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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 36

  • question_answer
    One mole of an ideal gas undergoes a reversible Carnot cycle with \[{{V}_{1}}=20L,\]\[{{V}_{2}}=40L,\] and \[{{T}_{1}}=300K\]. Let \[{{T}_{2}}=200K,\]\[{{C}_{v.m}}=(3/2)R.\] \[\Delta U\]and \[\Delta V\] for adiabatic reversible compression are, respectively,

    A) \[\Delta U=150\,RJ\,mo{{l}^{-1}},\]      \[\Delta V=20\left[ 1-{{\left( \frac{3}{2} \right)}^{1.5}} \right]L\]

    B) \[\Delta U=0,\,\,\Delta V=-20{{\left( \frac{3}{2} \right)}^{1.5}}L\]

    C) \[\Delta U=-150RJ\,mo{{l}^{-1}},\,\,\Delta V=-20\,{{\left( \frac{3}{2} \right)}^{1.5}}L\]

    D) \[\Delta U=0,\,\Delta V=20\left[ 1-{{\left( \frac{3}{2} \right)}^{1.5}} \right]L\]

    Correct Answer: A

    Solution :

    [a] Adiabatic reversible compression: \[\Delta T=({{T}_{1}}-{{T}_{2}})=100K\]             \[\Delta U={{C}_{v,m}}({{T}_{1}}-{{T}_{2}})=\frac{3}{2}R(100K)\]             \[=150\,R\,J\,mo{{l}^{-1}}\]             \[\Delta V={{V}_{1}}\left[ 1-{{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{Cv,m/R}} \right]\]             \[=20L\left[ 1-{{\left( \frac{300}{200} \right)}^{3/2}} \right]\]             \[=-16.74L\]


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