1. Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 balbuena@tamu.edu Website: http://research.che.tamu.edu/groups/Balbuena/teaching.html http://research.che.tamu.edu/groups/Balbuena/teaching.html TA: Pete Praserthdam, sigmaupsilonpi@hotmail.comsigmaupsilonpi@hotmail.com Graduate Teaching Fellow: Leonardo Gomez-Ballesteros, leogomezb@tamu.eduleogomezb@tamu.edu

2. TA office hours Pete Praserthdam, sigmaupsilonpi@hotmail.com sigmaupsilonpi@hotmail.com Office hours: Wednesdays, 2-3pm, JEB 632

3. TEAMS Please group in teams of 4-5 students each Designate a team coordinator Team coordinator: Please send an e-mail to balbuena@tamu.edu stating the names of all the students in your team (including yourself) no later than next Mondaybalbuena@tamu.edu First HW is due January 27.

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

5. 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

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

7. Phase Diagram Pure Component a d c b e  What happens from (a) to (f) as volume is compressed at constant T. f

8. P-T for pure component

9. P-V diagrams pure component

10. 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

11. 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 G l = G v Equality of the molar or specific Gibbs free energies (chemical potentials) of each phase

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

13. Phase equilibrium: 2-phases and n components Two phases, a and b and n components: Equilibrium conditions:  i a =  i b (for i = 1, 2, 3,….n) T a = T b P a = P b

14. A liquid at temperature T The more energetic particles escape A liquid at temperature T in a closed container Vapor pressure

15. Fugacity of 1 = f 1 Fugacity of 2 = f 2

16. For a pure component   =   For a pure component, fugacity is a function of T and P

17. For a mixture of n components  i  =  i  for all i =1, 2, 3, …n in a mixture: Fugacity is a function of composition, T and P

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

19. Raoult’s law

20. Model the vapor phase as a mixture of ideal gases: Model the liquid phase as an ideal solution

21. VLE according to Raoult’s law:

23. Homework # 1 download from web site Due Wednesday, 1/27