JEE Main & Advanced Physics Kinetic Theory of Gases JEE PYQ-Kinetic Theory Of Gases

  • question_answer
    For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at \[127{}^\circ C.\] At 2 atm pressure and at\[~227{}^\circ C,\]the rms speed of the molecules will be :                                  [JEE Main 9-4-2019 Morning]

    A)  \[80\text{ }m/s\]           

    B)       100 5 m/s

    C)  \[80\sqrt{5}m/s\]          

    D)       \[100\text{ }m/s\]

    Correct Answer: B

    Solution :

    [b] \[{{V}_{rms}}=\sqrt{\frac{3RT}{{{M}_{\text{w}}}}}\Rightarrow {{\text{v}}_{rms}}\propto \sqrt{T}\]
    Now,\[\frac{\text{v}}{200}=\sqrt{\frac{500}{400}}\Rightarrow \frac{\text{v}}{200}=\frac{\sqrt{5}}{2}\]
    \[\Rightarrow \text{v}=100\sqrt{5}m/s\]
    Option [b]


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