A sphere with diameter of `80cm` is held at a temperature of `250^(@)C` and is radiating en-ergy If the intensity of the radiation detected at a distance of `2.0m` from the sphere 's cnetre is `102 W//m^(2)` What is the emissivity of the shere ? .

Explanation

From inverse square law `I prop (1)/(r^(2))`
`(I_(2))/(I_(1)) =("Intensity on the surface of the shere")/("Intensity at a distance 2.0m from the centre") = (r_(1)^(2))/(r_(2)^(2))`
`:.I_(2)=I_(1)((r_(1)^(2))/(r_(2)^(2)))=102((2.0)/(0.4))^(2)=2.55xx10^(3)W//m^(2)`
The power at the surface of the sphere
`P =I_(2) (4 pi r_(2)^(2)) =2.55 xx 10^(3) xx 4 pi (0.4)^(2)` and
`P =e sigma AT^(4) (or) 2.55 xx 10^(3) xx 4 pi (0.4)^(2)` =
`e xx 5.57 xx 10^(-8) xx 4 pi (0.4)^(2) xx (523)^(4)`
`:. e = (2.55 xx 10^(3))/(5.67 xx 10^(-8) xx (523)^(4)) =0.61` .