JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer An engine has an efficiency of \[1/6\]. When the temperature of sink is reduced by \[{{62}^{o}}C,\] its efficiency is doubled. Temperatures of source and sink are

    A)  \[{{99}^{o}}C,{{37}^{o}}C\]          

    B)  \[{{124}^{o}}C,{{62}^{o}}C\]

    C)  \[{{37}^{o}}C,{{99}^{o}}C\]          

    D)  \[{{62}^{o}}C,{{124}^{o}}C\]

    Correct Answer: A

    Solution :

     From \[\eta =1-\frac{{{T}_{2}}}{{{T}_{1}}},\]\[\frac{{{T}_{2}}}{{{T}_{1}}}=1-\eta =1-\frac{1}{6}=\frac{5}{6}\] ?(i) In 2nd case: \[\frac{{{T}_{2}}-62}{{{T}_{1}}}=1-\eta '=1-\frac{2}{6}=\frac{2}{3}\]   ?(ii) Using (i), \[{{T}_{2}}-62=\frac{2}{3}{{T}_{1}}=\frac{2}{3}\times \frac{6}{5}{{T}_{2}}=\frac{4}{5}{{T}_{2}}\] or \[\frac{1}{5}{{T}_{2}}=62,\,{{T}_{2}}=310K=310K=310-273={{37}^{o}}C\] \[{{T}_{1}}=\frac{6}{5}{{T}_{2}}=\frac{6}{5}\times 310=372K=372-273={{99}^{o}}C\]

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