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

Options

A. `10^(4)`
B. 625
C. 256
D. 16

Answer

B

Explanation

According to stefan's law,the radiation energy emitted per second per unit area of a black body =`sigmaT^(4)`,where `sigma` is called stefen's constant.
Energy emitted `oo` `AT^(4)impliesEoo 4pir^(2)T^(4)`
Where A =area of the body,T=temprature in Kelvin when sun expands such that its radius becomes 100 times its present radius and its surface temprature becomes half.Then energy emitted by it is
`Eoo4pi(100)^(2)r^(2)((T)/(2))^(4)`.
`oo((100)/(4))^(2)E` total energy emitted will be increased by
`(E^(1))/(E)=(100//4^(2)E)/(E)=625`.