Question

If the temperature of the Sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$. The ratio of power radiated by it would become:

• A. $64$ times
• B. $16$ times
• C. $32$ times
• D. $4$ times

Answer 1

The correct option is A $64$ times

From Stefan's law, the energy radiated by sun is given by:-

$P=\sigma eA{T}^4$

In $Ist$ case:-

$P_1=\sigma e\times 4\pi R^2\times T^4$

In $2nd$ case:-

$P_2=\sigma e\times 4\pi (2R{)}^2\times (2T{)}^4$

Required ratio of power radiated $=\frac{P_2}{P_1}=\frac{\sigma e\times 4\pi (2R{)}^2\times (2T{)}^4}{\sigma e\times 4\pi R^2\times T^4}=64$

So, correct answer is $\left(A\right)$.