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Homework Help: Equation of State, ideal gas

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data

    Often I bump into the relation [itex]p=\rho c_s^2[/itex], where p is the pressure, rho the density and cs the speed of sound in the ideal gas. It is apparently called the equation of state for an ideal isothermal gas.

    I know about [itex]pV=NkT[/itex], which becomes [itex]p=\rho kT[/itex], but does this mean that [itex]c_s^2=k_BT[/itex]?
  2. jcsd
  3. Dec 11, 2013 #2
  4. Dec 11, 2013 #3
    The ρ in your two equations is not the same quantity.
    In the first equation it may be mass density (but it looks like you are missing a γ), in the second is number density. But again, the molar mass is missing.
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