Q: Assuming the sun to be a spherical body of radius R at a temperature ‘T’ K, evaluate the total radiant power incident on earth, at a distance r from the sun. (Take r_{0} is radius of earth ‘s’ Stefan’s constant)

(a) $ \displaystyle \frac{4\pi {r_0}^2 R^2 \sigma T^4}{r^2} $

(b) $ \displaystyle \frac{\pi {r_0}^2 R^2 \sigma T^4}{r^2} $

(c) $ \displaystyle \frac{4\pi {r_0}^2 R^2 \sigma T^4}{4\pi r^2} $

(d) $ \displaystyle \frac{ R^2 \sigma T^4}{r^2} $

Ans: (b)

Sol:

$ \displaystyle I = \frac{\sigma . 4\pi R^2 T^4}{4\pi r^2} $

$\displaystyle E = I. \pi r_0^2 = \frac{\pi r_0^2 R^2 \sigma T^4}{r^2} $