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JEE Main & Advanced Physics Kinetic Theory of Gases Sample Paper Topic Test - Kinetic Theory of Gases

  • question_answer
    An adiabatic vessel contains \[{{n}_{1}}=3\] moles of a diatomic gas. The moment of inertia of each molecule is \[I=2.56\times {{10}^{-46}}\,kg\,\,{{m}^{2}}\] and root mean angular velocity is\[{{\omega }_{0}}=5\times {{10}^{12}}\,rad/s\]. The temperature of the gas in the vessel is

    A) 250 K

    B) 500 K

    C) 1000 K

    D) 1500 K

    Correct Answer: A

    Solution :

    [a]: Degree of freedom associated with rotational motion of diatomic gas molecules = 2
    Average rotational energy per molecule
    \[=l{{\omega }^{2}}_{rms}=2\times \frac{1}{2}kT=kT\]
    Hence initial temperature \[{{T}_{1}}\] of diatomic gas
    \[=\frac{1}{2}l\omega _{0}^{2}=k{{T}_{1}}\] which give \[{{T}_{1}}=250\,K\]


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