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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2004

  • question_answer
    At which of the following temperature the root mean square velocity of gaseous hydrogen molecules will be equal to root mean square velocity of oxygen molecules at \[47{}^\circ C\]. ?

    A)  20 K          

    B)  80 K

    C)  - 73 K                                   

    D)  3 K

    Correct Answer: A

    Solution :

    \[{{c}_{rms}}=\sqrt{\frac{3RT}{M}}\] or            \[{{c}_{rms}}\propto \sqrt{\frac{T}{M}}\] \[\Rightarrow \]               \[\frac{{{T}_{1}}}{{{M}_{1}}}=\frac{{{T}_{2}}}{{{M}_{2}}}\] or            \[\frac{T}{{{M}_{{{H}_{2}}}}}=\frac{273+47}{{{M}_{{{O}_{2}}}}}\] or            \[\frac{T}{2}=\frac{320}{32}\] \[\Rightarrow \]               \[T=20K\]                                


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