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JEE Main & Advanced Chemistry States of Matter / पदार्थ की अवस्थाएँ - गैस एवं द्रव Question Bank Molecular speeds

  • question_answer
    Molecular velocities of the two gases at the same temperature are \[{{u}_{1}}\] and \[{{u}_{2}}\]. Their masses are \[{{m}_{1}}\] and \[{{m}_{2}}\] respectively. Which of the following expressions is correct [BHU 1994]

    A)                 \[\frac{{{m}_{1}}}{u_{1}^{2}}=\frac{{{m}_{2}}}{u_{2}^{2}}\]        

    B)                 \[{{m}_{1}}{{u}_{1}}={{m}_{2}}{{u}_{2}}\]

    C)                 \[\frac{{{m}_{1}}}{{{u}_{1}}}=\frac{{{m}_{2}}}{{{u}_{2}}}\]           

    D)                 \[{{m}_{1}}u_{1}^{2}={{m}_{2}}u_{2}^{2}\]

    Correct Answer: D

    Solution :

               \[\frac{{{U}_{1}}}{{{U}_{2}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}.\frac{{{T}_{1}}}{{{T}_{2}}}}\]              \[\because {{T}_{1}}={{T}_{2}}\]                                 \[\frac{{{U}_{1}}^{2}}{{{U}_{2}}^{2}}=\frac{{{m}_{2}}}{{{m}_{1}}}\]          \[\therefore {{m}_{1}}{{U}_{1}}^{2}={{m}_{2}}{{U}_{2}}^{2}\]


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