Question

Find the speed of sound in mixture of 20%hydrogen, 40% water vapour in volume

Answer 1

Explanation:

Without Temperature =27°C we an't proceed with calculations

According to Laplace formula, the speed of sound is given by 

V=√γRT/M----------equation(1)

Molecular weight of mixture of gases:

Mmix=(n1M1+n2M2)/n1+n2

=1x4+2x32/1+2

=68/3 x 10⁻³kg/mol

As Helium is Mono atomic so

 Cv=3R/2

while oxygen is diatomic [Cv=5R/2]

hence(Cv)mix=(n1Cv1+n2Cv2)/n1+n2

=1x(3/2)R+ 2x(5/2)R/1+2

=13R/6

(Cp)mix=(Cv)mix +R

=13/6+R=19/6

γmix=Cp/CV

=19R/6/13R/6

=19/13

Now substituting the values of M and γ in equation 1 with T=200 K and r=8.31J/mol

V=√(19/3)(8.31x300)/68/3 x 10⁻³)

=400.9m/s