Week4.PropertiesofPureSubstancesII

GENESYSLaboratory

Objectives1. Introducetheconceptofapuresubstance2. Discussthephysicsofphase-changeprocesses3. IllustratetheP-v,T-v,andP-TpropertydiagramsandP-v-Tsurfacesofpuresubstances4. Demonstratetheproceduresfordeterminingthermodynamicpropertiesofpuresubstancesfromtablesofpropertydata5. Describethehypotheticalsubstance“idealgas”andtheideal-gasequationofstate6. Applytheideal-gasequationofstateinthesolutionoftypicalproblems7. Introducethecompressibilityfactor,whichaccountsforthedeviationofrealgasesfromideal-gasbehavior8. Presentsomeofthebest-knownequationsofstateGENESYSLaboratory

Property Tables Formostsubstances,therelationshipsamongthermodynamicpropertiesaretoocomplextobeexpressedbysimpleequations.Therefore,thermodynamicpropertiesarefrequentlypresentedintheformoftables.Someproperties(T,P)canbemeasuredeasily,butothers(u,h,s)cannotbemeasureddirectlyandarecalculatedbyusingtherelationsthatrelatethemtomeasurableproperties.Theresultsofthesemeasurementsandcalculationsarepresentedintablesinaconvenientformat.

200 0 2 2 3 6 3 2 2

1 1 vu uu

R T C bR T a a cP B R T A ev T v v v v T v

ga g --æ ö æ ö= + - - + + + +ç ÷ç ÷è øè ø

GENESYSLaboratory

Property Tables I• Propertytable:thermodynamicspropertiesaretabulatedintheformoftables-Saturated liquid and saturated vapor states

ion vaporizatofenthalpy or ion vaporizatofheat latent and between difference and between difference

vaporsaturated of volumespecificliquid saturated of volumespecific

=

=

=

=

=

fgfg

fgfg

g

f

hhhvvv

vv

A partial list of Table A-4GENESYSLaboratory

Linear Interpolation1. Determinespecificvolumeattemperatureof215˚Candpressureof10bar2. Needalinearinterpolation

GENESYSLaboratory

Property Tables II- Saturated liquid-Vapor mixture

A two-phase system can be treatedas a homogeneous mixture forconvenience

•WetVapor:mixtureofsaturatedliquidandsaturatedvapor• Quality (=drynessfraction)x:ratioofthemassofvaportothetotalmass(c.f.1-x:wetness)

• Saturatedmixtureareconsideredtobemixedwell,formingahomogenousmixture• Thepropertiesofthis“mixture”willsimplybetheaverageproperties.

gmmmm m

mm

x

f+=+=

=

vaporliquidtotal

total

vapor

where

GENESYSLaboratory

Summary

HomogeneousmixtureRealAssumption

GENESYSLaboratory

Property Tables III- Saturated liquid-Vapor mixture

Quality is related to the horizontaldistances on P-v and T-v diagrams

3

( )(1 )

or (m / kg)

where

f g

t avg f f g g

f t g t avg t g f g g

avg f g

avg f fg

fg g f

ave f

fg

V V VV mv m v m v m vm m m m v m m v m v

v x v xv

v v xvv v v

v vx

v

= +

= ® = +

= - ® = - +

Þ = - +

Þ = +

= -

-=

(kJ / kg) (kJ / kg)

avg f fg

avg f fg

u u xuh h xh

= +

= +

f gv v v< <

Inthesamemanner,GENESYSLaboratory

Property Tables IV- Superheated Vapor

- Compressed Liquid

A partial listing of Table A-6

Lowerpressure(P<Psat atagivenT)Highertemperature(T>TsatatagivenP)Higherspecificvolumes(υ>υgatagivenPorT)Higherinternalenergies(u>ug at agivenPorT)Higherenthalpies(h>hgatagivenPorT)Higherpressure(P>Psat atagivenT)Lowertemperature(T<TsatatagivenP)Lowerspecificvolumes(υ<υfatagivenPorT)Lowerinternalenergies(u<uf at agivenPorT)Lowerenthalpies(h<hfatagivenPorT)• Stronglydependsontemperatureratherthanpressure▶ totreatcompressedliquidassaturatedliquidatthegiventemperature

Tfyy @@

GENESYSLaboratory

Summary

Hereisatip!0)Atleasttwoconditionsarerequiredtodeterminethestate1) Notethetypeoffluid(e.g.water,R-134etc)2) IfTisgiven,drawT-v diagramanduseTemperatureTable3) IfPisgiven,drawP-v diagramandusePressureTable4) IfPandTisgiven,itwouldbesuperheatedgas.IfthegivenTisgreaterthanthesaturatedTemperature,itisdefinitelyasuperheatedgas.Otherwise,itisacompressibleliquid5)Thereisexceptions

GENESYSLaboratory

Reference State and Reference Values•Thevaluesofu,h,andscannotbemeasureddirectly• Theyarecalculatedfrommeasurablepropertiesusingtherelations betweenthermodynamicproperties• Those relationsgivethechangesinproperties,notthevaluesofpropertiesatspecifiedstates• Needtochooseaconvenientreferencestate• Assignavalueofzeroforaconvenientpropertiesatthatstate• Ex)water:thestateofsaturatedliquidat0.01oC istakenasthereferencestate,uandhareassignedzerovalues• Refriegerant-134a,thestateofsaturatedliquidat-40oC istakenasthereferencestate,andhandsareassignedzerovalue

GENESYSLaboratory

The Ideal-Gas Equation of State• Equationofstate:Anyequationthatrelatesthepressure,temperature,andspecificvolumeofasubstance• Ideal-gasequationofstate- Thesimplestandbestknownequationofstateforsubstancesinthegasphase- PredictstheP-v-T behaviorofagasquiteaccuratelywithinsomeproperlyselectedregion

P =absolutepressureT =absolutetemperaturev=specificvolumeR =GasConstantdifferentforeachgasRu :universalgasconstant&sameforallsubstancesM :molarmass(molecularweight)

or TPv RT P Rv

æ ö= = ç ÷è ø

MRR u=

Ru=8.31447kJ/kmol.K8.31447kPa.m3/kmol.K0.0831447bar.m3/kmol.K1.98588Btu/lbmol.R10.7316psia.ft3/lbmol.R1545.37ft.lbf/lbmol.R•Molarmass:themassofonemoleofasubstance ingrams,or

themassofonekmol inkilograms•Massofsystem=molarmassⅹmolenumber:m=MN(kg)

GENESYSLaboratory

Compressibility Factor-A Measure of Deviation from Ideal-Gas Behavior

• CompressibilityFactor(Z):Acorrectionfactorthatcanaccuratelyaccountfordeviationfromideal-gasbehavioratagiventemperatureandpressure

PRTv

vvZ

ZRTPv

RTPvZ

actual

ideal

actual

=

=

=

=

where

or or

crR

crR T

TTPPP == and

• GasesbehavedifferentlyatagivenTandP,buttheybehaveverymuchthesameatTandPnormalizedwithrespecttotheircriticalTandPwhere PR :reducedpressure,TR :reducedtemperature,vR :Pseudo-reducespecificvolume• Principleofcorrespondingstates:TheZfactorforallgasesisapproximatelythesameatthesamereducedpressureandtemperature

GENESYSLaboratoryGENESYSLaboratory

actR

cr cr

vvRT P

=

Compressibility ChartGeneralizedcompressibilitychart1.Atverylowpressure(PR≪1),gasesbehaveasanidealgasregardlessoftemperature2.Athightemperature(TR≫2),idealgasbehaviorcanbeassumedwithgoodaccuracyregardlessofpressure(exceptwhenPR≫1).3.Thedeviationofagasfromideal-gasbehaviorisgreatestinthevicinityofthecriticalpoint

SaturatedvaporstatesSaturatedliquidstates

GENESYSLaboratory

The Ideal-Gas Equation of State (Continue)

TRvPvNVTNRPVNRRMNmR

mRTPVmvV

u

uu

=®==®===®=

)(

2

22

1

11

TVP

TVP=

•manygasessuchasair,nitrogen,oxygen,hydrogen,helium,argon,neon,krypton,andcarbondioxide-Treatedasidealgases•Watervaporinsteampowerplantsandrefrigerantvaporinrefrigeratorsshouldnotbetreatedasidealgases.-Thepropertytablesshouldbeusedforthesesubstances•Watervaporinlowpressure- treatedasidealgas Percentageoferrorinvolvedinassumingsteamtobeanidealgas,andtheregionwheresteamcanbetreatedasanidealgaswithlessthan1percenterror

Attwodifferentstates

GENESYSLaboratory

Other Equations of State

( )

cr

cr

cr

cr

PRTb

PTRa

RTbvvaP

8 and

6427

where

22

2

==

=-·÷øö

çèæ +

:Theintermolecularattractionforces:Volumeoccupiedbythemoleculesthemselves

2

aPv

æ ö+ç ÷è ø

( )v b-

GENESYSLaboratory

Summary

GENESYSLaboratory

• TherelationsbetweenthermodynamicpropertiesP-v-T- UsingpropertyTableforwater,refrigerantvapor- Usingidealgasequationofstateforothergases