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If the temperature of the sun were to in...

If the temperature of the sun were to increase form T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be

A

4

B

16

C

32

D

64

Text Solution

Verified by Experts

The correct Answer is:
D
From Stefan’s law, the energy radiated by sun is given by `P=sigmaeAT^(4)`.
`"In "1^(st)"case", " " P_(1)=sigmaexx4piR^(2)xxT^(4)`
`"In "2^(nd) "case", " "P_(2)sigmaexx4pi(2R)^(2)xx(2T)^(4)`
`=sigma exx4piR^(2)xxT^(4)xx64=64P_(1)`
The rate at which energy received at earth is : `E=(P)/(4piR_(S)^(2))xxA_(E)`
Where , `A_(E)=` area of earth and `R_("SE")=` distance between sun and earth
So , `"In" 1^(st)` case .
`E_(1)=(P_(1))/(4piR_(SE)^(2))xxA_(E),E_(2)=(P_(2))/(4piR_(SE)^(2))xxA_(E)=64E_(1)`. Hence , ratio is 64.
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