Write and explain Stefan - Boltzmann's law.

Explanation

Radiation energy can be transformed to large ditances in absence of medium.
Total electromagnetic energy produced from a substance at absolute temperature T depends on its dimension, its emissivity and its temperature.
The energy emitted in unit time (H) from perfect black body is as below.
`H=A sigmaT^(4)` (For perfect black body)
where A is area and T is absolute temperature.
This relation was proved by scientist Stefan in 1879 experimentally and then Boltzmaan proved it in 1884 theoretically. Hence, it is called Stefan-Boltzmann law.
`sigma` is called Stefan-Boltzmaan constant. Its SI unit value is `5.67xx10^(-8)" W m"^(-2)K^(-4)` and dimensional formula `[M^(1)L^(0)T^(-3)K^(-4)]`.
Emissivity : The ratio of total emissive power of a surface to the total emissive power of the surface of perfectly black body, kept under the same conditions, is called the .emissivity. (e) of that surface.
`:.` emissivity (e) `=("Total emissive power")/("emissive power of perfect black")`
For perfect black body emissivity `e=1`
Absorptivity : On irradiating a surface, the ratio of the radiant energy absorbed to the amount of radiant energy incident on the surface is called .absorptivity. (a) of that surface.
`:." a = "("radiant energy absorbed")/("radiant energy incident")`
For a complete black body `a=1`.
From Stefan - Boltzmaan.s law, we can write,
`H=Ae"sigmaT^(4)` . . .(1)
where A = area, e = emissivity, `sigma=` Stefan-Boltzmaan.s constant, T = absolute temperature and H = heat radiated in unit time.
If substance of temperature T is kept in surroundings temperature `T_(S)` (where `TgtT_(S)`) then net rate of radiation of heat for substance.
`H="e"sigma"A"(T^(4)-T_(S)^(" "4))` . . . (2)
For complete black body,
`H=sigmaA(T^(4)-T_(S)^(" 4"))`
where `sigma=` Stefan - Boltzmaan.s constant.
A = Area of substance