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

Answer

C

Explanation

Power radiated by the sun at `t^(@)C=sigma(t+273)^(4)4pi r^(2)`
Power received by a unit surface
`=(sigma(t+273)^(4)4pi r^(2))/(4pi R^(2))=(r^(2)sigma(t+273)^(4))/(R^(2))`