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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