Question
Assuming the sun to be a spherical body of radius $R$ at a temperature of $T \mathrm{~K}$. Evaluate the total radiant power, incident on earth, at a distance $r$ from the sun (A) $\frac{4 \pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}}$(B) $\frac{\pi r_{0}^{2} R^{2} \sigma T^{4}}{r^{2}}$(C) $\frac{r_{0}^{2} R^{2} \sigma T^{4}}{4 \pi r^{2}}$(D) $\frac{R^{2} \sigma T^{4}}{r^{2}}$where $r_{0}$ is the radius of the earth and $s$ is Stefan's constant.
Step 1
Step 1: The total power radiated by the sun is given by Stefan's law, which is $P = \sigma \cdot 4\pi R^{2} T^{4}$, where $\sigma$ is Stefan's constant, $R$ is the radius of the sun, and $T$ is the temperature of the sun. Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Assuming the sun to have a spherical outer surface of radius $r$ radiating like a black body at temperature $t^{\circ} \mathrm{C}$, the power received by a unit surface (normal to the incident rays) at a distance $R$ from the centre of the sun is ( $\sigma$ is stefan's constant) (a) $4 \pi r^{2} \sigma t^{4}$ (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) $\frac{r^{2} \sigma(1+273)^{4}}{R^{2}}$
Heat and Kinetic Theory of Gases
Round 1
(a) Determine the power of radiation from the Sun by noting that the intensity of the radiation at the distance of Earth is $1370 \mathrm{W} / \mathrm{m}^{2}$. Hint: That intensity will be found everywhere on a spherical surface with radius equal to that of Earth's orbit. (b) Assuming that the Sun's temperature is 5780 K and that its emissivity is 1, find its radius.
Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t°C. The power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is (o is the Stefan's constant.)
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD