Question

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature $t{}^{o}C,$ the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is

• 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. $\frac{r^2\sigma {(t+273)}^4}{R^2}$

Answer 1

Answer: (D)

From Stefan's law, the rate at which energy is radiated by sun at its surface is $P=\sigma \times 4\pi r^2{T}^4$
[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 $I=\frac{P}{4\pi R^2}$ $=\frac{\sigma \times 4\pi r^2{T}^4}{4\pi R^2}$ $=\frac{\sigma r^2{T}^4}{R^2}$ $=\frac{\sigma r^2{(t+273)}^4}{R^2}$

where $\sigma$ is the Stefan's constant.