The Sun is a perfect black body of radius r and surface temperature T. According to Stefan’s law, the energy radiated by the Sun per second per unit area is equal to σT4.
Where σ is Stefan’s Constant. Hence, the total energy radiated per second by the Sun will be given by:
E = Surface area of the sun X σT4
so, E = 4πr2 X σT4 … …. (1)
Let imagine a sphere with Sun at the centre and the distance between the Sun and Earth R as the radius (Fig). The heat energy from the Sun will necessarily pass through this surface of the sphere.
If S is the solar constant, the amount of heat energy that falls on this sphere per unit time is
E = 4πr2 S … … … (2)
By definition, equations (1) & (2) are equal.
so, 4πr2 σT4 = 4πr2 S
then, T4 = R2S/σr2
so, T = [R2S/σr2]1/4
or, T = (R/r)1/2 (S/σ)1/4
Knowing the value of R, r, S and σ the surface temperature of the Sun can be calculated.