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

  • question_answer
    A cubical box with porous walls containing an equal number of \[{{O}_{2}}\] and \[{{H}_{2}}\] molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature T. The ratio of \[{{v}_{rms}}\]of \[{{O}_{2}}\]molecules to that of the \[{{v}_{rms}}\]of \[{{H}_{2}}\]molecules, found in the chamber outside the box after a short interval is                                   

    A)  \[\frac{1}{2\sqrt{2}}\]

    B) \[\frac{1}{4}\]

    C) \[\frac{1}{\sqrt{2}}\]

    D) \[\sqrt{2}\]

    Correct Answer: B

    Solution :

    [b] Temperature remain constant so
    \[{{v}_{rms}}\propto \frac{1}{\sqrt{M}}\]Þ \[\frac{{{v}_{{{O}_{2}}}}}{{{v}_{{{H}_{2}}}}}=\sqrt{\frac{{{M}_{{{H}_{2}}}}}{{{M}_{{{O}_{2}}}}}}=\sqrt{\frac{1}{16}}=\frac{1}{4}\]


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