Explain Surface Temperature of the Sun - QS Study
QS Study

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 radius (Fig). The heat energy from the Sun will necessarily pass through this surface of the sphere.

a4

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.