Question

What is Stefan Boltzmann law ?

Answer 1

Hint: Learn about black body radiation thoroughly and learn the law related to black body radiation. Stefan rose in 1879 formulated a law about the radiant energy of black body, five years later he proved his theory empirically. The same was derived theoretically by Ludwig Boltzmann of Austria and hence became Stefan- Boltzmann law.

Complete answer:
A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. Stefan- Boltzmann deduced the energy radiating through the surface of a black body. Stefan- Boltzmann law states that the radiated energy through the unit surface of a black body per unit time is proportional to the fourth power of the absolute temperature of it. It can be expressed as,
\[E \propto {T^4}\]
where, \[E\] is the radiation energy by the unit surface of the black body per unit time and \[T\] is the absolute temperature of the black body.
By introducing a constant of proportionality we can write the equation as,
\[E = \sigma {T^4}\]
where, \[\sigma \] is the Stefan –Boltzmann constant the value of it is \[\sigma = 5.67 \times {10^{ - 8}}J{s^{ - 1}}{m^{ - 2}}{K^{ - 4}}\].

Note: When a normal body called a grey body, which does not absorbs all the electromagnetic radiation coming to it the Stefan – Boltzmann law becomes \[E = \varepsilon \sigma {T^4}\]. Emissivity is the ratio of the energy radiated through per unit time per unit area to that of the energy radiated by a black body per unit time per unit area. Hence, for a perfect blackbody emissivity is always one. \[\varepsilon = 1\].