Suppose that the sun expands, so that its diameter becomes 10 times its present diameter and its surface temperature becomes half of its present value. Then the total energy emitted by the sun per unit time, will increase by a factor of

Options

A. 4.25
B. 5.25
C. 6.25
D. 7.25

Answer

C

Explanation

The total energy emitted by the sun per unit time is
`Q=sigmaAT^(4)=sigma*4piR^(2)T^(4)`
`thereforeQ_(2)/Q_(1)=(R_(2)/R_(1))^(2)xx(T_(2)/T_(1))^(4)`
`=(10)^(2)xx(1/2)^(4)=100xx1/16`
`thereforeQ_(2)/Q_(1)=6.25`