# How do I calculate thermochemical properties of mixed gases?

I'm working on a rocket project, and my design of engines is stalled. I need to be able to calculate the Cp, Cv, and R for mixtures of O2/CH4 (stoichiometric or fuel-rich mix) and CO2/H2O (result of combustion, probably carrying some CH4 from the fuel film cooling of the chamber walls.) I'm working on LOX/LCH4 engines. (I don't know how to do subscripts here yet.)

I'd posted this in physics, but all I got was the remark that I "hadn't posted a question" - but not all questions carry a question mark. But, if you insist: How do I calculate Cp, Cv, and R for mixtures of gases of vague proportions and unknown quantities? The gasts in question are a mixture of oxygen/methane, and a mixture of water steam/carbon dioxide/methane (the methane is leftover from FFC of the chamber walls.)

JDK

• Yes, science-based Stack Exchange sites do enforce fairly rigid question and answer format. A question should have a specific answer wherever possible and it should be easy to identify which is the correct answer. Name two gases and specify a range of mixture fractions and temperature and see if that generates an answer Once you have your first good answer you can generalized in a second question, or it's possible that the answer for one mixture will apply to many. Also, it's best if you show some research effort within your question;
– uhoh
Feb 15, 2021 at 12:03
• For example, search for "compressibility of gas mixtures" and see what you find, then state your findings in the question. People are more likely to provide a good answer if you show some effort a prior research, even if your results were not helpful. Thanks!
– uhoh
Feb 15, 2021 at 12:04
• You can do subscripts with HTML like this: CH<sub>4</sub> (which works in posts but not comments, as it turns out), and with latex like this: $CH_4$ giving $CH_4$ (which works in both posts and comments, but has a rather different presentation to normal text). Feb 21, 2021 at 16:50
• I see - I've got to learn LaTeX anyhow, I've gotten a copy downloaded, I just haven't had time to work with it yet. And thanks for the advice on asking questions - it's a format I'm unused to. Feb 22, 2021 at 10:08

Use a mass-weighted average, e.g.

$$C​_{p_{mixture}}​​= ​\frac{m_1}{m_{mixture}}​​​​ C​_{p_1}​​+ ​\frac{m_2}{m_{mixture}}​​​​ C​_{p_2}$$

May not apply depending on what you actually mean by

vague proportions and unknown quantities

obviously you have to know something.

• I do - I just need to finish the calculations on the fuel mix ratio (how I want to run FFC and all that, getting the final fuel-rich ratio.) So, I haven't calculated the proportions as of yet (they'll probably end up somewhere around 2.5-2.7, if the literature I've been reading is anything to go by,) and the quantities will, of course, be kg/sec, once i figure out mass flow for desired thrust (~25kN, and ~2.5kN for verniers. Can this be expanded for mixes of more than two gases? Feb 16, 2021 at 0:38
• @JDKelley yes, just use the appropriate mass fractions for as many gases as you like. We used mass (mass of gases in the combustion chamber) but flowrate may be OK. Feb 16, 2021 at 1:48