JEE Main & Advanced AIEEE Solved Paper-2010

  • question_answer
      A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is-       AIEEE  Solved  Paper-2010

    A) 0.25                       

    B) 0.5                         

    C)        0.75       

    D)        0.99

    Correct Answer: C

    Solution :

    \[\eta =\left( 1-\frac{{{T}_{2}}}{{{T}_{1}}} \right)\] \[\because \]\[{{T}_{1}}V_{1}^{\gamma -1}={{T}_{2}}V_{2}^{\gamma -1}\] \[\therefore \]\[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}={{\left( \frac{1}{32} \right)}^{\gamma -1}}\] Putting \[\gamma =7\text{ }/\text{ }5\] \[\eta =\left( 1-\frac{1}{4} \right)=\frac{3}{4}=0.75\]


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