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

  • question_answer
    An object is at a temperature of \[{{400}^{o}}C\]. At what temperature would it radiate energy twice as fast?  The temperature of the surroundings may be assumed to be negligible         [MP PMT 1990; DPMT 2002]

    A)            \[{{200}^{o}}C\]                  

    B)            \[200\ K\]

    C)            \[{{800}^{o}}C\]                  

    D)            800 K

    Correct Answer: D

    Solution :

               \[\frac{{{E}_{2}}}{{{E}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{4}}\]Þ \[\frac{2}{1}={{\left( \frac{420+273}{T} \right)}^{4}}\]\[={{\left( \frac{673}{T} \right)}^{4}}\] Þ \[T={{2}^{1/4}}\times 673\] = 800K.


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