Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: 240 JEB balbuena@tamu.edu Web site: https://secure.che.tamu.edu/classes/balbuena/CHEN 354- Thermo II-Fall 10/CHEN 354-Thermo II-Fall 10.htm Or: www.che.tamu.edu/balbuena (use VPN from home) Click on Research Page CoursesCHEN 354-Spring 10 TA: Diego Ortiz JEB 401 diego.ortiz@chemail.tamu.edu

TA office hours Thursdays 3 to 5 pm Or by appointment, please e-mail Diego to diego.ortiz@chemail.tamu.edu Office: 401 JEB

TEAMS Please group in teams of 4-5 students each Designate a team coordinator Team coordinator: Please send me an e-mail stating the names of all the students in your team (including yourself) no later than this coming Friday First HW is due Thursday, September 9.

Introduction to phase equilibrium Chapter 10 (but also revision from Chapter 6)

Equilibrium Absence of change Absence of a driving force for change Example of driving forces Imbalance of mechanical forces => work (energy transfer) Temperature differences => heat transfer Differences in chemical potential => mass transfer

Energies Internal energy, U Enthalpy H = U + PV Gibbs free energy G = H – TS Helmholtz free energy A = U - TS

Phase Diagram Pure Component f e d c b a Describe process from (a) to (f) as volume is compressed at constant T.

P-T for pure component

P-V diagrams pure component

Equilibrium condition for coexistence of two phases (pure component) Review Section 6.4 At a phase transition, molar or specific values of extensive thermodynamic properties change abruptly. The exception is the molar Gibbs free energy, G, that for a pure species does not change at a phase transition

Now we are going to do a class exercise

n = constant => ndG =0 => dG =0 Equilibrium condition for coexistence of two phases (pure component, closed system) d(nG) = (nV) dP –(nS) dT Pure liquid in equilibrium with its vapor, if a differential amount of liquid evaporates at constant T and P, then d(nG) = 0 n = constant => ndG =0 => dG =0 Gl = Gv Equality of the molar or specific Gibbs free energies (chemical potentials) of each phase

Chemical potential in a mixture: Single-phase, open system: Chemical potential of component i in the mixture

Phase equilibrium: 2-phases and n components Two phases, a and b and n components: Equilibrium conditions: mia = mib (for i = 1, 2, 3,….n) Ta = Tb Pa = Pb

For a pure component ma = mb For a pure component, fugacity is a function of T and P

For a mixture of n components mia = mib for all i =1, 2, 3, …n in a mixture: Fugacity is a function of composition, T and P

Lets recall Raoult’s law for a binary We need models for the fugacity in the vapor phase and in the liquid phase

Raoult’s law Model the vapor phase as a mixture of ideal gases: Model the liquid phase as an ideal solution

VLE according to Raoult’s law:

Homework # 1 Read MathCad Basics (download pdf files from web site) Work Example 10.3 (page 359) using MathCad. Present and explain your Mathcad solution in your HW solution In part (a) make a graph of P-x1-y1 In part (c) make a graph of T-x1-y1 Due Thursday, September 9th