search

mostafa-razavi / ITIC-paper

0 stars 0 forks source link

New Derivation vs. Old Derivation #47

Open mostafa-razavi opened 5 years ago

mostafa-razavi commented 5 years ago

Summary of what @jrelliottoh said:

Eq 3 and 4 of the att pdf seem to be missing the lnZ terms. Did you have some discussion that I didn’t know about? How did these terms go missing?

image

image

As I mentioned the lnZ terms are missing in Eqs 3,4. Also Eqs 11,12 are undefined at the limit ln(0). Giant steps backward. What’s going on here? Why create issues then resolve them later? How is that progress? This generates more confusion, not less. Eqs 3 and 4 are simply wrong as far as I can tell.

image

Without the lnZ terms, they are not equal to G(T,p)-Gig(T,P). Only the G(T,P)’s are equal at eq, not the [A(T,V)+PV]’s.

A-Aig = integrl( [dA/dV – dAig/dV]dV ) cf EL2ed 8.8-8.27. If you want to derive 8.27 directly start with A-Aig = integrl( [dA/dV – dAig/dV]dV ) and follow the analogous procedures illustrated for 8.8-8.27.

Summary of what @ramess101 said:

How are they wrong? Note that these are not departures of A. Well the reviewer wanted us to show how Z-1/rho is derived by starting with Z/rho. The progress is that this derivation is more thorough in defining all of the pathways (Eq 7-10) starting from the fundamental equations (5-6)

mostafa-razavi commented 5 years ago

@jrelliottoh @ramess101

Only the G(T,P)’s are equal at eq, not the [A(T,V)+PV]’s.

I used Refprop saturation data for C12 to test the above statement. It turns out that at equilibrium [A+PV]'s are equal. Compare the last two columns. Here is the spreadsheet that I used (A+PV-test.xlsx). Am I missing something?

    Liquid Vapor Liquid Vapor Liquid Vapor Liquid Vapor
Temperature Pressure Volume Volume Helmholtz Helmholtz Gibbs Gibbs A+PV A+PV
(K) (MPa) (cm³/g) (cm³/g) (kJ/g) (kJ/g) (kJ/g) (kJ/g) (kJ/g) (kJ/g)
300 2.08E-05 1.34357 702848.7 -0.114429 -0.129071 -0.114429 -0.114429 -0.114429 -0.114429
400 0.006489 1.494114 2980.177 -0.024875 -0.044204 -0.024866 -0.024866 -0.024866 -0.024866
500 0.129424 1.712287 172.357 -0.00051 -0.022596 -0.000289 -0.000289 -0.000289 -0.000289
600 0.807137 2.160732 24.6667 -0.036638 -0.054804 -0.034894 -0.034894 -0.034894 -0.034894