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JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    The molecules of a given mass of a gas have r.m.s. velocity of \[200\text{ }m{{s}^{-1}}\]at \[27{}^\circ C\] and \[1.0\times {{10}^{5}}\text{ }N{{m}^{-2}}\] pressure. When the temperature and pressure of the gas are respectively, \[127{}^\circ C\]and \[0.05\times {{10}^{5}}\text{ }N{{m}^{-2}},\]the r.m.s. velocity of its  molecules

    A) \[100\sqrt{2}\]   

    B)        \[\frac{400}{\sqrt{3}}\]

    C) \[\frac{100\sqrt{2}}{3}\]

    D)        \[\frac{100}{3}\]

    Correct Answer: B

    Solution :

    [b] Here \[{{v}_{1}}=200\text{ }m/s;\] temperature \[{{T}_{1}}=27{}^\circ C=27+273=300k\] temperature \[{{T}_{2}}=127{}^\circ C=127+273=400k,\] V=? R.M.S. Velocity, \[V\propto \sqrt{T}\] \[\Rightarrow \frac{v}{200}=\sqrt{\frac{400}{300}}\Rightarrow v=\frac{400}{\sqrt{3}}m/s\]


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