Specific Internal Energy of a diatomic gas

[Carusun]

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?

 

[Andrew Mason]

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?

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.

AM

 

[Carusun]

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!