question_answer

Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun.                                                                                    [AIEEE 2006]

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.