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

Options

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

Answer

A

Explanation

Energy incident =`IpiR^(2) = 912 xx piR^(2)`

Energy emitted , assuming temp of the sphere at steady state to be `T,`
`sigma xx 4pi R^(2)(T^(4) - 300^(4))`
At quilibrium, `sigma xx 4pi R^(2)(T^(4) - 300^(4)) = 912 xx piR^(2)`
`implies T^(4) - 300^(4) = (912)/(5.7 xx 10^(-8) xx 4) = 40 xx 10^(8)`
`therefore T^(4) = (40+81) xx 10^(8)`
`therefore T = 331.66 approx 330K`