specific heat ratio of a gas mixture
specific heat ratio of a gas mixture
(OP)
Is the specific heat ratio (isentropic expansion factor) of a gas mixture simply a molar weighted average of the individual heat ratios? If not, how is it calculated?
I apologize if this is not the correct forum for this question. The other forums that might be more appropriate seem to be seldom used.
I apologize if this is not the correct forum for this question. The other forums that might be more appropriate seem to be seldom used.
Jim Buckley
ASRC Aerospace
Cleveland





RE: specific heat ratio of a gas mixture
RE: specific heat ratio of a gas mixture
Good luck,
Latexman
RE: specific heat ratio of a gas mixture
So I think you should first obtain Cp by a weighted average, then determine Cp/Cv=Cp/(Cp-R)
prex
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RE: specific heat ratio of a gas mixture
David
RE: specific heat ratio of a gas mixture
I'm working with 79% Helium, 21% Oxygen. k He = 1.667, k O2 = 1.4.
The first way I calculated the specific heat ratio (k), I simply used the mole fraction average of the separate k's.
Mole fractions = .79 * 4.003 / (.79 * 4.003 + .21 * 32) = .32 He; .68 O2.
1) kmix = .32 * 1.667 + .68 * 1.4 = 1.485
The second way, I used my interpretation of dvd's answer above:
Cpmix = .32 * 5.19 + .68 * .919 = 2.2857
Cvmix = .32 * 3.12 + .68 * .659 = 1.4465
2) kmix = 2.2857 / 1.4465 = 1.58
The third way, according to prex's answer, confirmed by "Rocket Propulsion Elements" by Sutton&Biblarz is to use the molar values for Cp and Cv:
k=Cpmix / (Cpmix - R')
Cpmix = .32 x 20.786 + .68 * 29.38 = 26.63 J/kg/mol
3) kmix = 26.63 / (26.63 - 8.3145) = 1.454
I'm going to go with 3).
Jim Buckley
ASRC Aerospace
Cleveland
RE: specific heat ratio of a gas mixture
RE: specific heat ratio of a gas mixture
- Steve
RE: specific heat ratio of a gas mixture
cp=1.1536 kJ/kg/K
cv=0.79185 kJ/kg/K
k=1.4569
MW = 23.040
R is not given, but cp-cv=0.362 kJ/kg/K
I think the third method that you mentioned works pretty good.
David
RE: specific heat ratio of a gas mixture
If you are converting mass % to mole %, you did it wrong. You have to divide by MW. Most of the time I've seen concentration of gas mixtures in volume %, which is the same as mole %.
Good luck,
Latexman
RE: specific heat ratio of a gas mixture
Where would you divide by MW in my mole fraction equation? I'm looking for the easiest way to calculate the molar fraction. My method seems to laborious.
Jim Buckley
ASRC Aerospace
Cleveland
RE: specific heat ratio of a gas mixture
Good luck,
Latexman
RE: specific heat ratio of a gas mixture
RE: specific heat ratio of a gas mixture
Mass fractions = .79 * 4 / (.79 * 4 + .21 * 32) = .32 He; .68 O2.
1) kmix = .32 * 1.667 + .68 * 1.4 = 1.485
Good luck,
Latexman
RE: specific heat ratio of a gas mixture
Why not using a simulator such as Hysys, Pro/II, Aspen Plus or Promax?
"We don't believe things because they are true, things are true because we believe them."
RE: specific heat ratio of a gas mixture
Thanks for the suggestion but
1) I'm a mechanical engineer. I'm trying to derive the thrust for a simple model rocket engine (.1 inch throat) which is part of a larger model to be tested in our 1'x1' Mach 6 wind tunnel. I only need to do this once and then I have to move on to other stuff like analyzing the stress in the model and all the support and actuating components.
2) I want to know how to do it. I don't want a computer to give me the answer if I don't know how to do it manually.
2) I thought the answer to deriving the specific heat ratio for a gas mixture as simple as He & O2 would be so easy as to not need any software.
3) I never heard of those simulators before. But I'm sure they aren't free. Besides, it would be too much hassle to obtain and get permission to install software to perform a one-time calculation.
:)
Jim Buckley
ASRC Aerospace
Cleveland
RE: specific heat ratio of a gas mixture
That is exactly the right answer. The recommendation to "just dump it into a simulator" jumps to the fingertips of far too many of us, far too often.
I expect you have everything you need on this and you're moving forward to the next issue. Good luck with the project.
Just an aside (from an ME who also can't afford Hysis and wouldn't install it if it was free), I purchased RefProp from NIST last year for around $100 and have been amazed at how often it has been useful for just looking up a couple of numbers. It has the ability to give you a ton of calculated parameters for pure components or any mixture you want to input. It is a bunch easier than the tedium of getting the pure-component values from a table and then manipulating them to get the mixture values--everyone needs to do that by hand a couple of times and then never again.
David