A spherical black body with a radius of 12cm radiates 450W power at 500K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Options

A. `225`
B. `450`
C. `900`
D. `1800`

Answer

D

Explanation

(d) The energy radiated per second by a black body is
given by Stefan's Law
`E/t=sigmaT^4xxA,` Where A is the surface area.
`E/t=sigmaT^4xx4pir^2 (:' For a sphare, A=4pir^2)`
Case (i) : `E/t=450, T=500K,r=0.12m`
`:. 450=4pisigma(500)^4(0.12)^2.....(i)`
Case (ii): `E/t=?, T=1000k,r=0.06m`
`:. E/t=4pisigma(1000)^4(0.06)^2.....(ii)`
Dividing (ii) and (i), we get
`(E//t)/450=((1000)^4(0.06)^2)/((500)^4(0.12)^2)=2^4/2^2=4`
`rArrE/t=450xx4=1800W`