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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    One mole of an ideal gas undergoes a reversible Carnot cycle with \[{{V}_{1}}=10L,\], \[{{V}_{2}}=20L\] and \[{{T}_{1}}=400K,\] Let \[{{T}_{2}}=300K,\]\[{{C}_{v,m}}=(3/2)R\,\,\Delta H\] and \[\Delta V\]for isothermal reversible compression are respectively,

    A) \[\Delta H=0,\,\Delta V=10\left[ 1-{{\left( \frac{4}{3} \right)}^{3/2}} \right]\]

    B) \[\Delta H=250\,\,RJ\,\,mo{{l}^{-1}},\,\Delta V=-10{{\left( \frac{3}{4} \right)}^{3/2}}\]

    C) \[\Delta H=0,\,\,\Delta V=-10{{\left( \frac{4}{3} \right)}^{3/2}}\]

    D) \[\Delta H=-250\,RJ\,mo{{l}^{-1}},\,\Delta V=10\left[ 1-{{\left( \frac{3}{4} \right)}^{3/2}} \right]\]

    Correct Answer: C

    Solution :

    [c] Isothermal reversible compression \[\Delta T=0,\] \[\Delta U=0,\] \[\Delta H=0\] \[\Delta V={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{{{C}_{v,m/R}}}}({{V}_{1}}-{{V}_{2}})\] \[={{\left( \frac{400}{300} \right)}^{3/2}}(-10L)=-10{{\left( \frac{4}{3} \right)}^{3/2}}\]


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