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A container of fixed volume has a mixtur...

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

A

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

B

The ratio of speed of sound in the gas mixture to that in helium gas is `sqrt(6//5)`.

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`C_(V("mix"))= ((1)/((3)/(2)R) + (1)((5)/(2)R))/(2) = 2R`
`C_(P("mix")) = 3R " " gamma_("mix") = (3)/(2) implies f =4`
Average energy/mole = `f(1)/(2)RT= 2RT`
`((V_("sound"))"mixture")/((V_("sound"))"He") = (sqrt(RT)/(2))/(sqrt(5RT)/(12)) = sqrt(6)/(5)`
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