JEE Main & Advanced Physics Transmission of Heat Question Bank Graphical Questions

  • question_answer
    The adjoining diagram shows the spectral energy density distribution \[{{E}_{\lambda }}\]of a black body at two different temperatures. If the areas under the curves are in the ratio 16 : 1, the value of temperature T is            [DCE 1999]

    A)            32,000 K

    B)            16,000 K

    C)            8,000 K

    D)            4,000 K

    Correct Answer: D

    Solution :

                       \[\frac{{{A}_{T}}}{{{A}_{2000}}}=\frac{16}{1}\]        (given)                    Area under \[{{e}_{\lambda }}-\lambda \] curve represents the emissive power of body and emissive power \[\propto {{T}^{4}}\]                    (Hence area under  \[{{e}_{\lambda }}-\lambda \] curve) \[\propto {{T}^{4}}\]            Þ\[\frac{AT}{{{A}_{2000}}}={{\left( \frac{T}{2000} \right)}^{4}}\]Þ \[\frac{16}{1}={{\left( \frac{T}{2000} \right)}^{4}}\]Þ \[T=4000K.\]


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