MHT CET · Physics · Thermal Properties of Matter
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
- A \(8 \mathrm{~T}_1\)
- B \(4 \mathrm{~T}_1\)
- C \(2 \mathrm{~T}_1\)
- D \(16 \mathrm{~T}_1\)
Answer & Solution
Correct Answer
(C) \(2 \mathrm{~T}_1\)
Step-by-step Solution
Detailed explanation
\( \begin{aligned} & \frac{\mathrm{P}_2}{\mathrm{P}_1}=\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4 \\ & \therefore 16=\left(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\right)^4 \\ & \therefore \frac{\mathrm{T}_2}{\mathrm{~T}_1}=2 \end{aligned} \)
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