Assuming the Sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant powered incident of Earth at a distance r from the sun
where `r_0` is the radius of the Earth and `sigma` is Stefan's constant.

Options

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

Answer

D

Explanation

Energy radiated by sun per unit time `=sigmaT^(4)xx4piR^(2)`
`rArr` Energy received per unit time per unit area on earth
`=(sigmaT^(4)xx4piR^(2))/(4pir^(2))=(sigmaT^(4)xxR^(2))/(r^(2))`
[ Here `pir_(0)^(2)` is the projected area of earth that receives this power]