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

From Stefan's law, if the emissive power of a body at absolute temperature `T` be `e`, then the energy emitted by its unit area per second is `sigma T^4 xx e`, also if `A` is the surface area of the body, then
`E = sigma T^4 eA`
where `R' = 100 R and T' = (T)/(2)` then energy emitted is
`E' prop 4 pi (100 R)^2 ((T)/(2))^4`
`prop (100/4)^(2)xx4 pi R^(2)T^(4)`
`:. E' = ((100)/(4))^2 xx E`
`:. (E')/(E) = 625`.