Question

A bulb contains 5 moles of He gas (Molecular weight= 4). When Ne Gas (Molecular weight 20) is added to this bulb what will be the ratio of Earlier and now of Sound velocity?

(1) 1/4 (2) 1/2 (3) 1 (4) 4 (5) 2  

Amount of Ne gas not given.

Answer 1

Moelcular mass of He = 0.004 kg/mol
Molecular mass of Ne = 0.02 kg/mol

For γ of mixture , we should find Cv and Cp

Cv for helium = 3R/2 { because monoatomic }

Cv for neon = 3R/2 { because monoatomic }

Cv mixture = (5 × 3R/2 + n × 3R/2)/(5 + n) = 3R/2

So, Cp = Cv + R = R + 3R/2 = 5R/2

Now,
Ymix = Cp/Cv = 5/3

Mmix = 0.004*5+n*0.02/(5+n) = 0.00667 kg/mol
(if number of moles of Ne = 1)

Speed of sound when only Helium = Sqrt (5/3*8.314*T/0.004)
Now, speed of sound in mixture = Sqrt (5/3*8.314*T/0.00667)

ratio = 1.29:1 (if n =1)

ratio = 1.732:1 (if n =5)

Therefore, to get correct answer, we need to know the number of moles of the Neon gas.

Please do not consider it as an incomplete answer. Just need to know the moles of Neon.