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

  • question_answer
    A black body radiates energy at the rate of 1 ´ 105 J / s ´m2 at temperature of 227o C. The temperature to which it must be heated so that it radiates energy at rate of  1 ´ 109J/sm2, is                                                         [DPMT 2004]

    A)            5000 K                                     

    B)            5000 oC

    C)            500 K                                       

    D)            500 oC

    Correct Answer: A

    Solution :

                       \[\frac{{{E}_{2}}}{{{E}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\] Þ \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{E}_{2}}}{{{E}_{1}}} \right)}^{1/4}}={{\left( \frac{{{10}^{9}}}{{{10}^{5}}} \right)}^{1/4}}=10\]            Þ \[{{T}_{2}}=10{{T}_{1}}=10\times (273+227)=5000\,K\]


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