Consider a mixture of 2 mole helium and 4 mole of oxygen. Compute the speed of sound in this gas mixture at 300 K.

Explanation

The mixture of helium and oxygen
`M_("mix") = (n_(1) M_(1) + n_(2) M_(2))/(n_(1) + n_(2)) = ((2 xx 4) + (4 xx 32))/(2 + 4) = (136)/(6)`
`M_("mix") = 22.6 xx 10^(-3)` kg/mol
Helium is an mono atomic , `C_(V_(1)) = (3R)/(2)`
Oxygen is an diatomic , `C_(V_(2)) = (5R)/(2)`
Oxygen is an diatomic , `C_(V_(2)) = (5R)/(2)`
`(C_(V))_("mix") = (n_(1) C_(v_(1)) + n_(2) C_(v_(2)) )/(n_(1) + n_(2)) = (( 2 xx (3R)/(2)) + (4 xx (5R)/(2)))/(2 + 4)`
`(C_(V))_("mix") = (13)/(R)`
`(C_(p))_("mix") = (C_(V))_("mix") + R " " gamma_("mix") = ((C_(p))_("mix"))/((C_(V))_("mix")) = (19)/(R) xx (6)/(13 R)`
`= (13 R)/(6) + R = (19 R)/(6) " " gamma_("mix") = (19)/(13)`
According to Laplace correction , Speed of sound ,
Extend root length litre this `v = sqrt((gamma RT)/(M)) = sqrt((19)/(13) xx (8.31 xx 300)/(22.6 xx 10^(-3))) , v = 400.9 ms^(-1)`