A perfectly black body emits a radiation at temperature ' $\mathrm{T}_1$ ' $\mathrm{K}$. If it is to radiate…

A perfectly black body emits a radiation at temperature ' $\mathrm{T}_1$ ' $\mathrm{K}$. If it is to radiate at 16 times this power, its temperature ' $\mathrm{T}_2$ ' $\mathrm{K}$ should be
  1. $8 \mathrm{~T}_1$
  2. $4 \mathrm{~T}_1$
  3. $2 \mathrm{~T}_1$
  4. $16 \mathrm{~T}_1$

Solution

$\begin{aligned} & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4 \\ & \therefore 16=\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4 \\ & \therefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=2 \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

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