Question

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:

• A. $10^4$
• B. 625
• C. 256
• D. 16

Answer 1

Answer: (B)

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 $\sigma T^4 \times e$, also if $A$ is the surface area of the body, then
$E=\sigma T^4 e A$
when $R^{\prime}=100 R$ and $T^{\prime}=\frac{T}{2}$ then energy emitted is
$E^{\prime} \propto 4 \pi(100 R)^2\left(\frac{T}{2}\right)^4 $
$ \propto\left(\frac{100}{4}\right)^2 \times 4 \pi R^2 T^4$
$\therefore E^{\prime}=\left(\frac{100}{4}\right)^2 \times E $
$ \therefore \frac{E^{\prime}}{E}=625 $