Question

Parallel rays of light of intensity I=912 Wm${}^{-2}$ are incident on a spherical black body kept in surroundings of temperature 300 K . Take Stefan constant $\sigma =5.7\times 1^{-8}W{m}^{-2}{K}^{-4}$ 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. 330 K
• B. 660 K
• C. 990 K
• D. 1550 K

Answer 1

Answer: (A)

In steady state
Energy incident per second = Energy radiated per second
$\therefore I\pi R^2=\sigma (T^4-T_0^4)4\pi R^2\Rightarrow i=\sigma (T^4-T_0^4)4$
$\Rightarrow T^4-T_0^4=40\times 10^8\Rightarrow T^4-81\times 10^8=40\times 1^8$
$\Rightarrow T^4=121\times 10^8\Rightarrow T=330K$