Q. Assuming the sun to have a spherical outer surface of radius $r$, radiating like a black body at temperature $t℃,$ the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is Where $\sigma$ is the stefan’s constant.
A) $\frac{4\pi r^{2}\sigma t^{4}}{R^{2}}$
B) $\frac{r^{2}\sigma(t + 273)^{4}}{4\pi R^{2}}$
C) $\frac{16\pi^{2}r^{2}\sigma t^{4}}{R^{2}}$
D) $\frac{r^{2}\sigma(t + 273)^{4}}{R^{2}}$
Explanation
(d) From Stefan’s law, the rate at which energy is radiated by sun at its surface is
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$\ \ P = \sigma \times 4\pi r^{2}T^{4}$
(Sun is a perfectly black body as it emits radiations of all wavelengths and so for it $e$=1)
The intensity of this power at earth’s surface(under the assumption R>>$r_{0})$ is
$I = \frac{P}{4\pi R^{2}} = \frac{\sigma \times 4\pi r^{2}T^{4}}{4\pi R^{2}}$
$= \ \frac{\sigma r^{2}T^{4}}{R^{2}} = \frac{\sigma r^{2}(t + 273)^{4}}{R^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.