Suppose the sun expands, so that its radius becomes 100 times its present radius and its surface temperature becomes half its present value. The total energy emitted by it will increases by a factor of :

Options

A. 16
B. 625
C. 256
D. 1000

Answer

B

Explanation

According to Stefan.s law, total energy radiated by sun per unit time is
`E=sigmaT^(4)A=sigmaT^(4).4piR^(2)`
`:.(E_(2))/(E_(1))=((T_(2))/(T_(1)))^(4).((R_(2))/(R_(1)))^(2)=(((T)/(2))/(T))^(4).((100)/(R))^(2)`
`=(1)/(16)xx1000`
`E_(2)=625E_(1)`
correct choice is (b).