A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at…

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)
  1. The average energy per mole of the gas mixture is 2RT
  2. The ratio of speed of sound in the gas mixture to that in helium gas is 65
  3. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 12
  4. The ratio of the rms speed of helium atoms to that of hydrogen molecules is 12

Solution

CVmix=132R+152R2=2R
CPmix=3R
γmix=32⇒f=4
Average energy/mole =f12RT=2RT
VsoundmixtureVsoundHe=RT25RT12=65
VrmHeVrmsH2=3RT43RT2=12 ;

Asked in: JEE Advanced 2015 (Paper 1)

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