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JEE Main & Advanced Physics Transmission of Heat Question Bank Radiation Stefan's law

  • question_answer
    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            [KCET 2002]

    A)             256/81                                    

    B)             64/27

    C)             16/9                                        

    D)             4/3 

    Correct Answer: A

    Solution :

                       According to Wein's law lmT = constant  Þ \[{{\lambda }_{{{m}_{1}}}}{{T}_{1}}={{\lambda }_{{{m}_{2}}}}{{T}_{2}}\Rightarrow {{T}_{2}}=\frac{{{\lambda }_{{{m}_{1}}}}}{{{\lambda }_{{{m}_{2}}}}}{{T}_{1}}=\frac{{{\lambda }_{0}}}{3{{\lambda }_{0}}/4}\times {{T}_{1}}=\frac{4}{3}{{T}_{1}}\]             Now \[P\propto {{T}^{4}}\Rightarrow \frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]Þ \[\frac{{{P}_{2}}}{{{P}_{1}}}={{\left( \frac{4/3\ {{T}_{1}}}{{{T}_{1}}} \right)}^{4}}=\frac{256}{81}\]


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