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(A) According to Wien's displacement law,$\lambda_m T = 	ext{constant}$.Given initial wavelength $\lambda_{m1} = \lambda_o$ and final wavelength $\la

Vedclass · Accepted Answer

$256/81$

Vedclass · Answer

(A) According to Wien's displacement law,$\lambda_m T = 	ext{constant}$.Given initial wavelength $\lambda_{m1} = \lambda_o$ and final wavelength $\lambda_{m2} = \frac{3\lambda_o}{4}$.Using the relation $\lambda_{m1} T_1 = \lambda_{m2} T_2$,we get $T_2 = \frac{\lambda_{m1}}{\lambda_{m2}} T_1 = \frac{\lambda_o}{3\lambda_o/4} T_1 = \frac{4}{3} T_1$.According to the Stefan-Boltzmann law,the power radiated $P$ is proportional to $T^4$,i.e.,$P \propto T^4$.Therefore,the ratio of the powers is $\frac{P_2}{P_1} = \left( \frac{T_2}{T_1} ight)^4$.Substituting the value of $T_2$,we get $\frac{P_2}{P_1} = \left( \frac{4/3 T_1}{T_1} ight)^4 = \left( \frac{4}{3} ight)^4 = \frac{256}{81}$.

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda_o$. The temperature of the black body is now changed such that the energy is maximum around a wavelength $\frac{3\lambda_o}{4}$. The power radiated by the black body will now increase by a factor of

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