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he fascinating world

of

Thermodynamics

Instructor

Dr. Madhusree Kundu

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Thermodynamics

Lecture # 3

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Pure Substance

The pure substance is one that has ahomogeneous and invariable chemicalcomposition.

A pure substance may exist in manyphases, but the chemical composition is

same in all the phases.

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In our analysis, we will deal only withsimple compressible substances andsubstances whose surface effects,

magnetic effects, and electric effects arenegligible.

Example: liquid water, water vapor, ice, a

mixture of liquid water and water vaporare all pure substances.

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Depending on the nature of substance,

applied pressure and temperature, thechange in molar volume of the

substances may be large, the

substances are compressible and wherethe change in molar volume is less

then those are incompressible.

Liquids and solids are generally

incompressible, gases are compressible

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Properties of a puresubstance

What we need to study about a pure substance?

The phases in which a pure substance

may exist.

The number of independentproperties of pure substance.

Methods of presenting thermodynamic

properties.

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Properties of a puresubstance

Example:We need to know properties ofwater to determine pipe diameter throughwhich it has to flow.

Example:We need to know properties ofsteam in order to design a boiler.

Understanding the properties andbehavior of substances is essential fordesigning and sizing various equipment.

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Phase Rule The number of intensive parameters

that can be varied independently toestablish the intensive state of a system,

is called the degree of freedom, F of

the system and is given by the

celebrated phase rule of J. Willard

Gibbs (1875).

F=N- +2, where N is the number of

components, is the number of

coexisting phases.

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The intensive state of a system containing

N chemical species, and phases in

equilibrium is characterized by the

intensive variables pressure(P),

temperature T and (N-1) mole fractionsfor each phase. These are called phase

rule variables

The number of phase rule variables are

2+(N-1) .

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The masses of the phases are not phase

rule variables. The masses of the phases

have nothing to do with the intensive state

of the system.

Example:Liquid water is in equilibrium

with its vapour, Find the degree of

freedom of the system?

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This result is in agreement with the well

known fact that at a given pressure water ishaving only one boiling point. Either

temperature or pressure can be varied

independently when water is in equilibriumwith its vapour

Applying phase rule F=N- +2. Here

N=1, =2, Hence F=1.

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Example:Liquid water is in equilibrium

with a mixture of water vapour and

nitrogen. Determine F

Applying phase rule F=N- +2. Here

N=2, =2, Hence F=2.

T and P may be independently varied, but

once they are fixed, The system described

can exist in equilibrium only at a

particular composition of of the vapour

phase.

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Vapor-Liquid-Solid Phase

Equilibrium in a PureSubstance

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Constant pressure change from liquid to

vapor phase for pure substance

InitialConditions:T= 20OCP= 100 kP

Tincreasesconsiderably

increasesslightlyPremains const.(100 kP)

Tremains const.(99.6 OC)

increases verymuchPremains const.(100 kP)

Tincreasesincreases

Premainsconst.

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Phase Equilibrium in a PureSubstance

Saturation temperature means thetemperature at which vaporization takes

place at a given pressure. This pressure

is called the saturation pressurefor thegiven temperature.

Example: For water at 99.6OC the

saturation pressure is 100 kP, and forwater at 100 kP the saturation

temperature is 99.6OC.

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Vapor-pressure curve of a puresubstance

A point on this

diagram represents

a state of thesubstance. Any point

lying on the curve is

a saturated state.

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0

200

400

600

5 50 100 150 200

Tsat,oC

Psat,kPa

475.8kPa

101.35kPa

Temp,

Tsat,oC

Saturation

pressure,Psat, kPa

0.01 0.6113

5 0.4

10 0.87

30 4.25

50 12.35

100 101.3

150 475.8

200 1554

250 2973

Generating vapor-pressure curve of water

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Phase Equilibrium in a PureSubstance

At saturation temperature and pressure, If a

substance exists as vapor, it is calledsaturated vapor.

At saturation temperature and pressure,

If a substance exists as liquid, it is called

saturated liquid.

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If for given pressure, the temperature of

liquid is lower than saturation temperature,

it is called a subcooled liquid(T < TS) or a

compressed liquid(P > PS).

If for given pressure, the temperature ofvapor is greater than saturation

temperature, it is called a superheated

vapor.The substances called gases are actually

highly superheated vapors.

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Quality has meaning only forsubstance at saturated state.

A substance exists as part liquid and

part vapor at saturation temperature.

Quality, x= mass of vapor/ total mass

Quality is an intensive property.

Example:For saturated vapor,

quality, x = 100%

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Quality, x

Only defined when the system containstwo-phase mixture of a single substance.

x= m

mg

Liquid, mf

Vapor, mg

gf mmm

Saturated

Saturated

P, Tsat

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A piston cylinder contains 5 kg of water

liquid-vapor mixture, in which 3 kg is inliquid phase. Find the quality. (How muchpercent of the mixture is in vapor phase?)

x=

Example

m

mg

Liquid,

mf=3kg

Vapor, mg

gf mmm kg3 fm5kg,m

2kg3kg5kg

mmm fg

40%or4.05

2

kg

kg

m=5kg

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A piston cylinder contains 5kg of water-watervapor mixture, in which 80% is in vapor phase.How much liquid is in the mixture?

Example

mmx g /

Liquid,

mf=1kg

Vapor, mg

gf mmm

5kg,m

xm-m

mmm gf

m=5kg

0.2x-1

1kg0.8)-(15kg

x)-m(1

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Generating the T-vdiagram

P=1 atm

T=20oC

State 1

heat

W1

W2W3

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Generating the T-vdiagram

P=1MPa

T=20oC

State 1

heat

W1

W2W3

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Temperature-Volume Diagram for

water (showing liquid & vapor phases)

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T-vdiagram of a pure substance

Tc

vc

Subcritical

isobars

Supercritical

isobar

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Liquid+vapor region

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Compressed liquid region

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Superheated vapor region

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Supercritical fluid region

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Supercritical fluid region

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Important PointsThe boiling temperature of a pure substance

increases with pressure. The specific volumes vfandvgof the saturated liquid and vapor also change withpressure.The normal boiling temperatureof a pure substanceis the temperature at which it boils under a pressure

of exactly 1 atm.A series of isobars can plotted on a T-v diagram. Ifthe locus of all saturated liquid and vapor states areconnected, a dome enclosing the region of two phases(liquid+vapor) results.

Each pure substance has one isobar that becomeshorizontal (flat) at only one point: critical point. Thispoint coincides with the top of the two-phase dome.

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Important Points

The T-v diagram contains three single phase regions(liquid, vapor, supercritical fluid), a two-phase(liquid+vapor) region, and two important curves - thesaturated liquid and saturated vapor curves. The numberof regions and curves will increase when we considersolids.The saturated liquid and vapor curves meet at the criticalpoint, which represents the highest temperature andpressure in which vapor and liquid phases can coexist.The single phase liquid region is also called subcooledliquid because, at a given pressure, temperature will bebelow the boiling temperature.The single phase vapor region is also called superheatedvapor because, at a given pressure, temperature willalways be above the boiling temperature.