JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Topic Test - Kinetic Theory Of Gases-2

  • question_answer
    A gaseous mixture contains equal number of hydrogen and nitrogen molecules. Specific heat measurements on this mixture at temperatures below 100 K would indicate that the value of \[\gamma \] (ratio of specific heats) for this mixture is

    A) 3/2

    B) 4/3

    C) 5/3

    D) 7/5

    Correct Answer: C

    Solution :

    [c] Below 100 K only translational degree of freedom is considered. Hence \[{{\gamma }_{mixture}}=\frac{\frac{{{\mu }_{1}}{{\gamma }_{1}}}{{{\gamma }_{1}}-1}+\frac{{{\mu }_{2}}{{\gamma }_{2}}}{{{\gamma }_{2}}-1}}{\frac{{{\mu }_{1}}}{{{\gamma }_{1}}-1}+\frac{{{\mu }_{2}}}{{{\gamma }_{2}}-1}}\] according to question, \[{{\mu }_{1}}={{\mu }_{2}}\] and \[{{\gamma }_{1}}={{\gamma }_{2}}\]\[=1+\frac{2}{3}=\frac{5}{3}\]
    \[\Rightarrow {{\gamma }_{mix}}={{\gamma }_{1}}=\frac{5}{3}\]


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