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JEE Main & Advanced Physics Transmission of Heat Sample Paper Topic Test - Transmission Of Heat

  • question_answer
    The energy spectrum of a black body exhibits a maximum around a wavelength \[{{\lambda }_{0}}\]. The temperature of the black body is now changed such that the energy is maximum around a wavelength \[3{{\lambda }_{0}}/4\]. The power radiated by the black body will now increase by a factor of

    A) 256/81

    B) 64/27

    C) 16/9

    D) 4/3

    Correct Answer: A

    Solution :

    [a] According to Wien's law, wavelength corresponding to maximum energy decreases. When the temperature of black body increases, i.e., \[{{\lambda }_{m}}T\] constant, \[\Rightarrow \]       \[\frac{{{T}_{2}}}{{{T}_{1}}}=\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{{{\lambda }_{0}}}{3{{\lambda }_{0}}/4}=\frac{4}{3}\]. Now according to Stefan's law, \[\frac{{{E}_{2}}}{{{E}_{1}}}\,={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}={{\left( \frac{4}{3} \right)}^{4}}=\frac{256}{81}\]


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