Discussion Forum

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 constant   $\sigma=5.7\times 10^{-8}W m^{-2}K^{-4}$  and assume that the energy exchange with surrounds is only through radiation. The  final steady-state temperature of the black body is close to 

Answer:

Explanation:

In steady-state

Energy incident per second = Energy radiated per second

 $\therefore $     $ I\pi R^{2}=\sigma(T^{4}-T_{0}^{4})4$

 $\Rightarrow$          $ I=\sigma(T^{4}-T_{0}^{4})4$

 $\Rightarrow$             $T^{4}-T_{0}^{4}=40\times 10^{8}$

$\Rightarrow$        $T^{4}-81\times 10^{8}=40\times 10^{8}$

$\Rightarrow$          $T^{4}=121\times 10^{8}$

$\Rightarrow$              T=330K