JEE Main & Advanced Sample Paper JEE Main Sample Paper-39

  • question_answer
    A black body at a temperature of \[227{}^\circ C\]radiates heat at the rate of 20 cal \[{{m}^{-2}}\text{ }{{s}^{-1}}.\]When its temperature rises to \[727{}^\circ C\] the heat radiated will be

    A)  40 units                      

    B)  160 units

    C)  320 units                    

    D)  640 units

    Correct Answer: C

    Solution :

     Heat radiated by black body \[E=\sigma A{{T}^{4}}\Rightarrow E\alpha {{T}^{4}}\] \[or\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}\]or\[\frac{20}{{{E}_{2}}}={{\left( \frac{500}{1000} \right)}^{4}}={{\left( \frac{1}{2} \right)}^{4}}=\frac{1}{16}\] \[\Rightarrow \]\[{{E}_{2}}=16\times 20\,cal\,{{m}^{-2}}{{s}^{-1}}\]\[=320\,cal\,{{m}^{-2}}{{s}^{-1}}\]


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