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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Critical Thinking

  • question_answer
    A Carnot engine whose low temperature reservoir is at 7°C has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees should the temperature of the high temperature reservoir be increased  [UPSEAT 2005]

    A)            840 K                                       

    B)            280 K

    C)            560 K                                       

    D)            380 K

    Correct Answer: D

    Solution :

                       Initially \[\eta =\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}}\]Þ \[0.5=\frac{{{T}_{1}}-(273+7)}{{{T}_{1}}}\]                    Þ        \[\frac{1}{2}=\frac{{{T}_{1}}-280}{{{T}_{1}}}\]Þ \[{{T}_{1}}=560K\]            Finally \[{{\eta }_{1}}'=\frac{{{T}_{1}}'\,-{{T}_{2}}}{{{T}_{1}}^{\prime }}\]Þ\[0.7=\frac{{{T}_{1}}'\,-\,(273+7)}{{{T}_{1}}^{\prime }}\]Þ\[{{T}_{1}}'=933K\] \ increase in temperature \[=933-560=373K\approx 380K\]


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