RAJASTHAN PMT Rajasthan - PMT Solved Paper-2002

  • question_answer
    If a temperature of hot body is increased by 10%, then the increase in emitted radiation will be:

    A)  10%                      

    B)         40%

    C)  46%      

    D)         100%

    Correct Answer: C

    Solution :

                    Emitted radiation\[E\propto {{T}^{4}}\] \[\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}\]     \[\begin{align}   & ^{=}{{\left( \frac{T}{T+\frac{T\times 10}{100}} \right)}^{4}} \\  & ={{\left( \frac{10}{11} \right)}^{4}}=\frac{10000}{14641} \\ \end{align}\] Increase in emitted radiation \[\begin{align}   & =\frac{{{E}_{2}}-{{E}_{1}}}{{{E}_{1}}}\times 100 \\  & =\frac{14641-10000}{100}=46%\,(App) \\ \end{align}\]


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