1. Tardigrade
  2. Question
  3. Physics
  4. 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-Boltzmann constant σ=5.7 × 10-8 Wm -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

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Q. 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-Boltzmann constant $\sigma=5.7 \times 10^{-8}\, Wm ^{-2} \,K ^{-4}$ 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

JEE AdvancedJEE Advanced 2014

Solution:

Rate of radiation energy lost by the sphere
$=$ Rate of radiation energy incident on it
$\Rightarrow \sigma \times 4 \pi r^{2}\left[T^{4}-(300)^{4}\right]=912 \times \pi r^{2} $
$\Rightarrow T=\sqrt{11} \times 10^{2} \approx 330 \,K$