Q115 / 200 · NEET 2012 (Screening) · Physics
If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q$ ?
( $\sigma$ stands for Stefan's constant.)
- A$Q / 4 \pi R^2 \sigma$
- B$\left(\mathrm{Q} / 4 \pi \mathrm{R}^2 \sigma\right)^{-1 / 2}$
- C$\left(4 \pi R^2 Q / \sigma\right)^{1 / 4}$
- Correct answerD$\left(Q / 4 \pi R^2 \sigma\right)^{1 / 4}$
Solution
From Stefan' law,
$E=\sigma T^4$
So, the rate energy production
$\begin{aligned}
& Q=E \times A \\
& Q=\sigma T^4 \times 4 \pi R^2
\end{aligned}$
Temperature of star
$T=\left(\frac{Q}{4 \pi R^2 \sigma}\right)^{1 / 4}$
Hence, the correct answer is option: 'D'.