L. D. COLLEGE OF ENGINEERING
RUBBER TECHNOLOGY
Sub:- THERMODYNAMICS OF ELASTOMERS &
POLYMERS
The Phase Rule & Phase Diagram
Some basic concepts
• Phase– A homogeneous region with distinct structure
and physical properties– In principle, can be isolated– Can be solid, liquid or gas
• Phase Diagram– Representation of phases present under a set of
conditions (P, T, Composition etc.)
F = C - f + 2F = # degrees of freedom
The number of intensive parameters that must be specified in order to completely determine the system
f = # of phasesphases are mechanically separable constituents
C = minimum # of components (chemical constituents that must be specified in order to define all phases)
The Phase Rule
Gibbs Phase RuleFor a closed, homogeneous system of constant composition (e.g., an ideal gas), we require twoparameters of state (for example, T and p) in order to describe it. For a heterogeneous systemin equilibrium, consisting of one component (e.g., water substance) and two phases (e.g., liquidand vapour), we require only one parameter of state (for example, T).
This example may be expressed more generally in terms of Gibb’s phase rule:
where =number of independent state variables at equilibrium c=number of components =number of phasesWe assume here that the masses of the components and phases are specified. As an example, For equilibrium between a pure plane surface of water and its vapour, we require only one state
Gibb’s Phase Rule
P + F = C + 2 P=number of phasesC=number of componentsF=number of degrees of freedom (number of independent variables)
Modified Gibbs Phase Rule (for incompressible systems)
P + F = C + 1
Pressure is a constant variable
F = C - P + 2
F = C - P + 1
Application of the phase rule
At triple point, P=3, C=1, F=0i.e. this is an invariant point
At phase boundary, P=2, C=1, F=1
In each phase, P=1, C=1, F=2
The Phase Rule
There are two types of phase components as per below;
=> One Component Systems
=> Two Component Systems
1 - C Systems
1. The system SiO2
1 - C Systems
2. The system H2O
2 - C Systems1. Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8)
2-C Eutectic Systems Example: Diopside - Anorthite
No solid solution
A simple phase diagram
Triple point(Invariant point)
Solid
Liquid
Vapor
Pressure
Temperature
Phase boundary
System: H2O
Construction of a simple phase diagram
• Conduct an experiment• Take 10 metal samples(pure Cu, Cu-10%Ni,
Cu-20%Ni, Cu-30%Ni………, pure Ni)• Melt each sample and then let it solidify• Record the cooling curves• Note temperatures at which phase
transformations occur
Results
L
S
L S
t
T
L
L + S
TL
TS S
L
L + S
TL
TS
Pure CuCu-10%Ni
Cu-20%Ni
L
L S
Pure Ni
S
TNi
TCu
The Eutectic Phase Diagram
T
A BWt%B
L
a+Lb+L
a+b
E
TE
CE
ab
LiquidusSolidusSolvus
L a + (b TE, CL=CE)
Thank You