Transmission Of Heat Question 348
Question: Assuming the sun to be a spherical body of radius R at a temperature of TK, evaluate the total radiant power, incident on earth, at a distance from the sun. Where r0 is the radius of the earth and a is Stefans constant.
Options:
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} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] From Stefans law, the rate at which energy is radiated by sun at its surface is (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 earths 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}} $ The area of earth which receives this energy is only one-half of total surface area of earth, whose projection would be $ \pi r _{0}^{2} $ . \ Total radiant power as received by earth$ =,\pi r _{0}^{2}\times ,1 $ $ =\frac{\pi r _{0}^{2}\times ,\sigma R^{2}T^{4}}{r^{2}},=,\frac{\pi r _{0}^{2}R^{2},\sigma T^{4}}{r^{2}} $
BETA
