chemical engineering thermodynamics ii dr. perla b. balbuena: jeb 240 web site: 20

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Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 [email protected] Web site: https://secure.che.tamu.edu/classes/balbuena/CH EN%20354-Thermo%20II-Spring%2012/CHEN%20354-The rmo%20II-Spring%2012.htm or: http://research.che.tamu.edu/groups/balbuena/co urses.htm (use VPN from home) CHEN 354-Spring 12 TA: Mian Huang; e-mail:[email protected]

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TEAMS Please group in teams of 4-5 students each Designate a team coordinator Team coordinator: Please send me an stating the names of all the students in your team (including yourself) no later than next Monday First HW is due January 26 th

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Page 2: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

• Or by appointment, please e-mail to Mian Huang:[email protected]

Page 3: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 4: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Introduction to phase equilibrium

Chapter 10 (but also revision from Chapter 6)

Page 5: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 6: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Energies• Internal energy, U

• Enthalpy H = U + PV

• Gibbs free energy G = H – TS

• Helmholtz free energy A = U - TS

Page 7: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Phase Diagram Pure Component

a

d

c

b

e

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

f

Page 8: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

P-T for pure component

Page 9: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

P-V diagrams pure component

Page 10: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 11: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 12: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Chemical potential in a mixture:

• Single-phase, open system:

i

inTPinPnT

dnnnGdT

TnGdP

PnGnGd

j,,,,

)()()()(

i :Chemical potential of component i in the mixture

Page 13: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 14: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

A liquid at temperature T

The more energetic particles escape

A liquid at temperature T in a closed container

Vapor pressure

Page 15: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Fugacity of 1 = f1 Fugacity of 2 = f2

222̂ fxf id

111̂ fxf id

Page 16: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

For a pure component =

iiii fRTTG ln)(

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

Page 17: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 18: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 19: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Raoult’s law

Page 20: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

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

Page 21: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

VLE according to Raoult’s law:

222

111

xPPy

xPPysat

sat

Page 22: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20
Page 23: Chemical Engineering Thermodynamics II Dr. Perla B. Balbuena: JEB 240 Web site:  20

Homework # 1

download from web site

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