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. 450
B. 1000
C. 1800
D. 225

Answer

C

Explanation

According to Stefan-Boltzman law, rate of energy radiated by a black body is given as `E= sigma AT^(4) = sigma 4pi R^(2)T^(4)`
Given `E_(1) = 450W, T_(1) = 500K, R_(1) = 12cm`
`R_(2) = (R_(1))/(2), T_(2) = 2T_(1), E_(2)` = ?
`(E_(2))/(E_(1)) = (sigma 4pi R_(2)^(2)T_(2)^(4))/(sigma 4pi R_(1)^(2) T_(1)^(4)) = ((R_(2))/(R_(1)))^(2) ((T_(2))/(T_(1)))^(4) = (1)/(4) xx 16 = 4`
`E_(2) = E_(1) xx 4 = 450 xx 4= 1800W`