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

Answer

C

Explanation

The sun is assumed to be a perfectly black body as it emits radiations of all wavelengths. Hence we can apply Stefan's law to its radiations
`orQ/t orP=sigmaAT^(4)=sigma*4pir^(2)T^(4)=sigma4pir^(2)(t+273)^(4)`
where T is the absolute temperature.
This is incident on the earth's surface. The earth is at a distance R from the centre of the sun.
`therefore` The solar energy is distributed over an area `4piR^(2)`
`therefore` Power received by unit area is given by
`thereforeP'=P/(4piR^(2))=(sigma*4pir^(2)(t+273)^(4))/(4piR^(2))`
`thereforeP'=sigma(r/R)^(2)*(t+273)^(4)`