A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are)

Engineering

Physics

Displacement and Pressure Wave Equation of Sound

Question

The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6 / 5}$

The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2

The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/ $\sqrt{2}$

The average energy per mole of the gas mixture is 2RT

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Average energy per mole of mixture

$= \frac{(\frac{3}{2} RT + \frac{5}{2} RT)}{2} = \frac{8 RT}{4} =2RT$

$C_{v_{1} mix} = (\frac{3}{2} R + \frac{5}{2} R) \frac{1}{2} = 2 R$

$C_{P_{1} mix} = (\frac{5}{2} R + \frac{7}{2} R) \frac{1}{2} = 3 R$

$λ_{mix} = \frac{3}{2}; Y_{He} = \frac{5}{3}$

$So, \frac{V_{mix}}{V_{He}} = \sqrt{\frac{Y_{mix} RT}{M_{mix}} . \frac{M_{He}}{Y_{He} RT}} = \sqrt{\frac{3}{2} . \frac{4}{3} . \frac{3}{5}} = \frac{V_{rms, He}}{V_{rms, H_{2}}} = \sqrt{\frac{M_{H_{2}}}{M_{He}}} = \sqrt{\frac{2}{4}} = \frac{1}{\sqrt{2}}$