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

  • question_answer
    A body radiates energy \[5W\] at a temperature of  \[{{127}^{o}}C\]. If the temperature is increased to \[{{927}^{o}}C\], then it radiates energy at the rate of  [MP PET 1994;BHU 1995; CPMT 1998; AFMC 2000]

    A)            \[410W\]                               

    B)            \[81\ W\]

    C)            \[405\ W\]                            

    D)            \[200\ W\]

    Correct Answer: C

    Solution :

                       Rate of energy \[\frac{Q}{t}=P=A\varepsilon \sigma {{T}^{4}}\] Þ \[P\propto {{T}^{4}}\] Þ \[\frac{{{P}_{1}}}{{{P}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\]\[={{\left( \frac{927+273}{127+273} \right)}^{4}}\]\[\Rightarrow {{P}_{1}}=405\ W\]


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