PHASE RULE

Prof. H. K. KhairaProfessor in MSME Deptt.

MANIT, Bhopal

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.

The Gibbs Phase Rule

• The phase rule isf = c – p + 2

Wheref = degrees of freedomc = number of componentsp = number of phases

at equilibrium for a system of any composition.

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.

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

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.

Chapter 7

Examples of Two Phases

10t/℃

A

DC

0.00611

0.01

solid

gas

liquid

O

P /

10 5

Pa

374.2

218 atm

H2O phase diagram: P — T

Line

Point

Region

99.974

1 atm

0.0024

I

R

S

Y

Tf TbT3

11

H2O phase diagram: P — TRegion (s, l, g):

f=2, one phase

t/℃

A

D C

0.00611

0.01

solid

gas

liquid

O

P /

10 5

Pa

374.2

218 atm

99.974

1 atm

0.0024

I

R

S

Y

Tf TbT3

Line (OA, AD, AC):

f=1, two phases in equilibrium

Point (A):

f=0, three phases in equilibrium

Tc

Simple Example

13

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

One-component phase equilibrium

Hence, for a one-component system (pure water)

Physical Chemistry

Chapter 7

Phase Rule in Metallurgical Systems

• But in case of metallurgical systems, the pressure is kept constant.

• Hence the Phase Rule gets modified toF = C – P + 1