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  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 constant σ =5.7 × 1-8 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 constant $\sigma =5.7 \times 1^{-8} Wm ^{-2} K^{-4}$ 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 MainJEE Main 2014Thermodynamics

Solution:

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

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