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JCECE Medical JCECE Medical Solved Paper-2010

  • question_answer
    The molecules of a given mass of a gas have a rms velocity of 200 m/s at \[27{{\,}^{o}}C\]and \[\text{1}\text{.0 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{5}}}\,\text{N/}{{\text{m}}^{\text{2}}}\]pressure.  When  the temperature is\[\text{127}{{\,}^{o}}\text{C}\] and pressure is \[0.5\times {{10}^{5}}N/{{m}^{2}},\] the rms velocity in m/s will   be

    A)  \[\frac{100\sqrt{2}}{3}\]

    B)  \[100\sqrt{2}\]

    C)  \[\frac{400}{\sqrt{3}}\]

    D)  None of these

    Correct Answer: C

    Solution :

     Rms velocity doesnt depend upon pressure, it depends upon temperature only ie \[{{v}_{rms}}\propto \sqrt{T}.\] \[\Rightarrow \]\[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\Rightarrow \frac{200}{{{v}_{2}}}=\sqrt{\frac{(273+27)}{(273+127)}}=\sqrt{\frac{300}{400}}\] \[\Rightarrow \] \[{{v}_{2}}=\frac{400}{\sqrt{3}}m/s\]


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