body radiator (an object that emits energy from the entire EM spectrum), we can find the rate of energy emission (luminosity) given the objects surface area and surface temperature.

If the object is a sphere (like a star), we can use $L = 4 \pi {r}^{2} \sigma {T}^{4}$

For a given object with a constant surface area, the Stefan-Boltzmann law says that luminosity is proportional to the temperature raised to the fourth power.