The surface temperature of the sun is `'T'K` and the solar constant for a plte is `'s'`. The sun subtends an angle `theta` at the planet. Then,

Options

A. `spropT^(4)`
B. `spropT^(2)`
C. `sproptheta^(2)`
D. `sproptheta`

Explanation

(a) Let radius of sun`=R`
Distance of earth from the sun`=d`
Power radiated from the sun `=(4piR^(2))sigmaT^(4)=P`
Energy receied /area/s`=S=P/(4pid^(2))`
`=4piR^(2)sigma(T^(4))/(4pid^(2))=sigmaT^(4)(R^(2))/(d^(2))=1/4 sigma T^(4)((2R)/d)^(2)`
Angle subtended by sun at earth `alpha=(2R)/d`
`S=` constant `xxT^(4)xxalpha^(2)`
`:. SpropT^(4)`