(D) According to $Wien's$ displacement law,$\lambda_{\max} T = \text{constant}$.Let the initial temperature be $T$ and the final temperature be $T'$.G

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(D) According to $Wien's$ displacement law,$\lambda_{\max} T = \text{constant}$.Let the initial temperature be $T$ and the final temperature be $T'$.Given $\lambda_{\max, 1} = \lambda_0$ and $\lambda_{\max, 2} = \frac{3}{4}\lambda_0$.Using the law: $\lambda_0 T = \left(\frac{3}{4}\lambda_0\right) T' \Rightarrow T' = \frac{4}{3}T$.According to the $Stefan-Boltzmann$ law,the power radiated by a black body is $P = A \sigma T^4$,which implies $P \propto T^4$.Therefore,$\frac{P_2}{P_1} = \left(\frac{T'}{T}\right)^4$.Substituting the values: $n = \left(\frac{4/3 T}{T}\right)^4 = \left(\frac{4}{3}\right)^4 = \frac{256}{81}$.

Class 11 Physics 2 Thermal Properties of Matter: Heat Transfer Radiation by Stefan's Boltzmann Law

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The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is

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A
$\frac{3}{4}$
B
$\frac{4}{3}$
C
$\frac{81}{256}$
D
$\frac{256}{81}$

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2 Thermal Properties of Matter: Heat Transfer

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Radiation by Stefan's Boltzmann Law

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The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is

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$A$ black metal foil is kept at a distance $d$ from a circular heater. The power absorbed by the foil is $P$. If the temperature of the heater and the distance are both doubled,the power absorbed by the foil will be ..... $P$.

Find the emissive power from the $0.3 \, cm^2$ surface of a tungsten filament bulb at $3000 \, K$ temperature. Take emissivity $e = 0.4$ for the tungsten bulb. (in $, W$)

Two spheres $S_{1}$ and $S_{2}$ have radii $R$ and $3R$ and temperatures $T$ and $T/3$ respectively. If they are coated with a material of the same emissivity, and the rate of radiation of $S_{1}$ is $E$, then the rate of radiation of $S_{2}$ is:

$A$ body radiates energy at a rate of $5 \ W$ at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then it radiates energy at the rate of ...... $W$.

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