The emissivity of a perfect black body is increased to 16 times by increasing its temperature. If the…

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
  1. $4 \mathrm{~T}$
  2. $8 \mathrm{~T}$
  3. $2 \mathrm{~T}$
  4. $16 \mathrm{~T}$

Solution

According to Stefan's law, $\begin{aligned} & \mathrm{E}=\sigma \mathrm{T}^4 \\ & \frac{\mathrm{E}}{16 \mathrm{E}}=\frac{\sigma \mathrm{T}^4}{\sigma \mathrm{T}_2^4} \\ & \Rightarrow \mathrm{T}_2{ }^4=16 \mathrm{~T}^4 ; \mathrm{T}_2=2 \mathrm{~T} \end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 2)

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