Assuming the sun to be a spherical body of radius R at a temperature of T,K, evaluate the total radiant power, incident on earth, at a distance r from the sun. (`r_(0)` is the radius of the earth and `sigma` is stefan's constant)

Options

A. `4pir_(0)^(2)R^(2)sigmaT^(4)//r^(2)`
B. `pir_(0)^(2)R^(2)sigmaT^(4)//r^(2)`
C. `r_(0)^(2)R^(2)sigmaT^(4)//4piR^(2)`
D. `R^(2)sigmaT^(4)//r^(2)`

Answer

B

Explanation

According to Stefan's law Power radiated by Sun =`sigma(4piR^(2))T^(4)`
Intensity of the sun received by the earth =`("Power of the sun")/(4pir^(2))`
I =`(sigma4piR^(2)T^(4))/(4pir^(2)) = (sigmaR^(2)T^(4))/(r^(2))`
Radiant power incident on the earth = `I(pir_(0)^(2))`
where (`pir_(0)^(2))` is the projection of the earth's area receiving the energy from the sun .
`P = (sigmaR^(2)T^(4))/(r^(2)) (pir_(0)^(2))`