Help with Thermodynamics equations

[Ángel Martin]

(12-31-2016 01:58 PM)SlideRule Wrote:  ps: is this a proper interpretation of your modified Martin's cubic Equation of State?

I'm perusing the Article "Development of an Equation of State for Gases" by Joseph J. Martin & Yu-Ghun Hou pages 142-151 in Vol.1 No.2 of A.I.Ch.E. Journal and am having a bit of difficulty pairing your equations to one of the 60 equations in the article. I guess I'm also far too rusty, it's not clicking yet.

Yes I think this is the same one - although the pressure in the left term should be Pr reduced, (i.e. Pr = P/Pc) instead of the nominal pressure. You're definitely on the right track - I don't know why that EOS was the selected one for the study back then, but it seemed to strike the teacher's fancy on a number of points. I have a reprint of another Joseph Martin's articles ("Cubic Equations of State: Which?") from I&EC Fundamentals, Vol. 16 page 81 - May 1976. It must be an earlier one because that equation is not covered - the exponent in the reduced temperature must have been a later addition...

The PCS method is very intriguing, even if I understand the accuracy isn't going to be its forte. Still the results should be within some acceptable range, which right now they aren't. There are multiple points where the model can be a fluke, for instance:

1.- it assumes a reference state ("dead state" for entropy) at zero degrees Celsius (273 K), where it assigns 100 kcal/kg for enthalpy and 1 kcal/kg.K for entropy... does this make sense?? Obviously this has a huge impact in the final values, although it would be irrelevant when calculating magnitude changes between two {P,T} conditions.

2.- it uses the Pitzer correlation to calculate the enthalpy of vaporization - but the formula is applied with To = 273 K instead of the boiling temperature (Tb) at the given pressure. It justifies it saying the error introduced by this is small, and the advantage is that there's no need to know the Tb. The formula used is:

Hvap = R.(Tc/M) {10.95 w [(1- Tr)^0.456 + 7.08*(1- Tr)^0.354 ]
with w the acentric factor of the substance.

3.- the internal energy U is expressed as U = P.V- R.T/M . I don't remember seeing this anywhere else so can't tell it's a proper expression. Dimensionally it is correct, though.

4.- and then there is the issue with the equations used to calculate the discrepancies of enthalpy and entropy. Are those correct? What's the definition used to obtained them from the EOS? I can identify some partial derivatives in the expressions, like dPr/dTr(v=cte) embedded into the entropy discrepancy equation...

Attached is the MOD files (includes also the unit conversion MOD that should be present) in case you want to check the results on V41. The program is labeled "FREON". There are five routines for common refrigerants included in the ROM so you can enter the name at the initial prompt to load all the constants automatically. These are "R11", R12", "R13", "R22", and "NH3".

Then enter T and P - with their units - and the program will do its thing, determining the region (superheated, saturated, or liquid) and calculating the results. Turbo mode will help, the execution it's relatively slow. A manual is already posted at TOS (first entry in the 'What's New" section), with the equations listed there as well.

Thanks for looking into this one!