### 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, which
are now all given exact values (i.e., form part of the
basis of SI units) and
give the Stefan-Boltzmann constant the above exact value.
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 if spherical.

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

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

**Referenced by pages:**

power law

stellar radius determination

stellar structure

Index