specific heat ratio of a gas mixture

[buckley8]

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.


Jim Buckley
ASRC Aerospace
Cleveland

 

[dvd]

The specific heat of a mixture is the sum of the products of mole fraction times the specific heat of that gas component. Calculate the mixture cp value and divide by the mixture cv value to get the mixture k value.

 

[Latexman]

I would say if the c_p values are molar values, use mole fractions, however c_p values are often mass values. In that case, use mass fractions.

Good luck,
Latexman

 

[prex]

Perry's Chemical Engineer's Handbook gives some informations on your problem:

The only practical recourse at present for calculating the heat capacities of mixtures of solids, liquid or gases,...,is to weight the pure component or phase heat capacities by weight, mole, or volume fractions, the choice being dictated by the units of the heat capacities being weighted....For miscible mixtures, the accuracy of such weighting varies from excellent in the case of low-density gases to quite poor...

There's also a graph showing that, as one would expect, for real gases at high temperatures (with respect to T_c) and low pressures (with respect to P_c) the difference C_p-C_v approaches well the real gas constant.

So I think you should first obtain C_p by a weighted average, then determine C_p/C_v=C_p/(C_p-R)

prex

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[zdas04]

Prex's technique is what I use, but you have to be careful to get the mixture gas constant using the same averaging technique that you used for c(p) (i.e., if you used mass averaging for c(p) then you have to use mass averaging for the MW you use to get the mixture gas constant). Small changes in this ratio can make a big difference in your calculated temp.

David

 

[buckley8]

Wow, that all makes this clear as mud. It reminds me why I cared so little for chemistry in high school and college. Could never get a definitive, uncomplicated answer then either

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

 

[sailoday28]

buckley8 (Mechanical)Apparently all responces are for a perfect gas.

 

[SomptingGuy]

We use mass-weighted enthalpy values for a finite difference calc. Heywood is very good in this area.

- Steve

 

[zdas04]

I went to NIST's RefProp database and got the official numbers (at 0C and 101 kPa)

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

 

[Latexman]

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

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

 

[buckley8]

Thanks Latexman. I've been told that the volume % of a gas = the mole % and I've read it too but I didn't understand it until I worked the numbers.

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

 

[Latexman]

Is the 79% Helium and 21% Oxygen in mass or volume (mole) %? First, we have to know what you are starting with. It was not stated, everyone assumed something.

Good luck,
Latexman

 

[hacksaw]

using perry's (Redlich-Kwong) k=1.469 at 0 degC

 

[Latexman]

If I Assume the concentrations are in volume % and convert to mass %:

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

 

[sheiko]

buckley8,

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."

 

[buckley8]

Sheiko,

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

 

[zdas04]

buckly8,
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