Question

State and explain Stefan's law of radiation.

Answer 1

Stefan's law:

A totally black body's radiant energy released per unit time per unit area is precisely proportional to the fourth power of its absolute temperature.

Let R- be the amount of radiant energy emitted by the blackbody per unit time per unit area.

T - - be the absolute temperature.

Then, R∝ T⁴

R = σ T⁴           ....(i)

where, a is constant called as Stefan's constant and σ =5.7 x 10^-8 Jm^-1 s^-2 K^-4 or JWm^-2 K^-4.

Dimension of σ = [L⁰ M¹ T^-3 K^-4]

Thus, the power emitted by a totally black body is determined solely by its temperature and not by its colour, materials, surface type, or other factors.

By definition of emissive power,

${\displaystyle R=\frac{Q}{At}}$

∴ Equation (i) becomes

${\displaystyle \frac{Q}{At}=\sigma T^4}$

For non-blackbody bodies, the energy radiated per unit area per unit time remains proportional to the fourth power of absolute temperature.

R = e σAT₀⁴         ...(iii)