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Assuming the sun to be a spherical body of radius  R at the temperature  of TK, evaluate the total radiant power, incident on earth, at a distance r  from the sun .

 

Where r_{0}  is the radius of the earth and \sigma is Stefan's constant.

Option: 1

\frac{R^{2}\sigma T^{4}}{r^{2}}


Option: 2

\frac{4\pi r ^{2}_{0}R^{2}\sigma T^{4}}{r^{2}}


Option: 3

\frac{\pi r ^{2}_{0}R^{2}\sigma T^{4}}{r^{2}}


Option: 4

\frac{ r ^{2}_{0}R^{2}\sigma T^{4}}{4\pi r^{2}}


Answers (1)

best_answer

Total power radiated by sun =\sigma (4\pi R^{2}).T^{4}

Intensity of this radiation at a distance of r=\frac{\sigma.(4\pi R^{2}).T^{4}}{4\pi r^{2}}=\sigma T^{4} \left(\frac{R^{2}}{r^{2}} \right )

Amount of energy received on the earth =\sigma T^{4} \left(\frac{R}{r} \right )^{2}.\pi r_{0}^{2}

Correct option is 3.

Posted by

Kuldeep Maurya

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