Question

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

• A. ${10}^4$
• B. 625
• C. 256
• D. 16

Answer 1

The correct option is B 625

$Q=\sigma AT4=\sigma \times \pi r^2\times T4$

$Q^{\prime }\Rightarrow \sigma \times (\pi \times (1000{)}^2)\times {\left(\frac{T}{2}\right)}^4$

$Q^{\prime }=\sigma \times \pi r^2\frac{\left(10000\right)}{16}\times T^4$

$Q^{\prime }=Q\times (25\times 25)$

$Q^{\prime }=\left(625\right)$ times $Q$