What determines how matter behaves?  Thermodynamics.
1. What determines how matter behaves?
Final Stable State  Equilibrium State
Gibbs free energy: Minimum (at specific T, P)
Classical thermodynamics  Macroscopic phenomena.
2. 
Statistical thermodynamics  Microscopic description
Particles : atoms, electrons, molecules.

Quantum mechanics
Probability (distribution function)

3. Thermodynamics V.S. Kinetics
 Energy
Thermodynamics: 
 Equilibrium state
Reaction rate
Kinetics: 
Metastable state
4. Thermodynamic systems of materials
① material system:
 Unary or/ multi-component (binary, ternary, quaternary)
 Homogeneous/ Heterogeneous
 Closed/ Open
 Non-reacting/ Reacting
 Simple/ Complex
Simple system : energy changes due to mechanical, thermal,

and chemical variation.

② 
Complex system : energy changes due to gravitational, electrical, magnetic

and surface effects.
Introduction to the Thermodynamics of Materials
5. Thermodynamic Variables
State functions or process variables

Intensive or extensive variables
 State function: a quantity that depends on the condition of the system and
not on how the system arrived at that condition.
 State function is independent of path.
Zf
 Z  Z final  Z initial   dZ
Zi
e.g. P, V, T, Xk, S, U, G, H, A
 For a very complex process, △Z can be computed by the simplest
path connecting the initial and the final states.
 State function can be expressed by exact differential, dZ.
 Process variable: a quantity that only has meaning for a changing system
and its value for a process depends explicitly on the path.
Work , W W , W
e.g. 
QQ , Q
 Heat ,
W  F  d x
W 
path

F dx
1.  dZ  0, but
or


 W  0
Pr essure : P PdV 
Stress :   d 

2. Force :  Electric :   dq 
Magnetic :   dM 

Surface tension :   dA
 “Intensive” property may be defined to have a value at a point in the system.
It does not depend on the size of the system.
e.g. P, T, Xk, ρ(density), V , S , U , H , A, G
 “Extensive” property depends on the size of the system
e.g. V, S, U, H, A, G, nk
Introduction to the Thermodynamics of Materials
6. Concept of state
Microscopic state : statistical distribution of all constituent particles.
* 
Macroscopic state : phenomenological property of a system.
* Thermodynamic state of the simple unary system is uniquely fixed when teh
values of two independent variables are fixed.
* Any two properties could be chosen as the independent variables. P, T are the
most amenable to control.
* Consider a pure gas V = V(P,T). Equation of state?
If Eq. of state is known, we can calculate △V.
(P1, T1) -> (P2, T2), △V = (V2-V1) = ?
Two paths
① 1-> a-> 2
② 1-> b-> 2
V
V=V(P,T)
b
1  a 
isobaric

b  2

1  b isothermal
a  2

a
1
2
T
P1
P2
P
T1
T2
T2  V 

1  a : Va  Vb  T1  T  dT

P

Path 
a  2 : V  V  P2  V  dP
2
a
P1  P T

Introduction to the Thermodynamics of Materials
T2  V 
P2  V 
dT   
 V  V2  V1   

 dP
T1
P1
 P  T
 T  P
P2  V 

1  b, Vb  V1  P1  P  dP

T

Path 
b  2, V  V  T2  V  dT
b
2
T1  T  p

P2  V 
T2  V 
dP   
 V '  V2  V1   

 dT
P1
T1
 T  P
 P  T
V  V ' V is indep. of path.
V is state function, dV is exact differential.
 V 
 V 
V  V(T, P) dV  
 dT  
 dP
 T  P
 P  T
For any values of T1, P1, the gas system is at equilibrium only when it has
that unique volume, V1, which corresponds to T1 and P1.
P
7. Equation of state of an ideal gas
 Boyle' s law : constant T, P  1
V




Charles ' s law : constant P, V  T

T2
v
T1
V
V
P1
<
P2
T
Introduction to the Thermodynamics of Materials
 at T (Po  P) Boyle's law :
PoV T , Po   PV T , P 
at Po To  T  Charles' s law :
V Po , To  V Po , T 

To
T
T  0 o C  273.15K
Take :  o
 Po  1 atm
 Po 

T  V Po , To 
 P  V T , P 
To
PV PoVo

 Cons tan t.
T
To
Avogadro's hypothesis : Volume per " g - mole" of all " ideal gas" at 0 o C ,
P  1 atm is 22.414 l.
1 atm  22.414 l
atm  l
 0.082057
mole  273.15K
K  mole
 Ideal gas law (equation of state of ideal gas) :
 gas constant  R 
For one mole gas : PV  RT
For n mole gas : PV'  nRT
molar volume : V 
V'
n
N
 101325Pa  1013.25hPa
m2
1 atm  liter  101.325 J
Note : (1) 1 atm  101325
atm  liter
J
 8.314
K  mole
K  mole
(2) Absolute temperature scale (Kelvin)
R  0.082057
ice point : 0 o C , 32 o F
1 atm, H 2 O 
boil point : 100 o C , 212 o F
1802 Luis & Lussac : Thermal expansion coefficient of " permanent gas"
is a constant.
Thermal expansion coefficient :  
1  V 


V  T  P
Take V  Vo at 0 o C
 
1
273.15
for all gas when P  0
hypothetical gas : ideal gas
 When T  - 273.15 o C, mole volume of gas is zero,
 low temperature limit
 T  0K  -273.15o C
T(K)  T( o C)  273.15
Introduction to the Thermodynamics of Materials
Charles’s law:
P=0.5 atm
V
P=1 atm
P=2 atm
P=5 atm
-273.15℃
0K
0℃
T
273K
Introduction to the Thermodynamics of Materials