Uttarakhand PMT Uttarakhand PMT Solved Paper-2011

  • question_answer
    The rms velocity of\[C{{O}_{2}}\]at a temperature T (in K) is\[x\text{ }cm\text{ }{{s}^{-1}}\]. At what temperature (in K) the rms velocity of nitrous oxide would be\[4x\text{ }cm{{s}^{-1}}\]?

    A)  16 T             

    B)  2T

    C)  4T              

    D)  32 T

    Correct Answer: A

    Solution :

     \[U=\sqrt{\frac{3RT}{M}}\] \[\frac{{{U}_{C{{O}_{2}}}}}{{{U}_{{{N}_{2}}O}}}=\sqrt{\frac{{{T}_{C{{O}_{2}}}}\times {{M}_{{{N}_{2}}O}}}{{{M}_{C{{O}_{2}}}}\times {{T}_{{{N}_{2}}O}}}}\] \[\frac{x}{4x}=\sqrt{\frac{T\times 44}{44\times {{T}_{N{{O}_{2}}}}}}\] \[\frac{1}{4}=\sqrt{\frac{T}{{{T}_{N{{O}_{2}}}}}}\] \[{{T}_{{{N}_{2}}O}}=16T\]


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