Properties of Pure Substances and Property Diagram.pdf

Heat

1. Properties of Pure Substances and
Property Diagram

2. Pure Substance
Asubstancethathasafixedchemicalcompositionthroughoutthe
processunderconsiderationiscalledapuresubstancesuchas
water,air,andnitrogen.
Apuresubstancedoesnothavetobeofasingleelementor
compound.Amixtureoftwoormorephasesofapuresubstanceis
stillapuresubstanceaslongasthechemicalcompositionofall
phasesisthesame.

3. A pure substance is a system which is
(i) homogeneous in composition,
(ii) homogeneous in chemical aggregation, and
(iii) invariable in chemical aggregation.
Homogeneousincomposition‛meansthatthecompositionofeachpartofthe
systemisthesameasthecompositionofeveryotherpart.Compositionreferstothe
arrangement,ratio,andtypeofatomsinmoleculesofchemicalsubstances.Itdoesnot
matterhowtheseelementsarecombined.
Fig. 1: Illustrating the definition of a pure substance

4. ‚Homogeneousinchemicalaggregation‛meansthatthechemicalelementsmustbe
combined chemically in the same way in all parts of the system.
Example:
Inthefigure1thesystem(a)satisfiesthiscondition;forsteamandwaterconsistofidentical
molecules.
System(b)ontheotherhandisnothomogeneousinchemicalaggregationsinceintheupperpartofthe
systemthehydrogenandoxygenarenotcombinedchemically(individualatomsofHandOarenot
uniquelyassociated),whereasinthelowerpartofthesystemthehydrogenandoxygenarecombinedto
formwater.
Notehoweverthatauniformmixtureofsteam,hydrogengas,andoxygengaswouldberegardedas
homogeneousinbothcompositionandchemicalaggregationwhatevertherelativeproportionsofthe
components.

5. “Invariable in chemical aggregation‛ means that the state of chemical
combination of the system does not change with time (condition (ii)
referred to variation with position).
Thus a mixture of hydrogen and oxygen, which changed into steam
during the time that the system was under consideration, would not be a
pure substance.
Thus in summary, it is clear that only the system ‚a‛ of the above three
systems refers to as a pure substance.

6. Phase change of a pure substance was discussed earlier
PropertyDiagrams
Thephasesofasubstanceandtherelationshipsbetweenitspropertiesaremostcommonly
shownonpropertydiagrams.
Therearefivebasicpropertiesofasubstancethatareusuallyshownonproperty
diagrams.Theseare:pressure(P),temperature(T),specificvolume(n),specificenthalpy
(h),andspecificentropy(s).Whenamixtureoftwophases,suchaswaterandsteam,is
involved,asixthproperty,quality(x),isalsoused.
Therearesixdifferenttypesofcommonlyencounteredpropertydiagrams.Theseare:
Pressure-Temperature(P-T)diagrams,Pressure-SpecificVolume(P-v)diagrams,
Pressure-Enthalpy(P-h)diagrams,Enthalpy-Temperature(h-T)diagrams,Temperature-
entropy(T-s)diagrams,andEnthalpy-Entropy(h-s)orMollierdiagrams.

7. Pressure-Temperature (P-T) Diagram
Figure2istheP-Tdiagramforpurewater.AP-Tdiagramcanbeconstructedforanypure
substance.Thelinethatseparatesthesolidandvaporphasesiscalledthesublimationline.The
linethatseparatesthesolidandliquidphasesiscalledthefusionline.Thelinethatseparatesthe
liquidandvaporphasesiscalledthevaporizationline.Thepointwherethethreelinesmeetis
calledthetriplepoint.Thetriplepointistheonlypointatwhichallthreephasescanexistin
equilibrium.Thepointwherethevaporizationlineendsiscalledthecriticalpoint.At
temperaturesandpressuresgreaterthanthoseatthecriticalpoint,nosubstancecanexistasa
liquidnomatterhowgreatapressureisexerteduponit.
Figure 2: P-T Diagram for Water

8. Pressure-Specific Volume (P-v) Diagram
AP-vdiagramcanbeconstructedforanypuresubstance.
AP-vdiagramisdifferentfromaP-Tdiagraminoneparticularlyimportantway.Thereare
regionsonaP-vdiagraminwhichtwophasesexisttogether.Intheliquid-vaporregioninFigure
3,waterandsteamexisttogether.
Figure 3: P-v Diagram for Water

9. AtpointA,waterwithaspecificvolume(vf),givenbypointB,existstogetherwithsteamwitha
specificvolume(vg),givenbypointC.
ThedottedlinesonFigure3arelinesofconstanttemperature.
Thequalityofthemixtureatanypointintheliquid-vaporregioncanbefoundbecausethespecific
volumesofwater,steam,andthemixtureareallknown.Thequalitycanbefoundusingthe
followingrelationship.

10. Pressure-Enthalpy (P-h) Diagram
P-hdiagramcanbeconstructedforanypuresubstance.LiketheP-vdiagram,thereareregions
onaP-hdiagraminwhichtwophasesexisttogether.Intheliquid-vaporregioninFigure4,water
andsteamexisttogether.
Forexample,atpointA,waterwithanenthalpy(hf),givenbypointB,existstogetherwithsteam
withanenthalpy(hg),givenbypointC.
Figure 4: P-h Diagram for Water

11. The quality of the mixture at any point in the liquid-vapor region can be found using the following relationship

12. Enthalpy-Temperature(h-T)Diagram
Anh-Tdiagramforwaterisshowninfig.5.Asinthepreviouspropertydiagrams,thereareregions
ontheh-Tdiagraminwhichtwophasesexisttogether.Theregionbetweenthesaturatedliquidline
andthesaturatedvaporlinerepresentstheareaoftwophasesexistingatthesametime.Thevertical
distancebetweenthetwosaturationlinesrepresentsthelatentheatofvaporization.Ifpurewater
existedatpointAonthesaturatedliquidlineandanamountofheatwasaddedequaltothelatent
heatofvaporization,thenthewaterwouldchangephasefromasaturatedliquidtoasaturatedvapor
(pointB),whilemaintainingaconstanttemperature.
Figure 5: h-T Diagram for Water

13. As shown in Figure 5, operation outside the saturation lines results in a subcooled
liquid or superheated steam. The quality of the mixture at any point in the liquid-vapor
region can be found using the same relationship as shown for the P-h diagram.
Temperature-Entropy(T-s)Diagram
AT-sdiagramisthetypeofdiagrammostfrequentlyusedtoanalyzeenergytransfersystemcycles.
Thisisbecausetheworkdonebyoronthesystemandtheheataddedtoorremovedfromthesystem
canbevisualizedontheT-sdiagram.Bythedefinitionofentropy,theheattransferredtoorfroma
systemequalstheareaundertheT-scurveoftheprocess.Figure6istheT-sdiagramforpurewater.
AT-sdiagramcanbeconstructedforanypuresubstance.ItexhibitsthesamefeaturesasP-v
diagrams.

14. Figure 6: T-s Diagram for Water

15. At point A, water with an entropy (sf) given by point B, exists together with steam with an entropy (sg)
given by point C. The quality of the mixture at any point in the liquid-vapor region can be found using
the following relationship.

16. Enthalpy-Entropy(h-s)orMollierDiagram
TheMollierdiagram,isachartonwhichenthalpy(h)versusentropy(s)isplotted.Itissometimes
knownastheh-sdiagramandhasanentirelydifferentshapefromtheT-sdiagrams.Thechart
containsaseriesofconstanttemperaturelines,aseriesofconstantpressurelines,aseriesof
constantmoistureorqualitylines,andaseriesofconstantsuperheatlines.TheMollierdiagramis
usedonlywhenqualityisgreaterthan50%andforsuperheatedsteam.
Dr.Mollier,in1904,conceivedtheideaofplottingtotalheatagainstentropy,andhisdiagram
ismorewidelyusedthananyotherentropydiagram,sincetheworkdoneonvapourcyclescanbe
scaledfromthisdiagramdirectlyasalength;whereasonT-sdiagramitisrepresentedbyanarea.

17. Fig. 7: Enthalpy-entropy (h-s) chart.

18. Linesofconstantpressureareindicatedbyp1,p2etc.,linesofconstanttemperaturebyT1,T2,
etc.
Anytwoindependentpropertieswhichappearonthechartaresufficienttodefinethestate(e.g.,
p1andx1definestate1andhcanbereadofftheverticalaxis).
Inthesuperheatregion,pressureandtemperaturecandefinethestate(e.g.,p3andT4definethe
state2,andh2canbereadoff).
Alineofconstantentropybetweentwostatepoints2and3definesthepropertiesatallpoints
duringanisentropicprocessbetweenthetwostates.

20. Formation of steam
Iftheheatisimpartedtowater,ariseintemperaturewillbenoticedandthisrisewillcontinuetill
boilingpointisreached.Thetemperatureatwhichwaterstartsboilingdependsuponthepressureandas
suchforeachpressure(underwhichwaterisheated)thereisadifferentboilingpoint.Thisboiling
temperatureisknownasthetemperatureofformationofsteamorsaturationtemperature.
Therewillbeslightincreaseinvolumeofwaterduetowhichpistonmovesupandhenceworkis
obtainedasshowninFig.(ii).Thiswork,however,issosmallthatiscanbeneglected.

21. If supply of heat to water is continued it will be noticed that rise of temperature after the boiling point
is reached nil but piston starts moving upwards which indicates that there is increase is volume which
is only possible if steam formation occurs. The heat being supplied does not show any rise of
temperature but changes water into vapourstate (steam) and is known as latent heat or hidden heat.
Solongasthesteamisincontactwithwater,itiscalledwetsteam[Fig.(iii)]andifheatingofsteam
isfurtherprogressed[asshowninFig.(iv)]suchthatallthewaterparticlesassociatedwithsteamare
evaporated,thesteamsoobtainediscalleddryand
saturated steam.
If vg m3 is the volume of 1 kg of dry and saturated steam then work done on the piston will be
p(vg –vf)
where p is the constant pressure (due to weight ‘W’ on the piston).

22. Again,ifsupplyofheattothedryandsaturatedsteamiscontinuedatconstantpressuretherewillbe
increaseintemperatureandvolumeofsteam.Thesteamsoobtainediscalledsuperheatedsteamandit
behaveslikeaperfectgas.ThisphaseofsteamformationisillustratedinFig.(v).
Figure: Graphical representation of
formation of steam.

23. Important terms relating steam formation
Sensible heat of water (hf)
Itisdefinedasthequantityofheatabsorbedby1kgofwaterwhenitisheatedfrom0°C(freezingpoint)
toboilingpoint.Itisalsocalledtotalheat(orenthalpy)ofwaterorliquidheatinvariably.
Note.Thevalueofspecificheatofwatermaybetakenas4.18kJ/kgKatlowpressuresbutathigh
pressuresitisdifferentfromthisvalue.
Latent heat or hidden heat (hfg)
It is the amount of heat required to convert water at a given temperature and pressure into steam at the
same temperature and pressure. It is expressed by the symbol hfgand its value is available from steam
tables. The value of latent heat is not constant and varies according to pressure variation.
Dryness fraction (x)
The term dryness fraction is related with wet steam. It is defined as the ratio of the mass of actual dry
steam to the mass of steam containing it. It is usually expressed by the symbol ‘x’ or ‘q’.

24. Total heat or enthalpy of wet steam (h)
It is defined as the quantity of heat required to convert 1 kg of water at 0°C into wet steam at constant
pressure. It is the sum of total heat of water and the latent heat and this sum is also called enthalpy.
Superheatedsteam
Whensteamisheatedafterithasbecomedryandsaturated,itiscalledsuperheatedsteamandthe
processofheatingiscalledsuperheating.Superheatingisalwayscarriedoutatconstantpressure.
Theadditionalamountofheatsuppliedtothesteamduringsuperheatingiscalledas‘Heatof
superheat’andcanbecalculatedbyusingthespecificheatofsuperheatedsteamatconstantpressure
(cps),thevalueofwhichvariesfrom2.0to2.1kJ/kgKdependinguponpressureandtemperature

25. The advantages obtained by using ‘superheated’ steam are as follows :
i.Bysuperheatingsteam,itsheatcontentandhenceitscapacitytodoworkisincreasedwithout
havingtoincreaseitspressure.
ii.Superheatingisdoneinasuperheaterwhichobtainsitsheatfromwastefurnacegaseswhichwould
haveotherwisepasseduselesslyupthechimney.
iii.Hightemperatureofsuperheatedsteamresultsinanincreaseinthermalefficiency.
iv.Sincethesuperheatedsteamisatatemperatureabovethatcorrespondingtoitspressure,itcanbe
considerablycooledduringexpansioninanenginebeforeitstemperaturefallsbelowthatatwhich
itwillcondenseandtherebybecomewet.Hence,heatlossesduetocondensationofsteamon
cylinderwallsetc.areavoidedtoagreatextent

26. Volume of wet and dry steam
Ifthesteamhasdrynessfractionofx,then1kgofthissteamwillcontainxkgofdrysteamand(1–x)
kgofwater.Ifvfisthevolumeof1kgofwaterandvgisthevolumeof1kgofperfectdrysteam(also
knownasspecificvolume),thenvolumeof1kgofwetsteam
= volume of dry steam + volume of water.

27. Volume of superheated steam
Assuperheatedsteambehaveslikeaperfectgasitsvolumecanbefoundoutinthesamewayasthe
gases.
If,vg=Specificvolumeofdrysteamatpressurep,

28. Thermodynamic properties of steam and steam tables
Inengineeringproblem,foranyfluidwhichisusedasworkingfluid,thesixbasicthermodynamic
propertiesrequiredare:p(pressure),T(temperature),v(volume),u(internalenergy),h(enthalpy)and
s(entropy).Thesepropertiesmustbeknownatdifferentpressureforanalyzingthethermodynamic
cyclesusedforworkproducingdevices.Thevaluesofthesepropertiesaredeterminedtheoreticallyor
experimentallyandaretabulatedintheformoftableswhichareknownas‘SteamTables’.
Thepropertiesofwetsteamarethencomputedfromsuchtabulateddata.Tabulatedvaluesarealso
availableforsuperheatedsteam.Itmaybenotedthatsteamhasonlyonesaturationtemperatureateach
pressure.

31. External work done during evaporation
Internal latent heat
Thelatentheatconsistsoftruelatentheatandtheworkofevaporation.Thistruelatentheatis
calledtheinternallatentheatandmayalsobefoundasfollows:

32. Internal energy of steam
Itisdefinedastheactualenergystoredinthesteam.Thetotalheatofsteamissumofsensibleheat,
internallatentheatandtheexternalworkofevaporation.
Workofevaporationisnotstoredinthesteamasitisutilisedindoingexternalwork.Hencetheinternal
energyofsteamcouldbefoundbysubtractingworkofevaporationfromthetotalheat

33. Entropy of water

34. Entropy of evaporation

35. Entropy of wet steam

36. Entropy of superheated steam
Home work: Problem 3.1-3.23, Engineering
Thermodynamics By R.K. Rajput3
rd
Edition