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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2009

  • question_answer
    A black body at a temperature of \[227{}^\circ C\] radiates heat at the rate of 5 \[c{{m}^{-2}}{{s}^{-1}}.\] temperature of \[727{}^\circ C\] the rate of heat radiated per unit area in cal \[c{{m}^{-2}}{{s}^{-1}}\] is

    A)  400                                       

    B)  80

    C)  40                                         

    D)  15

    Correct Answer: B

    Solution :

    According to Stefan's law radiant energy emitted by a perfectly black body per unit area per sec (.ie, emissive power of black body) is directly proportional to the fourth power of its absolute temperature ie, \[E\propto {{T}^{4}}\] \[\Rightarrow \]               \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}\]                 \[\frac{5}{{{E}_{2}}}=\frac{{{(273+227)}^{4}}}{{{(273+727)}^{4}}}\] \[\Rightarrow \]               \[{{E}_{2}}=5\times {{\left[ \frac{1000}{500} \right]}^{4}}\]                 \[=5\times 16=80\,cal\,c{{m}^{-2}}\,{{s}^{-1}}\]


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