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

Answer

A

Explanation

From Stefan's law, it the emissive power of a body at absoulte temperature `T` be `e`, then the energy emitted by its unit area per second is `sigmaT^(4) xx e` also if `A` is the surface area of the body. Then
`E = sigma T^(4)eA`
When `R' = 100 R` and `T' = T//2` then energy emitted is
`E' prop 4pi (100R)^(2) ((T)/(2))^(4)`
`rArr E' prop (100/4)^(4) xx 4 pi R^(4)T^(4)`
`:. E' = (100/4)^(4) xx E rArr (E')/(E)=625`.