JEE Main & Advanced Physics Transmission of Heat Question Bank Radiation General Kirchoff's law Black body

  • question_answer
    If between wavelength \[\lambda \]and \[\lambda +d\lambda \], \[{{e}_{\lambda }}\]and \[{{a}_{\lambda }}\] be the emissive and absorptive powers of a body and \[{{E}_{\lambda }}\] be the emissive power of a perfectly black body, then according to Kirchoff's law, which is true                                     [RPMT 1998; MP PET 1991]

    A)            \[{{e}_{\lambda }}={{a}_{\lambda }}={{E}_{\lambda }}\]    

    B)            \[{{e}_{\lambda }}{{E}_{\lambda }}={{a}_{\lambda }}\]

    C)            \[{{e}_{\lambda }}={{a}_{\lambda }}{{E}_{\lambda }}\]      

    D)            \[{{e}_{\lambda }}{{a}_{\lambda }}{{E}_{\lambda }}\]= constant

    Correct Answer: C

    Solution :

                       According to Kirchoff?s law, the ratio of emissive power to absorptive power is same for all bodies is equal to the emissive power of a perfectly black body i.e.,                    \[{{\left( \frac{e}{a} \right)}_{body}}={{E}_{\text{Black}\,\text{body}}}\] for a particular wave length            \[{{\left( \frac{{{e}_{\lambda }}}{{{a}_{\lambda }}} \right)}_{\text{body}}}={{({{E}_{\lambda }})}_{\text{Black}\,\text{body}}}\] Þ \[{{e}_{\lambda }}={{a}_{\lambda }}{{E}_{\lambda }}\]


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