Phase Rule2

8/3/2019 Phase Rule2

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PHASE DIAGRAMS OF ONE

COMPONENT SYSTEMS

PHASE DIAGRAM OF WATER

PHASE DIAGRAM OF CARBON DIOXIDE

PHASE DIAGRAM OF SULPHUR


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PHASE DIAGRAM OF WATER

WATER is the most common e.g. of 1 C System

It can exists in 3 Phases (Ice, water, vapor)

Composition of each phase can be specified interms of water

Different phases of water can exist under

different conditions of T & P


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Salient characteristics of phase diagram of water

CURVE OA

Represents equilibrium between

liquid water & vapor at different

Temperatures

Water Vapor

So on curve OA, P=2, C=1

Applying phase rule

F= C-P+2 = 1-2+2 = 1

Hence the curve OA is univariant.

Curve OA is called vaporization curve or vapor pressure curve as it

gives vapor pressure of water at different temperatures


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At 100 C, the vapor press. of water is equal to atmos. press i.e. 1 atm

or 760 mm of Hg. So 100 C is the BP of water

Curve OA starts from point O,

which is the triple point of water

(0.0098 C, 4.58 mm) and ends

at point A which corresponds toTc and Pc (374 C, 218 atm)

Beyond this temp, water in liq.

Form can not exist.



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Consider a point P on the curve

OA.

At this point P, liq water and vapor

are in eqil.

If T is increased along line PX, bykeeping P constant, then liq phase

will disappear.

Similarly if P is decreased along

line PN by keeping T constant,

then liquid phase will disappear.

Hence, in the region towards right side of point P, only vapor phase

can exist


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Similarly, if T is decreased along line PY by keeping pressure

constant, or if P is increased along line PM by keeping T constant,

then vapor phase will disappear

Thus, in the region towards left

side of point P i.e. in AOC region,

only liquid phase can exist

CURVE OB

The curve OB represents eqil.

Between ice & vapor

Ice Vapor

So, on curve OB, P=2, C=1 Hence F=C=P+2= 1-2+2=1

So, Curve OB is univariant

Curve OB is called sublimation curve. Curve OB starts from point O and

extends upto point B (-273C)



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CURVE OC

The curve OC represents eqil. Between ice & vapor

So, on curve OC, P=2, C=1

Hence F=C-P+2= 1-2+2=1

So, Curve OC is univariant

Curve OC is called fusion curve.

It shows effect of press. On

melting point of ice.


Ice Water

As can be seen from the diagram, curve OC is inclined towards

pressure axis. This indicates that melting point of ice decreases as

pressure increases.


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Regions between curves

The curves OA, OB, OC aredividing the phase diagram in

three regions or areas i.e.

Area AOC, BOC and AOB.

In each of these areas only 1

phase is +nt.

The region bounded by 2 curves

give the conditions of T & P

under which a single phase can

exist.

AOC Represents water, BOC Represents ICE & AOB Represents

vapor phase



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In all these areas (AOC, BOC, AOB)

P=1 (WATER or ICE or VAPOR)

C=1 (WATER)

Applying phase rule

F = C P + 2 = 1 1 + 2 = 2

So the degrees of freedom in

these areas is 2 (i.e system isbivariant) as both T & P are

required to be fixed to specify the

state of system.


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Triple Point (O)

Where the curves OA, OB & OCmeet is called triple point.

At triple point, T is 0.0098C and P

is 4.58 mm

3 phases can co-exist at this pointIce Water Vapor

So at Triple point

P=3 (WATER,ICE, VAPOR)

C=1 (WATER)

Applying phase rule

F = C P + 2 = 1 3 + 2 = 0 (invariant) as both T & P are fixed


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When T is decreased at point A, water gets transformed into ice

and curve OB is obtained.If water present at point O is carefully

and slowly cooled then it is possible to

take water below its normal freezing

point without the formation of ice and

the curve OA' is obtained which

corresponds to super cooled water

The curve OA represents the

following eqil. Water VaporSuper cooled

This eqil. is called metastable eqilibrium because even a small

disturbance in the system will convert super cooled water into ice

and curve OA will be merged into OB

Meta stable curve (OA')


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Values of T & P in some cases of water

Freezing Point of water

- 0C, 1 atm

Boiling Point of water

- 100C, 1 atm

Triple Point of water

- 0.0098C, 4.58 mm

Melting Point of water

- 0C, 1 atm


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WATER VAPOUR

Clausius-Clapeyron equation

Humidity variables

Clausius-Clapeyron Equation

We wish to determine the equilibrium pressure along the three phase-equilibrium curves

(see last figure). As an example of the method, consider the liquid-vapour equilibrium

sketched below:

Benoit-Pierre-Emile Clapeyron (1799-1864) was a French civil engineer who worked on the design and construction of steam

engines. He is best known for the equation describing the equilibrium vapour pressure over a liquid. The equation was ignored

until Clausius and Kelvin revealed its true significance for thermodynamics.


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Phase Rule2

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