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

Options

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

Answer

D

Explanation

The energy radiated per second by a black body is given by Stefan’s law,
`(E)/(t)=sigmaT^(4)xxA` Where A is the surface area of the black body
`(E)/(t)=sigmaT^(4)xx4pir^(2)`
Since black body is sphere, `A=4pir^(2)`
Case (i) `(E)/(t)=450,T=500K,r=0.12m`,
`therefore450=4pisigma(500)^(4)(0.12)^(2)` ... (i)
Case (ii) `(E)/(t)=?T=1000K,r=0.06m` ... (ii)
Dividing Equation. (ii) by Equation.(i), we get :
`(E//t)/(450)=((1000)^(4)(0.06)^(2))/((500)^(4)(0.12)^(2))=(2^(4))/(2^(2))=4rArr(E)/(t)=450xx4=1800W`