Chapter 5: Helmholtz free energy A
Since the relationships among the thermodynamic properties of a system
determine the equilibrium in the system, it is important to establish these
relationships
Combining the 1st and the 2nd law
dU q w
dS
q
w PdV
T
dU T
Chapter 2: The First Law of Thermodynamics
Energy of a system
Kinetic energy: When a system is in motion, it has kinetic energy.
Many forms of kinetic energy
Vibration (the energy due to vibrational motion)
Rotation (the energy due to rotational motion
The chemical potential
If the composition changes, Gibbs free energy is not only the function of T
and P, but also the function of chemical species (n-number of moles)
G G(T , P, ni , n j , .)
Differentiation of G:
dG (
dG
dG
dG
dG
) P ,ni ,n j . dT ( )T
Chapter 4: The Statistical Interpretation of Entropy
Classical Thermodynamics - deal with macroscopic, measurable
properties of a system. But it gives little insight about the properties of
atoms and molecules in the system.
Entropy:
For adiabatic system,
Chapter 3: The Second Law of Thermodynamics
The first law of thermodynamics: energy conservation
State 1
U q w
State 2
Two extreme cases:
Heat Work
q = 0: U = -w
w = 0: U = q
Question:
If q 0 and w 0, is there a definite amount of work, which
the system
Einstein Theory-calculation of heat
capacity of a solid as a function of T
Consider a crystal containing n atoms;
each behaves as a harmonic oscillator
which vibrates with a fixed frequency
Einstein crystal
A harmonic oscillator can have the ith
energ
Heat engine
Convert some heat to work
Heat reservoir at
high temperature T2
q2
withdrawn
Heat
engine
q1
transferred
Cold reservoir at
low temperature T1
converted
Work, w
After a Carnot Cycle process: the system returns to its initial state
q2
P
t2
A
q2
For a reversible Carnot engine
Efficiency:
Heat reservoir t2
q2
w
Carnot
q1
Cold reservoir t1
w
q2
VB
V
V
V
RT1 ln D RT2 ln B RT1 ln B
VA
VC
VA
VA
V
V
RT2 ln B
RT2 ln B
VA
VA
RT2 ln
R(T2 T1 )ln
RT2 ln
VB
VA
VB
VA
T2 T1
T
1 1
T2
T2
For a Carnot Cycle proc
Partial molar quantities
The molar value of any property of a component of a mixture is
called the partial molar value of the property
A mixture with component i and j
The partial molar value of property Q
of component i in a mixture
Q
Qi ( )T , P ,n j
n
EMA 5106 Thermodynamics for Materials Science
INSTRUCTOR:
Dr. Jiyu Fang
Office:
ENGR-I, ROOM 207B
E-mail:
Jfang@mail.ucf.edu
Office hours:
M/W 10:00am-11:00am
OBJECTIVES:
To enable students to understand and apply the
concepts and principles of thermodyna
Chapter 9: The Behavior of Solution (Continue)
Partial molar Gibbs free energy of i in the solution: Change in Gibbs
free energy by mixing one mole of component i to the solution
G i (l ) G RT ln pi
o
i
Partial molar Gibbs free energy of the solution of
Regular solution
G M RT ( X A ln X A X B ln X B )
H
M
X A H
M
A
X BH
M
B
' ( X A X B2 X B X A2 ) ' X A X B
Raoult ideal solution
G M ,id RT ( X A ln X A X B ln X B )
H M ,id 0
The properties of a regular solution are best examined by the
concept of e
Effect of temperature on entropy if temperature is higher than melting
temperature
A(S,0)
A(l,T)
A(S,Tm)
Tm
c p(S )
298
T
ST S 298
A(l,Tm)
T
cl ( S )
Tm
T
dT S m
Richards rule: the entropy of the fusion
of metals should have the same value,
leading to a
Chapter 8: The Behavior of Gases
P-V-T relationship of gases
- Ideal gas
PV
1
RT
PV
1limitP0
- Real gas: Experimental observation
RT
When P approaches to 0, gas behaved as ideal gas.
P-V curves
(isothermal lines) for
real gas at different T
- Deceasing
The Behavior of Gases
P-V-T relationship of gases
There is a critical temperature
At critical Tcr
T < Tcr
Liquid and vapor can exist
T > Tcr
No liquid phase
For a closed system of fixed composition at constant temperature, the change in
Gibbs free energy
Problem 1. The Vapor pressure of solid NaF varies with temperature as
34450
ln p
2.01ln T 33.73
T
The Vapor pressure of liquid NaF varies with temperature
as
ln p
31090
2.52ln T 34.66
T
Calculate
1.The normal boiling temperature of NaF
2.The temperatu
Chapter 9: The Behavior of Solution
Solution
Strong interactions between atoms/molecules
The interactions are determined by atom/molecule size and
electro-negativity.
The interactions determine how extent a component is soluble
in a solution and whethe
Chapter 10: Gibbs Free Energy, Composition, and
Phase Diagram of Binary Systems
Phases:
Gas
Liquid
Solid
Phase diagram:
Phase diagram the stability of phases as
a function of temperature and composition.
Stable phases:
Lowest Gibbs free energy
Coexist
Chapter 10: Gibbs Free Energy - Composition
Phase Diagram of Binary Systems (Continue)
The influence of T on the activity of B with composition. The
activity was obtained from the intercepts with the XB = 1 axis, of
M
tangent drawn to the free energy curv
Gibbs free energy of formation of a solution:
G ' n A G A nB G B
a binary A-B system
Partial molar value G for A and B
Molar Gibbs free energy of the solution
G X AGA X BGB
dG
GA G XB
dX A
dG
GB G X A
dX B
XB
nB
n A nB
nA
XA
n A nB
These expressions re
Standard Gibbs free energy change
1
Reaction: H 2 O2 H 2O
2
G o 247,500 55.85T
If PO2=10-10 atm, T = 2000K
At T = 2000K
Equilibrium constant:
G o
K p exp(
)
RT
KP
247,500 55.85
3
K P exp(
) 3.521 10
8.314T 8.314
pH O
2
1/ 2
O2
pH p
2
the state of equili
Review
System: A matter, or a region in space
Surroundings (environments): The region outside the system.
Boundary: The surface that separates the system from its
surroundings.
System
Boundary
Surroundings
Open System: Both mass and energy can cross the b
Chapter 12: Reaction involving pure condensed phases and
gaseous phase
1
M ( s ) O2 MO( s )
(1)
2
M (g)
1
O2 MO( g )
2
(2)
Equilibrium:
pM and pMO are saturated pressures of M and MO
Gas reaction is equilibrium
For reaction (2):
p MO
G o
KP
exp(
)
1
Zachary Bruckner
za649098
2/11/16
Assignment 3
Dr. Laviola is a computer science major but works with for the department of electrical
engineering. I chose this presentation because electrical engineers and aerospace engineers work
hand in hand with proje
Zachary Bruckner
za649098
3/30/16
Assignment 6 Lab Visit #1
My first lab visit was at the Materials Characterization Facility for Dr. Sohn. This tour
was off campus so it felt like the work being done was not particularly associated with UCF. The
lab itse
Zachary Bruckner
za649098
2/25/16
Assignment 5
I attended Dr. Zaurins presentation who is a civil engineer. Dr. Zaurin talked about how
civil engineers improve the quality of life through better structures, batter transportation, and
making air and water
Zachary Bruckner
za649094
2/4/16
Assignment 2
The first presentation that I attended was Dr. Zheng who is an industrial engineer.
Industrial engineers and aerospace engineers have a common goal, to make our products more
efficient and safe for consumer us
Zachary Bruckner
za649098
3/30/16
Assignment 7 Lab Visit #2
My second lab visit was at the Center for Advanced Turbines and Energy Research for
Dr. Kapat. Entering the main facility was like entering a factory. It felt like entering a major
company with n