A spherical black body of radius `r` radiates power `P`, and its rate of cooling is `R`
(i)`P prop r`
(ii)`P prop r^(2)`
(iii)`R prop r^(2)`
(iv)`R prop (1)/(r)`

Answer

D

Explanation

(4) `P = e sigma A (T^(4) - T_(0)^(4)) = e sigma . 4 pi r^(2) (T^(4) - T_(0)^(4))`
`P prop r^(2)`
`ms (dT)/(dt) = e sigma A (T^(4) - T_(0)^(4))`
`(dT)/(dt) = (e sigma A (T^(4) - T_(0)^(4)))/(ms) = (e sigma 4 pi r^(2) (T_(4) - T_(0)^(4)))/(rho . (4)/(3) pi r^(3) s`
Rate of cooling `R = ( = (dT)/(dt)) prop (1)/(r )`