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JCECE Engineering JCECE Engineering Solved Paper-2010

  • question_answer
    The molecules of a given mass of a gas have a \[\text{rms}\] velocity of \[200\,\,m/s\] at \[{{27}^{o}}C\] and \[1.0\times {{10}^{5}}\,\,N/{{m}^{2}}\]  pressure.  When  the temperature is \[{{127}^{o}}C\] and pressure is \[0.5\times {{10}^{5}}N/{{m}^{2}}\], the \[\text{rms}\] velocity in \[m/s\] will

    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 doesn't 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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