The document discusses the phase rule, which relates the degrees of freedom, number of components, and number of phases in a system at equilibrium. It defines key terms like phase diagram, phase boundary, component, and phase. The phase rule statement is f=c-p+2, where f is degrees of freedom, c is number of components, and p is number of phases. For a single-component system like water, this means the degrees of freedom is 2 when one phase is present, 1 when two phases coexist, and 0 when three phases are in equilibrium. Examples are also given for solid, liquid, and gas phases in water and metallurgical systems where pressure is constant.

1. PHASE RULE
Prof. H. K. Khaira
Professor in MSME Deptt.
MANIT, Bhopal

2. The Phase Diagram
• Phase diagram: shows the regions of
pressure and temperature at which its
various phases are thermodynamically
stable.
• Phase boundary: a boundary between
regions, shows the values of P and T at
which two phases coexist in equilibrium.

4. The Gibbs Phase Rule
• The phase rule is
f=c–p+2
Where
f = degrees of freedom
c = number of components
p = number of phases
at equilibrium for a system of any composition.

5. The Gibbs Phase Rule
• Degree of freedom (f): It is the number of external
variables that can be changed independently
without disturbing the number of phases in
equilibrium. These are pressure, temperature and
composition.
• Component: a chemically independent constituent
of a system
• number of components (c): the minimum number
of independent species necessary to define the
composition of all the phase present in the system
• Phase: a state of matter that is uniform throughout
in chemical composition and physical state.

6. The Phase Rule
• Number of phase (p):
– Gas or gaseous mixture – single phase
– Liquid – one, two and three phases
• two totally miscible liquids – single phase
• a slurry of ice and water – two phases
– Solid
• a crystal is a single phase
• an alloy of two metals – two phases (immiscible)
• one phase (miscible)

7. Chapter 7
The Phase Rule
(a)
(b)
The difference between (a) a single-phase solution, in which the
composition is uniform on a microscopic scale, and (b) a
dispersion containing two phases, in which regions of one
component are embedded in a matrix of a second component.
7

8. Examples of Two Phases

10. H2O phase diagram: P — T
D
218 atm
C
Y
P / 10 5 Pa
I
solid
liquid
Line
S
Point
1 atm
Region
R
0.00611
gas
A
O
0.0024 0.01
T3
Tf
99.974
Tb
374.2
t/℃
10

11. H2O phase diagram: P — T
Region (s, l, g):
D
P / 10 5 Pa
218 atm
C
f=2, one phase
Y
I
solid
Line (OA, AD, AC):
liquid
S
f=1, two phases in
equilibrium
1 atm
R
0.00611
gas
A
Point (A):
O
0.0024 0.01
T3
Tf
99.974
Tb
t/℃
374.2
Tc
f=0, three phases in
equilibrium
11

12. Simple Example

13. Chapter 7
Physical Chemistry
One-component phase equilibrium
Hence, for a one-component system (pure water)
f＝1－p＋2＝3－p，(C＝1）
f ≥0, p ≥1, 3≥p≥1
p＝1，f＝2
p＝2，f＝1
p＝3，f＝0
13

14. Phase Rule in Metallurgical Systems
• But in case of metallurgical systems, the
pressure is kept constant.
• Hence the Phase Rule gets modified to
F=C–P+1