A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
(a)225 (b)450
(c) 900 (d)1800

Explanation

power radiated by black body is
`P=sigmae(4pir^(2))T^(4)`
`implies palphar^(2)T^(4)`
`implies (p_(1))/(p_(2))=(r^(2)T_(1)^(4))/(r_(2)^(2)T_(2)^(4))`
As `T_(2)=2T_(1)` and `r_(2)=(r_(1))/(2)`
`implies P_(2)=P_(1)xx4=450xx4=1800W`