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JEE Main 2006 (AIEEE) · Thermal Radiation: Black Body, Stefan & Wien

Thermal Radiation: Black Body, Stefan & Wien question from JEE Main 2006 (AIEEE)

Q102JEE Main 2006 · AIEEEMedium

Thermal Radiation: Black Body, Stefan & Wien

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $TK$ , evaluate the total radiant power incident on Earth at a distance $r$ from the Sun

Where r0 is the radius of the Earth and $\sigma$ is Stefan's constant.

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Answer: (b)

Power of the sun: $P = 4\pi R^2 \sigma T^4$ .
Intensity at distance $r$ : $I = \frac{P}{4\pi r^2} = \frac{R^2 \sigma T^4}{r^2}$ .
Earth intercepts this over its cross-section $\pi r_0^2$ .
$P_E = \pi r_0^2 R^2 \sigma \frac{T^4}{r^2}$ , so the answer is (b).

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