A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. What would be the power of radiation if radius were to be halved and the temperature is doubled ?

Answer

`[1800 W]`

Explanation

Here, `P_(1)=450 W, r_(1)=0.12m , T_(1)=500 K`,
`P_(2)= ?, r_(2)=(0.12//2)=0.06 m`,
`T_(2)=2xx500=1000 K`.
`P_(1)= A_(1)sigma T_(1)^(4)= 4 pi r_(1)^(2) sigma T_(1)^(4)`
`P_(2)= A_(2) sigma T_(2)^(4)= 4 pi r_(2)^(2) sigma T_(2)^(4)`
`(P_(2))/(P_(1))=(r_(2)^(2))(T_(2)^(4))/(r_(1)^(2)t_(1)^(4))`
or `P_(2)=P_(1)((r_(2))/(r_(1)^(2))) ((T_(2))/(T_(1)))^(4)`
`=450 ((0.06)/(0.12))^(2) ((1000)/(500))^(4) =1800 W`