Calculate velocity of sound in mixture of 1 mole He and 1mole O2 at 127 degrees Celsius - Physics - Semiconductor Electronics Materials Devices And Simple Circuits

Question

Calculate velocity of sound in mixture of 1 mole He and 1mole O2 at
127 degrees Celsius

Suman Acharya · Accepted Answer

Without Temperature =27°C we and 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:
M mix=(n 1M1+n 2M2)/n1+n2
=1x4+2x 32/1+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=(n1 Cv1+n 2 Cv2)/n1+n2
=1x(3/2)R+ 2x(5/2)R/1+2
=13R/6

(Cp)mix=(Cv)mix +R
=13/6+R=19/6

γ mix=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

Calculate velocity of sound in mixture of 1 mole He and 1mole O2 at 127 degrees Celsius .