A) \[4\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]
B) \[\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]
C) \[r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/4\pi {{r}^{2}}\]
D) \[{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}\]
Correct Answer: B
Solution :
[b] From Stefan's law, the rate at which energy is radiated by the sun at its surface is |
(sun is a perfectly black body as it emits radiations of all wavelengths and so for it ) |
The intensity of this power at the earth's surface (under the assumptionis |
The area of the earth which receives this energy is only one-half of total surface area of the earth, whose projection would be. |
Total radiant power as received by the earth |
where, % is the radius of the earth and a is Stefan's constant. |
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