Find the speed of sound in a mixture of 1 mol of helium
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You forgot to write " at temperature 27°C "
according to Laplace equation of speed of sound in gas is given by
Now, mixture contains 1 mole of Helium and 2 mole of oxygen,
Molecular mass of mixture :
= (1 × 4 + 2 × 32)/(1 + 2) = 68/3 g/mol = 68/3 × 10⁻³ Kg/mol
For γ of mixture , we should find Cv and Cp
Cv for helium = 3R/2 { because monoatomic }
Cv for oxygen = 5R/2 { because diatomic }
= (1 × 3R/2 + 2 × 5R/2)/(1 + 2) = 13R/6
So, = Cv + R = R + 13R/6 = 19R/6
Now,
Ymix = Cp/Cv = 19/13
Mmix = 0.068/3 kg/mol
Now, speed of sound in mixture =
= 400.9 m/s
according to Laplace equation of speed of sound in gas is given by
Now, mixture contains 1 mole of Helium and 2 mole of oxygen,
Molecular mass of mixture :
= (1 × 4 + 2 × 32)/(1 + 2) = 68/3 g/mol = 68/3 × 10⁻³ Kg/mol
For γ of mixture , we should find Cv and Cp
Cv for helium = 3R/2 { because monoatomic }
Cv for oxygen = 5R/2 { because diatomic }
= (1 × 3R/2 + 2 × 5R/2)/(1 + 2) = 13R/6
So, = Cv + R = R + 13R/6 = 19R/6
Now,
Ymix = Cp/Cv = 19/13
Mmix = 0.068/3 kg/mol
Now, speed of sound in mixture =
= 400.9 m/s
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