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 value in SI units is exactly defined (i.e., any finite number of digits is mathematically calculable, requiring no physical measurement) but is irrational, the above being its initial digits. It is based upon the constants π, the Boltzmann constant (k), Planck constant (h), and the speed of light (c). the latter three which are now all given exact SI-unit values, defining the current SI units as having these values. 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.