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

Answer

D

Explanation

From Stefan's law, the rate at which energy is radiated by Sun at its surface ( under the assumption ` R gt gt r _ 0 ) ` is
` I = ( P ) /( 4pi R ^ 2 ) = (sigma xx 4pi r ^ 2 T ^ 4 )/( 4pi R ^ 2 ) = ( sigma r ^ 2 T ^ 4 ) /( R^ 2 ) `
` = (sigma r ^ 2 ( t + 273 ) ^ 4 )/(R^ 2 ) `