PVT Behavior

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CHEMICAL ENGINEERING

THERMODYNAMICS

Course no: CHE C311 / F213

Instructors: Dr. Srinivas Krishnaswamy1st Semester 2012 2013

CHEMICAL ENGG. GROUP

BITS PILANI K. K. BIRLA GOA CAMPUS


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Contents

Phase equilibrium of a pure substance(T - , P - and P-T diagrams)

Saturation pressure, saturation temperatureand vapour pressure curveConcept of an ideal gas

Equations of stateIdeal gas lawReal gas: Compressibility


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Phase equilibr ium of a pure substance

PhaseHomogeneous distinct form of matter that is

solid, liquid or gasThe aim here is to study the phases in which

pure substances can exist and also the

condition of states as specified by its properties under which it may exist in a particular phase


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Note: pressure isconstant


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Phase equilibr ium of a pure substance on a T- diagram

a

Process a: Ice at 40 oC to iceat 0 oC (no phase change)

c Process c: Water at 0oC to water at

100 oC (no phase change)

e

Process e: Steam at 100 oC to highertemperature (no phase change)

NOTE: PRESSURE

CONSTANT

Process b: Ice at 0 oC to

water at 0 oC (phase change)

b Process d: Water at 100oC to

steam at 100 oC (phase change)

d

f g

g - f = fg

t

-40 oC

0 oC

100 oC


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Phase change occurs only at a particular temperature and pressure referred to as saturation

temperature and pressure respectively

For e.g. at 101325 Pa, water boils at 100 oC. Hence101325 is the saturation pressure corresponding

to temperature of 100 oCEvery temperature has a saturation pressure

corresponding to it and vice-versaPhase change can occur at any temperature provided the pressure corresponding to this

temperature is saturation pressure


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The relationship between T sat and P satcan be expressed inthe form of a curveknown as vapour-

pressure curve

Each point on thecurve representsequilibrium betweenliquid and vapour Tsat

P sat

0.1 MPa

100 oC

Liquidregion

Vapour

region

Vapour pressure curve for water


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Phase equilibr ium of a pure substance on a T- diagram

At higher pressuresAs saturation pressure increases saturation

temperature (for boiling and

condensation) increasesAs saturation pressure increases, fg decreases and becomes zero at apressure of 220.9 bar at which

f = g = 0.03155 m 3 /kgThis point is the critical point. No distinct

phases exist above this pressure andtemperature. Vapour is termed as gas

above critical point and cannot becondensed or converted back to liquid

At lower pressures

As saturation pressuredecreases the saturation

temperature for vaporizationdecreases

At lower pressures lines formelting and vaporization comeclose until at 0.006113 (0.01 oC)

bar they co join. This is thetriple point

All three phases co exit attriple point


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Effect of pressure


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Liquid-vapour region

only


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Phase equil ibr ium of a pure substance

Each point on the curve shown in the T- diagramrepresents the state of the substance

Saturation state State in which a substance exists ina single phase, is in equilibrium with another phase and is at saturation temperature and

pressureFor e.g. liquid water and steam are in equilibrium at

100 oC at 101325 Pa. Similarly at 0 oC liquidwater and ice are in equilibrium


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Liquid at X (at 0.3 MPa and

70 oC) is consideredsubcooled or compressed

Subcooled because

T = 70o

C < t sat (0.3 MPa)Compressed becauseP = 0.3 MPa > Psat (70 oC)

t

0o

C

t oC135 oC

70 oC

Note: decrease in at 0o

C

0.3 MPa

0.03 MPa

X


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Superheated stateIn this case temperature is above saturation

temperature corresponding to a given pressure

For e.g. t = 135 oC > 70 oC corresponding tosaturation pressure of 0.03 MPa. Hencewater will be vapour which is superheated


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Phase equil ibr ium of a pure substance on a P- diagram

P,

M Pa

0.1a

Process a: Vapourcompressed (no phase

change)

100 oC

b

Process b: Vapourcompressed further,

condensation occurs (phasechange)

c

Process c: Liquidcompressed, (no phase

change)


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Concept of an ideal gas

Region A : Hightemperature in excess of critical temperature

Region B : Low pressure

At a certain point bothbecome 1

Behaviour of gases underthese conditions ischaracterised by idealgas behaviour


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An ideal gas is one in whichIntermolecular forces of attraction or

repulsion are negligibleMolecules are perfectly elastic and rigid. No loss of momentum after collisions withcontainer wallsVolume occupied by gas molecules isnegligible as compared to the container volume

Concept of an ideal gas


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Equation of state

Properties can be correlated through a functionalrelation of the form

f(P, , T ) = 0This is called the equation of state

They are put in 3 categories:Theoretical : derived based on kinetic theory and

statistical thermodynamicsGeneralized : Makes use of Z or compressibility factor Empirical : Curve fitting data from experiments. Most

accurate, but could be limited by range


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I deal gas L aw

Unit mass basis

P = RT

Total mass basis

PV = mRT

Total mole basis

PV = nRT

Unit mole basis

P = RT

Note R is specific gas constant(J / kg. K)

R is the universal gas constant =R M where M = molecular

weight = 8314.4 J / kmol.K


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Real gas and compressibil i ty

Deviation from ideality occurs due to assumptionsthat are not strictly valid. Volume of gas is

comparable to vessel volume and alsointermolecular attraction cannot be ignoredSeveral equations of state exist accounting for this

deviationOne term used to signify departure from ideality is

named compressibility factor z or justcompressibility


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ideal = RT / P real = ( RT / P ) z z = P / RT

z = real / idealz is dimensionless and

becomes 1 for anideal gas

z < 1 means actualdensity is greater

z can be also be lessthan 1

z being in terms of P , T and is a

property

An equation of statecan be writtenhaving form

z = f( P, T ) and canbe plotted keeping

T constant(compressibility

chart)


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Different charts will be needed for differentgases. One single chart can however be

developed based on L aw of corresponding states Pressure temperature and specific volume areexpressed in dimensionless form using

P r

= P / P c;

r= /

c; T

r = T / T

c where subscript r and c denote reduced and

critical values respectively


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L aw of corresponding states

If two substance have the same reducedpressure and reduced temperature they

have the same reduced volume

Mathematically z = f ( P r , T r )


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At all temperatures z 1as P r 0At temperatures equal to twice the critical value

(T r = 2) and above, z = 1 over a wide range of pressures upto 5 times the critical pressureThe compressibility factor at critical point iscalled critical compressibility and is found to beequal to 0.275 for all substances


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Objective Assessment

Phase changeIdeal and non-ideal behaviour Equations of stateCompressibility factor Accentric factor

We are what we repeatedly do. Excellence, therefore,is not an act but a habit.

Aristotle

PVT Behavior

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