Thermal Properties of Matter - Result Question 29
30. Assuming the sun to have a spherical outer surface of radius $r$, radiating like a black body at temperature $t^{\circ} C$, the power received by a unit surface, (normal to the incident rays) at a distance $R$ from the centre of the sun is [2007]
(a) $\frac{r^{2} \sigma(t+273)^{4}}{4 \pi R^{2}}$
(b) $\frac{16 \pi^{2} r^{2} \sigma t^{4}}{R^{2}}$
(c) $\frac{r^{2} \sigma(t+273)^{4}}{R^{2}}$
(d) $\frac{4 \pi r^{2} \sigma t}{R^{2}}$
where $\sigma$ is the Stefan’s constant.
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Answer:
Correct Answer: 30. (c)
Solution:
- (c) Power radiated by the sun at $t^{\circ} C$
$ =\sigma(t+273)^{4} 4 \pi r^{2} $
Power received by a unit surface
$ =\frac{\sigma(t+273)^{4} 4 \pi r^{2}}{4 \pi R^{2}}=\frac{r^{2} \sigma(t+273)^{4}}{R^{2}} $
