Parallel rays of light of intensity `I=912Wm^(-2)` are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan’s constant `sigma=5.7xx10^(-8)Wm^(-2)K^(-4)` and assume that the energy exchange with the surrounding is only through radiation. The final steady temperature of the black body is close to

Options

A. `330 K`
B. `660 K`
C. `990 K`
D. `1550 K`

Answer

A

Explanation

In steady state
`I piR^(2) = sigma (T^(4) -T_(0)^(4)) 4pi R^(2)`
`rArr I = sigma (T^(4)-T_(0)^(4)) 4 rArr T^(4) -T_(0)^(4) = 40 xx 10^(6)`
`rArr T^(4) - 81 xx 10^(8) xx 40 xx 10^(8) rArr T^(4) = 121 xx 10^(8)`
`rArr T ~~ 330 K`