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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According to Wein's law λ λ m T = constant
$\Rightarrow \lambda_{m_1} \mathrm{T}_1 = \lambda_{m_2} \mathrm{T}_2 \Rightarrow \mathrm{T}_2 = \frac{\lambda_{m_1}}{\lambda_{m_2}} \mathrm{T}_1 = \frac{\lambda_0}{3 \lambda_0 / 4} \times \mathrm{T}_1 = \frac{4}{3} \mathrm{T}_1$ Now $\mathrm{P} \propto \mathrm{T}^4 \Rightarrow \frac{\mathrm{P}_2}{\mathrm{P}_1} = \left(\frac{\mathrm{T}_2}{\mathrm{T}_1}\right)^4 \Rightarrow \frac{\mathrm{P}_2}{\mathrm{P}_1} = \left(\frac{4/3 \mathrm{T}_1}{\mathrm{T}_1}\right)^4 = \frac{256}{81}$
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