A' black body radiates power ' $P$ ' and maximum energy is radiated by it at a wavelength $\lambda_0$. The…
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
64 P
256 P
4 P
16 P
Solution
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, $\mathrm{P}=\sigma \mathrm{AT}^4$
$\begin{aligned}
\therefore \quad \frac{\mathrm{P}_1}{\mathrm{P}_2} & =\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4=\left(\frac{1}{4}\right)^4=\frac{1}{256} \\
\mathrm{P}_2 & =256 \mathrm{P}_1=256 \mathrm{P}
\end{aligned}$