Chemical Engineering Thermodynamics II

• Dr. Perla B. Balbuena: JEB 240 balbuena@tamu.edu• Web site:

https://secure.che.tamu.edu/classes/balbuena/CHEN%20354-Thermo%20II-Spring%2012/CHEN%20354-Thermo%20II-Spring%2012.htmor:

• http://research.che.tamu.edu/groups/balbuena/courses.htm

(use VPN from home)CHEN 354-Spring 12

TA: Mian Huang; e-mail:norance1987@gmail.com

TA office hours • Thursdays 1:30 to 2:30 pm; Rm 501

• Or by appointment, please e-mail to Mian Huang:norance1987@gmail.com

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 next Monday

• First HW is due January 26th

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

a

d

c

b

e

What happens from (a) to (f) as volume is compressed at constant T.

f

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

Equilibrium condition for coexistence of two phases

(pure component, closed system)

d(nG) = (nV) dP –(nS) dTPure liquid in equilibrium with its vapor, if a differential amount of

liquid evaporates at constant T and P, then

d(nG) = 0n = constant => ndG =0 => dG =0

Gl = GvEquality of the molar or specific Gibbs free energies (chemical

potentials) of each phase

Chemical potential in a mixture:

• Single-phase, open system:

i

inTPinPnT

dnnnGdT

TnGdP

PnGnGd

j,,,,

)()()()(

i :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:

ia = i

b (for i = 1, 2, 3,….n)

Ta = Tb

Pa = Pb

A liquid at temperature T

The more energetic particles escape

A liquid at temperature T in a closed container

Vapor pressure

Fugacity of 1 = f1 Fugacity of 2 = f2

222̂ fxf id

111̂ fxf id

For a pure component =

iiii fRTTG ln)(

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

For a mixture of n components

i = i

for all i =1, 2, 3, …n

in a mixture:

iii fRTT ˆln)(

Fugacity is a function of composition,T and P

Lets recall Raoult’s law for a binary

lv

lv

ff

ff

22

11

ˆˆ

ˆˆ

We need models for the fugacity in the vapor phase and in the liquid phase

Raoult’s law

Raoult’s law• Model the vapor

phase as a mixture of ideal gases:

• Model the liquid phase as an ideal solution

ivi Pyf ˆ

isati

li xPf ˆ

VLE according to Raoult’s law:

222

111

xPPy

xPPysat

sat

Homework # 1

download from web site

Due Wednesday, January 25th, at the beginning of the class