# 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.)

Please help - I haven't found the solution myself, as of yet.

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 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 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). – Starfish Prime Feb 21 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. – JDKelley Feb 22 at 10:08

## 1 Answer

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? – JDKelley Feb 16 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. – Organic Marble Feb 16 at 1:48