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Speed of sound in an ideal gas

  1. Sep 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the speed of sound in argon gas at 30 degrees celcius. Argon is a monoatomic gas with atomic mass 40. Assume adiabatic and ideal gas conditions. The mass of a nucleuon is 1.67*10-27 kg=mp.

    2. Relevant equations

    Adiabatic constraint: pVγ=constant.

    Ideal gas equation: pV=nRT=NkT

    Speed of a sound wave: [itex]v=\sqrt{B/\rho}[/itex]

    3. The attempt at a solution

    From the adiabatic constraint: [itex]\text{d}p V^{\gamma} + \gamma p V^{\gamma-1} \text{d}V=0[/itex]

    [itex]B=-V\frac{\text{d}p}{\text{d}V}=\gamma p[/itex]

    Insert into ideal gas equation, using [itex]\rho=\frac{Nm}{V}[/itex] :

    [itex]B=\frac{\gamma \rho k T}{m}[/itex]

    Finally: [itex]v=\sqrt{\frac{B}{\rho}}=\sqrt{\frac{\gamma k T}{m}}[/itex]

    Insert values: m=40*mp=6,68*10-26 kg, k=1.38*10-23 J/K, T=303.15 K, γ=3/5=0.6

    This produces the result v=194 m/s.

    However, the answer key says the correct value is 323 m/s

    I have searched my solution attempt multiple times, unable to find my error. Any help will be greatly appreciated.
     
    Last edited by a moderator: Sep 30, 2011
  2. jcsd
  3. Sep 30, 2011 #2

    ehild

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    γ=Cp/Cv=5/3 for a mono-atomic gas.


    ehild
     
  4. Sep 30, 2011 #3
    Thank you. What an embarrasing mistake. :redface:
     
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