Question

Assuming the sun to be spherical body of radius R at a temperature of T K, evaluate the total radiant power incident on earth, at a distance frotm the sun-( when radius of earth is $r_0$)

• A. $4\pi r_0^2{R}^2\sigma T^4/r^2$
• B. $\pi r_0^2{R}^2\sigma T^4/r^2$
• C. $r_0^2{R}^2\sigma T^4/4\pi R^2$
• D. $R^2\sigma T^4/r^2$

Answer 1

The correct option is D $R^2\sigma T^4/r^2$

We know that,

$\frac{Energy}{Areaofenvelop}=\frac{\sigma T^4\times 4\pi R^2\times time}{4\pi R^2}$

Energy incident per unit area on earth $=\frac{\sigma T^4{R}^2\pi time}{r^2}$

$\therefore$ Power incident per unit area on Earth $=\left(\frac{R^2\sigma T^4}{r^2}\right)$

$\therefore$ Power incident on earth $={\pi r}_0^2\times \frac{R^2\sigma T^4}{r^2}$