### Stefan-Boltzmann constant

**(σ, Stefan's constant)**
(relates radiation power to temperature and surface area)

The **Stefan-Boltzmann constant** is a
physical constant relating the power radiated
from a black body to its temperature
according to the **Stefan-Boltzmann law**
(i.e., **Stefan-Boltzmann equation**,
which is not the same as the Boltzmann equation):
the energy radiated by a black body
is proportional to its surface and
the fourth power of its temperature:

*j*^{*} = σ*T*^{4}

*j*^{*} - energy radiated per unit surface area.
*T* - temperature.
- σ - Stefan-Boltzmann constant.

In SI units, it is:

σ = 5.670374419×10^{-8} W m^{-2} K^{-4}

It can be derived from the Boltzmann constant,
Planck constant, and the speed of light.
A consequence of the Stefan-Boltzmann equation:
the bolometric luminosity
of a black body (which approximates real astronomical objects)
is j^{*} times the surface area:

L_{bol} = Aσ*T*^{4}

- L
_{bol} - bolometric (i.e., total) luminosity.
- A - surface area of the object, π r²

(*physics,constant*)
**Further reading:**

http://en.wikipedia.org/wiki/Stefan-Boltzmann_constant

**Referenced by pages:**

power law

stellar radius determination

stellar structure

Index