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A point source of light of power P 0 is placed at a distance of 4 m from the centre of a thin hemispherical shell as shown in the figure, The shell has a radius of 3 m and it behaves like a perfect black body. If the temperature of the hemisphere is related to the power of the source as T 4 = P 0 n π σ ' where σ is the Stefan's constant, then find the value of n 10 .

Correct answer

27

Step-by-step solution

Total power emitted by shell due to radiation P out = σ 2 π R 2 + π R 2 T 4 = 3 π R 2 σ T 4 Power gained by the shell from P 0 : P in = P 0 2 π r 2 ( 1 - cos ⁡ 37 ° ) 4 π r 2 = P 0 10 Equating: P 0 10 = 3 π R 2 σ T 4 Gives T 4 = P 0 270 π σ n = 270 10 = 27

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