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MHT CET · Physics · Thermal Properties of Matter

A' black body radiates power ' \(P\) ' and maximum energy is radiated by it at a wavelength \(\lambda_0\). The temperature of the black body is now so changed that it radiates maximum energy at the wavelength \(\frac{\lambda_0}{4}\). The power radiated by it at new temperature is

  1. A 64 P
  2. B 256 P
  3. C 4 P
  4. D 16 P
Verified Solution

Answer & Solution

Correct Answer

(B) 256 P

Step-by-step Solution

Detailed explanation

According to Wien's displacement law,
\(\lambda_{\text {max }} \mathrm{T}=\) constant
\(\therefore \quad \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\lambda_{\max _2}}{\lambda_{\max _1}}=\frac{1 / 4 \lambda_0}{\lambda_0}=\frac{1}{4}\)
Power radiated for a blackbody, \(\mathrm{P}=\sigma \mathrm{AT}^4\)
\(\begin{aligned}
\therefore \quad \frac{\mathrm{P}_1}{\mathrm{P}_2} & =\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4=\left(\frac{1}{4}\right)^4=\frac{1}{256} \\
\mathrm{P}_2 & =256 \mathrm{P}_1=256 \mathrm{P}
\end{aligned}\)