09.01 - Criteria for Phase Equilibrium

Phase equilibrium in a pure fluid (uakron, 11min) can be contemplated in terms of the following question: Suppose propane exists at a set temperature in an uninsulated piston/cylinder with half the volume as vapor and half as liquid. What is the final pressure when the piston is pressed down. A proper thermodynamic answer leads to the consideration of the Gibbs energy, with implications that open up an entire new world of problems to be solved related to equilibrium partitioning for pure fluids and mixtures.

Comprehension Questions:

1. Write dG for the total piston/cylinder system in terms of the individual phases.
2. What is the criterion for equilibrium in a pure fluid?
3. What is the stable state (L,V,L=V) when G^L > G^V ?
4. For the vdW fluid at 62C, 0.35 MPa, the following roots were obtained: Z^L = 0.02598,
Z^V = 0.92718, A=0.08608, B=0.01820. What is the stable state (L,V,L=V)?
5. For the vdW fluid at 62C, 0.25 MPa, the following roots were obtained: Z^L = 0.01859,
Z^V = 0.94910, A=0.061487, B=0.013000. What is the stable state (L,V,L=V)?

Hint: (G-G^ig)/RT = -ln(Z-B)-A/Z + Z - 1 - ln(Z) where A=a*P/(R²T²); B=bP/RT; b=0.125*RT_c/P_c