What will be expression for the surface temperature of the sun?

Let’s suppose that the temperature on the surface of sun is T and radius R. Also suppose that the sun is a black body and is present at the centre of a hollow sphere having radius r.
r will be greater than R because sun is present inside the hollow sphere therefore the hollow sphere will be larger than the sun.
r=1.A.U.
According to Stefan’s law, the energy emission of sun per unit area per second will be calculated by the formula.
E= T⁴ —————- (1)
We know that the surface area of sun will be 4Electrostatic figure 2.67 r² because sun is of spherical shape.

So, the relation to calculate the total energy emitted by sun per second will be given by the relation:
4 R² E
= 4 R² T⁴ –From equation (1)
The total energy emitted by sun is nearly equal to that of the solar luminosity of the sun. So, we can relate these both equations.

4 R² T⁴ = 4 r²S
Or

If we will get the values of S, r, R and then value of T can be determined easily. After substituting the values the approximate value of T is found to be 5800K.