Transcript Slide 1

Chemical Engineering
Thermodynamics II
• Dr. Perla B. Balbuena: JEB 240
[email protected]
• Website: http://research.che.tamu.edu/groups/Balbuena/Courses/CHEN%20354Thermo%20II-%20Spring%2015/CHEN%20354-Thermo%20II-Spring%2015.htm
(use VPN from home)
• CHEN 354-Fall 14
TA: Julius Woojoo Choi, [email protected]
TAs office hours
• Julius Woojoo Choi, [email protected]
• 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 [email protected] 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
f
e
d
c
b
a
What happens 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
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 = G v
Equality of the molar or specific Gibbs free energies (chemical
potentials) of each phase
Chemical potential in a mixture:
• Single-phase, open system:
  (nG) 
  (nG) 
  (nG) 
d (nG)  
dP  
dT   
dni



 P  T ,n
 T  P ,n
i  ni  P ,T , n
j
mi :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
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
ˆf id  x f
1
1 1
ˆf id  x f
2
2 2
For a pure component
ma = mb
mi  Gi  i (T )  RT ln fi
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:
ˆ
mi  i (T )  RT ln fi
Fugacity is a function of composition,
T and P
Lets recall Raoult’s law for a
binary
v
l
1
1
ˆf 
ˆf v 
2
ˆf
ˆf l
2
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
ˆf v  Py
i
i
ˆf l  P sat x
i
i
i
VLE according to Raoult’s law:
Py1  P x
sat
1
1
Py 2  P x2
sat
2
Homework # 1
download from web site
Due Wednesday, 1/28