the properties of pure substance

8/4/2019 The Properties of Pure Substance

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THE PROPERTIES OF PURE SUBSTANCE

BY :

AZIZI B. AHMAD ( AZ ) 06DKM10F1107MUHAMMAD FITRI B. AHMAD NASRUDDIN ( FI3 ) 06DKM10F1105

ABDUL RAHIM B. SAFREN (RHIM) 06DKM10F1106

MOHAMED FUAD NUR HADI (FUAD) 06DKM10F1122


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Properties of Pure Substances

What is a Pure Substance?

Pure substance has homogeneous and invariable chemical composition.

It can exist in different phase, but should have uniform chemical composition

throughout the extend of mass.

( AZ )


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Solid-Liquid-Vapour Phase Equilibrium of Pure Substances

The present study is based on an experiment, in which a substance is heated at

constant pressure.

The substance is allowed to pass through three different phases, temperature and

specific volume are recorded.

The change of state occurring in this process are carefully studied and plotted inp-

v,p-tand t-v diagrams.

100 kPa

iceat -15C

100 kPa

Waterat 0C

100 kPa

Waterat 100C

100 kPa

Steamat 120C

( AZ )


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The heat required for change of solid to liquid phase is called latent heat of fusion.

Asaturation state is a state from which a change of phase may occur without a

change in pressure or temperature.

Ice at 0C is atsaturated solid state and water at 100C is atsaturated vapour

state for a pressure of 100kPa

T

v

For water

For another

substance

0C4C

100C

T-vdiagramforheatingofapuresubstanceatconstantpressure( AZ )


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T

v

-150C

00

C

40C

1000C

1200Cp=100kPa

( AZ )


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The variation of saturation temperature with pressure for water

( AZ )


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(FUAD)


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(FUAD)

(FUAD)


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(FUAD)


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(FUAD)


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(FUAD)


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(AZ)


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(RHIM)


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(FUAD)


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v m3/kg

T0C

1.9820.00103

95p = 0.8455 bar

v m3/kg

p bar

0.71870.00106

2.5T= 127.40C

(AZ)


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A pure substance can exist as part liquid and part vapour during a vaporisation

process and the part of saturated liquid decreases as it progresses. For

thermodynamic analysis of such mixtures, the proportions the liquid and vapour

phase is to be determined. It is done with the help of a new property called quality

(x) which is defined as the ratio of the mass of vapour to total mass of the mixture.

g

f g

mx

m m

!

The specific volume, internal energy, and enthalpy of a pure substance which is a

mixture of saturated liquid and saturated vapour can be evaluated by knowing its

quality as follows

f f

f f

f f

v v xv

u u xu

h h xh

!

!

!

(FI3)


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Thermodynamic propertiesinsuperheated vapour region

v m3/kg

T0C

vg = 0.1941vf = 0.0011274

180p = 10bar

x= 0.7 mixtureofsaturated liquidandsaturated vapour

f g f f fgu u x u u h h x h! !

f g f

f f g

u u x u u

h h x h

!

!

400

0.3066

Superheatedstate

PropertiesofSaturatedWater (LiquidVapor):TemperatureTable

PropertiesofSuperheated WaterVaporp = 10 bar

(FI3)


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The Ideal Gas EquationofState

Equationofstaterelatespressure,temperature,andspecificvolume. Anideal-

gasequationofstatewhichpredictsp v T behaviourofagasisgivenby

pv R!

Risgas constantofthegasunderconsideration RR

M!

Thedeviationfromidealbehaviourcanbeeasilyaccountedbyintroducingacorrectionfactorcalledcompressibilityfactor pv Z T !

Different gases behave differently from ideal behaviour as pressure and

temperature are varied.

But they behave alike if pressures and temperatures are normalised with respect

to critical pressures and temperatures.

Thus reduced pressure (pr) and reduced temperature (Tr) obtained by

normalisation is

andr r

cr cr

p Tp T

p T! !

( FI3 )


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The Ideal Gas Law

Ideal Gas Law

In perfect or ideal gas the change in density is directly

related

to the change of temperature and

pressure asexpressed by the Ideal Gas Law

( FI3 )


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TheIdeal Gas Law relatespressure,temperature,andvolumeof

anideal or perfect gas. The Ideal Gas Lawcanbeexpressed

withtheIndividual Gas Constant:

p V = mRT (1)

where

p = absolute pressure (N/m2,lb/ft2)

V = volume (m3, ft3)

m = mass (kg,lb)

R= individualgas constant(J/kg.oK,ft.lb/slugs.oR)

T = absolutetemperature (oK,oR)

Ideal Gas Law and the Individual Gas Constant- R

Thisequation (1) canbemodifiedto:

p = RT (2)

wherethedensity

= m / V (3)The Individual Gas Constant - R - dependsontheparticulargasandis

relatedtothemolecularweightofthegas.

Equation (1) canalsobemodifiedto

p1V1/T1 = p2V2/T2 (4)

expressingtherelationshipbetweendifferentstatesforagivenmassofgas.

( FI3 )


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The Ideal Gas Law and the Universal Gas Constant - Ru

TheUniversal Gas Constant isindependentoftheparticulargasandisthe

sameforall "perfect" gases. The Ideal Gas Lawcanbeexpressedwiththe

Universal Gas Constant:

p V = nRu T (5)

where

p = absolute pressure (N/m2,lb/ft2)

V = volume (m3, ft3)

n = is thenumberofmoles ofgas present

Ru = universalgas constant(J/mol.oK,lbf.ft/(lbmol.oR))

T = absolutetemperature (oK,oR)

( FI3 )


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Comparisonofcompressibilityfactorsfor some gases

( FI3 )


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TheVander waals equationofstate 2

a

p v b RTV

!

2 227

and

64 8

cr cr

cr cr

T Ta

p p

! !

TheVirialequationofstate

2 3 4 5...

a T b T c T d TRTp

v v v v v !

TheBeattie-Bridgemannequationofstate

2 3 21RT c Apv v Bv vT v

!

0 01 and 1

a bA A B B

v v

! !

( FI3 )


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Constant Volume Specific Heat

Themolarspecificheat atconstantvolumeisdefinedby

Usingthefirstlawofthermodynamics thiscanbeputintheform

Foramonoatomicidealgas,

Thisvalueagreeswellwithexperimentformonoatomicnoblegasessuchas

heliumandargon,butdoesnotdescribediatomicorpolyatomicgases sincetheirmolecularrotationsandvibrationscontributetothespecificheat. The

equipartitionofenergy predicts

( FI3 )


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Constant Pressure Specific Heat

Themolarspecificheat atconstantpressureisdefinedby

Usingthefirstlawofthermodynamics fora

constantpressureprocessthiscanbeputinthe

form

Fromtheidealgaslaw (PV=nRT) under

constantpressureconditionsitcanbeseenthat

Sincetheconstantvolume

specificheat is

itfollowsthat

Foranidealmonoatomicgas

RHIM


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CHARACTERISTIC EQUATION FOR GASES

Thecharacteristicequationforgasescanbederivedfrom Boyleslawand Charleslaw.

Boyleslawstatesthatatconstanttemperaturethevolumeofagasbodywillvary

inverselywithpressure. Charleslawstatesthatatconstantpressure,thetemperature

willvaryinverselywithvolume. Combiningthesetwo,thecharacteristicequationfora

systemcontaining m kg ofagascanbeobtainedas

PV = mRT (1)

Thisequationwhenappliedtoagivensystemleadstotherelation(2) applicablefor

allequilibriumconditionsirrespectiveoftheprocessbetweenthestates.

(P1V1/T1) = (P2V2/T2) = (P3 V3/T3) = (PV/T) = Constant (2)

RHIM


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Inthe SI system,theunitstobeusedintheequationarePressure,P N/m2, volume,

V m3,mass,m kg,temperature, T Kandgas constant,R Nm/kgKor J/kgK

(Note:K= (273 + C), J = Nm).

Thisequationdefinestheequilibriumstateforanygasbody. Foraspecifiedgasbody

withmassm, if two properties like P, V are specified then the third property T is

automatically specifiedbythisequation. Theequationcanalsobewrittenas,

Pv = RT (3)

wherev = V/mor specific volume. The value forR for air is 287 J/kgK.

RHIM


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ApplicationofAvagadroshypothesisleadstothedefinitionofanewvolumemeasure

calledmolalvolume. Thisisthevolumeoccupiedbythemolecularmassofanygasat

standardtemperatureandpressure. Thisvolumeaspertheabovehypothesiswillbethe

sameforallgasesatanygiventemperatureandpressure. DenotingthisvolumeasVm

andthe pressureas Pandthetemperatureas T,

For a gas a, PVm = Ma Ra T

For a gas b, PVm = Mb Rb T

AsP, T andVmarethe sameinboth cases.

MaRa = MbRb = M R = Constant

TheproductM R is called Universal gas constant and is denoted by the symbol

R. Itsnumericalvaluein SI systemis8314 J/kg mole K. For any gas the value of gas

constant Risobtainedbydividinguniversalgasconstantbythemolecularmassin kg

ofthatgas. Thegasconstant R foranygas (inthe SI system, J/kg K) canbecalculated

using,

R = 8314/M RHIM

the properties of pure substance

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