Q136 / 160 · AP EAMCET 2023 (15 May Shift 2) · Physics
The emissivity of a perfect black body is increased to 16 times by increasing its temperature. If the initial temperature is $\mathrm{T}$, then final temperature of that black body is
- A$4 \mathrm{~T}$
- B$8 \mathrm{~T}$
- Correct answerC$2 \mathrm{~T}$
- D$16 \mathrm{~T}$
Solution
According to Stefan's law,
$\begin{aligned}
& \mathrm{E}=\sigma \mathrm{T}^4 \\
& \frac{\mathrm{E}}{16 \mathrm{E}}=\frac{\sigma \mathrm{T}^4}{\sigma \mathrm{T}_2^4} \\
& \Rightarrow \mathrm{T}_2{ }^4=16 \mathrm{~T}^4 ; \mathrm{T}_2=2 \mathrm{~T}
\end{aligned}$
Hence, the correct answer is option: 'C'.