Thermodynamics Question (Maxwell Equal Area Construct)

[dweeegs]

Homework Statement

The problem is a long one. Basically we have to use Maxwell's Equal Area Construction. "With Mathcad, find Psat and the corresponding saturation volumes at T=400K for n-hexane based on the van der Waals' equation of state. Furthermore, turn Psat into a function of temperature T, i.e., define Psat(T) and identify the temperature range within which your Psat function works. Plot Psat versus T"

Homework Equations

Work done through a hypothetical reversible path under "dome" = Work done by expanding at constant Psat across "dome"

∫P(V)*dV = Psat*(Vv-Vl)dV

Equivalently, two areas enclosed by Psat and P(V) are equal; thus, the name "Maxwell's equal areas rule".

∫(Psat-P(V))*dV = ∫(P(V)-Psat)*dV

The integrals are from Vl to Vm, and Vm to Vv, respectively

The Attempt at a Solution

So this is all done with MathCad. First I defined all the parameters for Van der Waals (what Tc, Pc, a, and b were... and eventually what the filled in Van der Waals equation was). I have a couple questions...

Should I use Antoine Equation to find Psat? I did that already and found what Psat was at there temperature specified.

Secondly, I think I have to use the "find" function in MathCad. I'm definitely doing something wrong. I defined the second integral in the given equations and use a Bullian equal sign. I set up a matrix where each solution was a row, and then did find(Vv, Vl) to no avail.

Can someone please shed some light?

 

[KataKoniK]

Hello! It sounds like you have a good start on this problem. To answer your first question, yes, you should use the Antoine equation to find Psat. This equation is commonly used to estimate the vapor pressure of a substance at a given temperature.

As for using the "find" function in MathCad, this may not be necessary. Instead, you can use the Maxwell's equal area construction to find Psat and the corresponding saturation volumes. This involves plotting the pressure-volume curve for the Van der Waals equation and finding the two areas that are equal, as described in the equations you provided.

Once you have found Psat and the corresponding saturation volumes, you can define Psat as a function of temperature T using the Antoine equation. This will give you a relationship between Psat and T that you can use to plot Psat versus T.

As for the temperature range within which your Psat function works, this will depend on the accuracy of the Antoine equation and the Van der Waals equation. You may need to do some additional research or calculations to determine this range.

I hope this helps! Let me know if you have any further questions. Good luck with your problem!