Stefan-Boltzmann constant

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* = σT4

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

In SI units, it is roughly:

σ = 5.670374419×10-8 W m-2 K-4

Its SI value is exactly defined (any finite number of digits is calculable), based upon constants, but irrational, and the above are its initial digits: the constants are π, the Boltzmann constant (k), Planck constant (h), and the speed of light (c), the latter three which are now all given exact values, forming part of the basis of current SI units. 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:

Lbol = AσT4

• L_bol - bolometric (i.e., total) luminosity.
• A - surface area of the object, π r² if spherical.