# Homework Help: Thermodynamics Question (Maxwell Equal Area Construct)

1. Mar 18, 2012

### dweeegs

1. The problem statement, all variables and given/known data

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"

2. Relevant 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

3. 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?