Question

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

Answer 1

`IxxpiR^(2)=4piR^(2)sigma(T^(4)-300^(4))`
`(912)/(4xx5.7)xx10^(9)+300^(4)=T^(4)`
`implies4xx10^(9)+8.1xx10^(9)=T^(4)`
`121xx10^(8)=T^(4)`
`sqrt(11)xx10^(2)=T`
`T=330K`