A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. 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

(4) `u = e sigma AT^(4) = e sigma 4 pi r^(2) T^(4)`
`u prop r^(2) T^(4)`
`(450)/(n') = ((r )/(r//2))^(2) ((2T)/(2T))^(4) = (1)/(4)`
`u' = 1800 W`