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Homework Help: Specific Internal Energy of a diatomic gas

  1. Apr 19, 2006 #1
    Hi all, I'm stuck on a question, and I'm hoping you guys can help... Anyway, here it is:

    A J-shock in a Herbig-Haro object is propagating through neutral hydrogen gas at speed 100 kms-1. The gas has number density 107 m-3 and temperature 104 K.

    (d) The internal energy per unit mass of a gas is,
    U= ((gamma) - 1)^-1 * P/(rho). Use this to show that the specific internal energy of the post shock gas is, 3/2 * P(1)/(rho)(1)= 9/32 v(0)^2.

    In this question;

    (gamma) = the adiabatic constant, which, for H(2) is 7/5
    P(1) = Post shock pressure = 5/6 (rho)(0) v(0)^2
    (rho)(1) = 6(rho)(0)

    which I believe is all that should be required, symbol-wise.

    I can do this for a monatomic gas, but I'm having trouble getting the same result for a diatomic gas.
    Have I made a mistake in assuming that the shock is propagating through a diatomic gas?
  2. jcsd
  3. Apr 19, 2006 #2

    Andrew Mason

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    I am not sure I understand everything involved here, but I think the point may be that diatomic gas molecules have 5 degrees of freedom but that only three degrees of freedom (translation only) are involved in the propagation of a compression wave.

  4. Apr 21, 2006 #3
    That's great, thanks!

    I had actually gone through this question the first time just assuming it was a monatomic gas, then kicking myself when I remembered H was diatomic.
    Now, at least, I have a reason to do so, and am now kicking myself again...

    Many thanks! :biggrin:
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