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# Calculating k (=Cp/Cv) for Gas Mixture?

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## Calculating k (=Cp/Cv) for Gas Mixture?

(OP)
Hi guys. Anybody got a shortcut, that doesn't require a simulator, for calculating k=Cp/Cv for a gas mixture? Gas is 65% CO2, 35% CH3, water-saturated. My rules of thumb say stuff like Cp=(9/2)R and Cv=(7/2)R for "triatomic gas", but that doesn't help much for this gas mixture. And Cp-Cv=R gives me negative values for this particular gas, so that's out. I am within ideal gas approximation range if that helps. Thanks guys!

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

I would find the breakdown of the gas including water content is mass fraction, and then use those to weight the Cp and Cv you calculate for the triatomic gases (you can probably find the Cp and Cv for water at your conditions in tables) to get the "average" Cp and Cv for the mixture. If you expect reactions though, this method is not a good estimate.

Have you tried to find published thermodynamic literature for these compounds? I think that's the best route for accurate calculation without simulator.

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

Using the table on A-8 of my Crane TP410, 0.65*1.30 + 0.35*1.32 = 1.31.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

Real values for Cp are influenced by operating pressure and temperature, and more so in the case of non ideal compounds such as CO2. Use a suitable EOS package in Pro II or Hysis to generate these values if operating pressure is more than 200kpa or so.

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

ideal gas law assumption may work far from critical area, but there are several limits in operating conditions plus the difficult to estimate the water content (in your water saturated stream).
for these calc's the obvious reference is the Properties of Gases and Liquids which includes many examples about how to estimate thermodynamic properties,

as already suggested, a EOS allows to estimate the water content and enthalpy departure from ideal gas giving more accurate results...
it may be useful to compare values calculated with different methods,

herebelow the values calculated with ideal gas law, extended version of Peng Robinson available in Prode (Prode PRX) and GERG (2008)
mixture (mol. fract.) CO2 0.635 C3 0.35 H2O 0.015 at 288.15 K 1 Bar
cp (Kj/Kg-K)
ideal 1.13 (Prode database)
PRX 1.136
GERG 1.131

cv (Kj/Kg-K)
ideal 0.94 (as above)
PRX 0.94
GERG 0.935

at these conditions, all the values are in reasonable agreement,
however, if you repeat the same calc's at different conditions, for example 350 K 20 Bar, there are quite large differences in cp calculated with ideal and EOS based models
mixture (mol. fract.) CO2 0.635 C3 0.35 H2O 0.015 at 350 K 20 Bar

cp (Kj/Kg-K)
ideal 1.26 (Prode database)
PRX 1.38
GERG 1.39

cv (Kj/Kg-K)
ideal 1.07 (as above)
PRX 1.09
GERG 1.1

in your specific case in addition to the operating conditions, I would consider the application, for example if you need cp/cv for sizing a PSV (with API formulation) it must be cp/cv of ideal gas (API formulation requires that) or, as alternative you may use HEM or similar rigorous methods,
the same consideration for many other common problems...

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

The issues that Apetri brought up are the exact reason that I purchased REFPROP.exe from NIST for about $100. I have found it to be in very close agreement with all of the full-blown simulators every time I've had cause to compare. They have a free calculator on line, but it lacks many of the options that REFPROP has. I have been using it for about 10 years and it is still the best$100 I ever spent.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

KernOily,

I see two interpretations of your "CH3", methane and C3's. Which is it?

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

(OP)
Guys thanks for the great answers. Very much appreciated.

apetri - I have that text and flat forgot that I had it. I will look.

zdas - Thanks for the tip on the NIST software. That right there was worth the price of admission today. Thanks very much. On reading the FAQ at the NIST site, it sounds like it has problems doing saturated mixtures. Have you done those with it, and does it do flash calculations to determine the composition of the phases for liquid-vapor phase equilibrium?

### RE: Calculating k (=Cp/Cv) for Gas Mixture?

I've done a lot of cases where one species out of the mixture of gases changed state from one pressure/temperature to the next. The results either matched observed conditions or predicted cusps in performance. That is as close as I've come to a true saturated system.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

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