Question

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)`

Answer 1

Correct Answer - 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)`