Assuming the sun to have a spherical outer surface of radius `r` radiating like a black body at temperature `t^(@)C`. The power received by a unit surface (normal to the incident rays) at a distance `R` from the centre of the sun is
where `sigma` is the Stefan's constant.

Options

A. `(4 pi r^2 sigma t^4)/(R^2)`
B. `(r^2 sigma (t +273)^4)/(4 pi R^2)`
C. `(16pi^2r^2 sigma t^4)/(R^2)`
D. `(r^2 sigma (t+273)^4)/(R^2)`

Answer

D

Explanation

`P=sigma (t+273)^4 xx 4 pi r^2` [at `T=t^@C`]
Power received by a unit surface
`=(sigma(t+273)^4 4pi r^2)/(4 pi R^2)=(r^2 sigma(t+273)^4)/(R^2)`