Black-body radiation is a type of electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment or emitted by a black body held at constant, uniform temperature. The radiation has a specific spectrum and intensity that depends only on the temperature of the body.

A perfectly insulated enclosure that is in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided that hole is small enough to have negligible effect upon that equilibrium.

A black-body at room temperature appears black, as most of the energy it radiates is infra-red and cannot be perceived by the human eye. At higher temperature, it glows with increasing intensity and colors that will range from dull red to blindingly blue-white as the temperature increases.

Planck’s law of black-body radiation states

I(v,T)= (2hv^3)/c^2 1/(e^(hv/kT)-1)

Where I(v,T) is the energy per unit time radiated per unit area of emitting surface in the normal direction per unit soli angle per unit frequency by a black body at temperature T

H is the Planck constant

C is the speed of light in a vacuum

K is the Boltzmann constant

V is the frequency of the electromagnetic radiation

T is the absolute temperature of the body

Wien’s displacement law shows how the spectrum of black-body radiation at any temperature is related to the spectrum at any other temperature. A consequence of Wien’s displacement law is that the wavelength at which the intensity per unit wavelength of the radiation produced by a black body is at a maximum λmax which is a function of only temperature as seen below:

λ_max=b/T

Where b is the Wien’s displacement constant.

The Stefan-Boltzmann Law states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature as seen below:

j^*= σT^4

Where j* is the total power radiated per unit area, T is the absolute temperature and σ is the Stefan-Boltzmann constant