If the temperature of the Sun were to increase from T to 2T and its radius from R to 2R. The rat io of power, radiated by it would become

Options

A. 4
B. 16
C. 32
D. 64

Answer

D

Explanation

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.