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:

  1. (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}} $



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