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

Options

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

Answer

D

Explanation

Radiated power by blackbody `P = Q/t = A sigma T^(4)`
`rArr P prop AT^(4) prop r^(2)T^(4) rArr (P_1)/(P_2) = ((r_1)/(r_2))^(2)((T_1)/(T_2))^(4)`
`rArr (440)/(P_2) = (12/6)^(2) (500/1000)^(4)`
`rArr P_(2) = 1760W = 1800W`.