Chemical Engineering Thermodynamics II

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

http://research.che.tamu.edu/groups/Balbuena/Courses/CHEN%20354-Thermo%20II-%20Spring%2015/CHEN%20354-Thermo%20II-Spring%2015.htm

(use VPN from home)• CHEN 354-Fall 14

TA: Julius Woojoo Choi, drspchoi@gmail.com

TAs office hours

• Julius Woojoo Choi, drspchoi@gmail.com• Office hours: Thursdays, 4-5pm, Office

613

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 Monday

• First HW is due January 28.

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) 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:

i

i

nTPinPnT

dnn

nGdT

T

nGdP

P

nGnGd

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, 1/28