Calculate Heat Capacity Ratio of a Gas 1

[Tonylmiller]

I have heat capacity at constant pressure, Cp (but not Cv), critical compressibility, critical pressure, temperature, volume, and some other physical properties of the gas. The gas is tetrafluoroethylene, otherwise known as TFE or R1114.

Does anyone know of a way to estimate or calculate the specific heat ratio (Cp/Cv)? I do not want to assume ideal gas.

Thanks!

Tony

 

[sailoday28]

Having the equation of state allows calc of the Cv
a= dp/dt at constant volume
b=dv/dt at constant pressure

Cp-Cv=abT where T is the absolute temp

 

[quark]

For ideal gases Cp-Cv = R (individual gas constant)

Also check this link for real gases

http://scienceworld.wolfram.com/physics/SpecificHeat.html

Regards,

 

[sailoday28]

Following Quarks recommendation of a website, I still believe you will need an equation of state to calcuate the parameters of that website (alpha or K)
Perhaps others can provide those parameters or an equation of state.

 

[phex]

Nonetheless: Thanks alot, quark, for providing this excellent link.

chris

 

[25362]

1. The tabulated value at ambient conditions (not given) = 1.12.

2. The ChE issue of March 14, 1977 (Plant Notebook) gives a formula for estimating Cp/Cv for "real" gases, given Cp and the critical T and P, as follows:

Cp-Cv = R [1+(Pr/Tr²)(0.132+0.712/Tr)²]​

Then:

Cp/Cv = Cp/[Cp-(Cp-Cv)]​

Pr, Tr are the reduced properties.
R, the gas constant should be selected in accordance with the units for Cp.

The example given for ethyl ether for 80 deg C and 5 atm abs., shows an error of only 0.5%. I can not confirm or deny the accuracy of that formula presented by Claudio Caparelli, Eurotechnica, Italy.

 

[hacksaw]

real gas effects are definitely important the ratio but you'll need the equation of state. how close to saturation are your conditions?

 

[Tonylmiller]

Wow, you folk are amazing. Thanks for the help.

hacksaw, the conditions are 170 F and 175 psig. Cp looks like about .205 BTU/lb-f.

Molecular Weight 100.016
Atm Boiling Pt, F -105.3
Freezing Point, F -224.5
Critical Temperature, F 91.9
Critical Pressure, psia 571.9
Critical Volume, cu ft/lb 0.0275
Critical Compressibility Factor 0.266

Thanks again, everyone.

Tony

 

[hacksaw]

your MW apprears to coincide with with another fluid

are you certain about the molecular formula?

 

[25362]

Following Caparelli's equation, the value tabulated for "ambient" conditions, 1.12, wouldn't have to change much at the "new" conditions.

 

[sailoday28]

25362 (Chemical)
Could you provide Caparelli's equation or where I can find it?

 

[25362]

To sailoday28, see, please my post of Oct 4, above.

 

[mbeychok]

I would just like to add some commentary to the equation that Quark gave for an ideal gas.

(1) The literature can be very confusing because many authors never explain whether they are using the universal gas constant R (that applies to any ideal gas) or whether they are using R_s that only applies to a specific individual gas. The relationship between the two is: R_s = R/M where M is the molecular weight of the specific gas.

(2) The equation given by Quark Cp-Cv=R_s is correct only when the Cp and Cv are mass specific heats (e.g., Btu/lb-deg F or Joule/kg-deg K).

(3) When the Cp and Cv are molar specific heats (e.g., Btu/lbmol-deg F or Joule/kgmol-deg K), the correct equation is Cp-Cv=R.

Milton Beychok
mbeychok@xxx.net (replace xxx with cox)
(Visit me at www.air-dispersion.com)

 

[sailoday28]

As a follow up to
"2) The equation given by Quark Cp-Cv=R is correct only when the Cp and Cv are mass specific heats (e.g., Btu/lb-deg F or Joule/kg-deg K)."

If one has a handle on the compressibility factor, Z,
Where pv=ZRT
and Z does not vary significantly in the region of interest,
Then
Cp - Cv = ZR,
Where:
Z is non dimensional and Cp, Cv, are in the same units.