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Assuming the sun to have a spherical outer surface of radius r

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t⁰C, the power received by a unit surface, (normal to the inicident rays) at a distance R from the centre of the sun is

Options

(a) r²σ (t + 273)⁴ / 4πR²
(b) 16 π²r² σt⁴ / R²
(c) r²σ (t + 273)⁴ / R²
(d) 4 πr² σt⁴ / R²

Correct Answer:

r²σ (t + 273)⁴ / R²

Explanation:

Power radiated by the sun at tC
= σ (t + 273)⁴ 4πr²
Power received by a unit surface
σ (t + 273)⁴ 4πr² / 4πR²
r²σ (t + 273)⁴ / R²

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