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Assuming the sun to have a spherical out...

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.

A

`(r^2 sigma (t+ 273 )^4)/(4 pi R^2)`

B

`(16 pi^2 r^2 sigma t^4)/(R^2)`

C

`(r^2 sigma (t +273 )^4)/(R^2)`

D

`(4 pi r^2 sigma t^4 )/(R^2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Power P radiated by the sun with its surface temperature `( t + 273 )` is given by strfan .s Boltzmann law
`P = sigma e 4 pi r^2 (t + 273 )^4`
where r is the radius of the Sun and the Sun is treated as a black body where e=1 .
the radiant per uni area recived by the surface at a distance R from the centre of the sun is given by
` S =(P )/(4 pi R^2) = ( sigma 4 pi r^2 (t + 273 ) ^4 )/( 4 pi R^2) = (r^2 sigma (t + 273)^4)/( R^2)`
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