Question

Parallel rays of light of intensity $I=912W{m}^{-2}$ are incident on a spherical black body kept in surroundings of temperature $300$ K. Take Stefan-Boltzmann constant $\sigma =5.7\times {10}^{-8}W{m}^{-2}{K}^{-4}$ and assume that the energy exchange with the surrounding is only through radiation. The final steady state temperature of the black body is close to :

• A. $330K$
• B. $660K$
• C. $990K$
• D. $1550K$

Answer 1

The correct option is A $330K$

Stefan's law,

$Q=\sigma A_{surface}(T_2^4-T_1^4)$

Also,

$I=\frac{Q}{A_{parallel}}$

Note here,

$A_{surface}=4\pi r^2$

$A_{parallel}=\pi r^2$

$\therefore \sigma \ast 4\pi r^2(T_2^4-T_1^4)=I\times \pi r^2$

$\therefore \sigma \ast 4(T_2^4-{300}^4)=912$

$\therefore T_2^4={1.21}^{10}$

$\therefore T_2=331.66K\approx 330K$