Question

The earth receives solar radiation at a rate of 8.2 J/$c{m}^2$ - minute. Assuming that the sun radiates like a blackbody, calculate the surface temperature of the sun. The angle subtended by the sun on the earth is 0.53${}^{\circ }$ and the Stefan constant $\sigma =5.67\times {10}^{-8}W/m^2$ - K4.

• A. 6800 K
• B. 5800 K
• C. 7800 K
• D. 7800 K

Answer 1

The correct option is B 5800 K

Let the diameter of the sun be D and its distance from the earth be R. From the question,

$\frac{D}{R}\approx 0.53\times \frac{\pi }{180}$

=$9.25\times {10}^{-3}$ . ...(i)

The radiation emitted by the surface fo the sun per unit time is

At distance R, this radiation falls on an area $4\pi R^2$ in unit time. The radiation received at the earth's surface per unit time per unit area is, therefore,