工程热力学第三版答案英文第4章.docx
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工程热力学第三版答案英文第4章.docx
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工程热力学第三版答案英文第4章
4-4
Theworkdoneduringtheisothermalprocessshowninthefigureistobedetermined.
AssumptionsTheprocessisquasi-equilibrium.
AnalysisFromtheidealgasequation,
Foranisothermalprocess,
Substitutingidealgasequationandthisresultintotheboundaryworkintegralproduces
Thenegativesignshowsthattheworkisdoneonthesystem.
4-9
Refrigerant-134ainacylinderisheatedatconstantpressureuntilitstemperaturerisestoaspecifiedvalue.Theboundaryworkdoneduringthisprocessistobedetermined.
AssumptionsTheprocessisquasi-equilibrium.
PropertiesNotingthatthepressureremainsconstantduringthisprocess,thespecificvolumesattheinitialandthefinalstatesare(TableA-11throughA-13)
AnalysisTheboundaryworkisdeterminedfromitsdefinitiontobe
and
DiscussionThepositivesignindicatesthatworkisdonebythesystem(workoutput).
4-23
Asaturatedwatermixturecontainedinaspring-loadedpiston-cylinderdeviceisheateduntilthepressureandtemperaturerisestospecifiedvalues.Theworkdoneduringthisprocessistobedetermined.
AssumptionsTheprocessisquasi-equilibrium.
AnalysisTheinitialstateissaturatedmixtureat90C.Thepressureandthespecificvolumeatthisstateare(TableA-4),
Thefinalspecificvolumeat800kPaand250°Cis(TableA-6)
Sincethisisalinearprocess,theworkdoneisequaltotheareaundertheprocessline1-2:
4-29
Aninsulatedrigidtankisinitiallyfilledwithasaturatedliquid-vapormixtureofwater.Anelectricheaterinthetankisturnedon,andtheentireliquidinthetankisvaporized.Thelengthoftimetheheaterwaskeptonistobedetermined,andtheprocessistobeshownonaP-vdiagram.
Assumptions1Thetankisstationaryandthusthekineticandpotentialenergychangesarezero.2Thedeviceiswell-insulatedandthusheattransferisnegligible.3Theenergystoredintheresistancewires,andtheheattransferredtothetankitselfisnegligible.
AnalysisWetakethecontentsofthetankasthesystem.Thisisaclosedsystemsincenomassentersorleaves.Notingthatthevolumeofthesystemisconstantandthusthereisnoboundarywork,theenergybalanceforthisstationaryclosedsystemcanbeexpressedas
Thepropertiesofwaterare(TablesA-4throughA-6)
Substituting,
4-39
Asaturatedwatermixturecontainedinaspring-loadedpiston-cylinderdeviceisheateduntilthepressureandvolumerisetospecifiedvalues.Theheattransferandtheworkdonearetobedetermined.
Assumptions1Thecylinderisstationaryandthusthekineticandpotentialenergychangesarezero.2Therearenoworkinteractionsinvolvedotherthantheboundarywork.3Thethermalenergystoredinthecylinderitselfisnegligible.4Thecompressionorexpansionprocessisquasi-equilibrium.
AnalysisWetakethecontentsofthecylinderasthesystem.Thisisaclosedsystemsincenomassentersorleaves.Theenergybalanceforthisstationaryclosedsystemcanbeexpressedas
Theinitialstateissaturatedmixtureat75kPa.Thespecificvolumeandinternalenergyatthisstateare(TableA-5),
Themassofwateris
Thefinalspecificvolumeis
Thefinalstateisnowfixed.Theinternalenergyatthisspecificvolumeand225kPapressureis(TableA-6)
Sincethisisalinearprocess,theworkdoneisequaltotheareaundertheprocessline1-2:
Substitutingintoenergybalanceequationgives
4-43
Twotanksinitiallyseparatedbyapartitioncontainsteamatdifferentstates.Nowthepartitionisremovedandtheyareallowedtomixuntilequilibriumisestablished.Thetemperatureandqualityofthesteamatthefinalstateandtheamountofheatlostfromthetanksaretobedetermined.
Assumptions1Thetankisstationaryandthusthekineticandpotentialenergychangesarezero.2Therearenoworkinteractions.
Analysis(a)Wetakethecontentsofbothtanksasthesystem.Thisisaclosedsystemsincenomassentersorleaves.Notingthatthevolumeofthesystemisconstantandthusthereisnoboundarywork,theenergybalanceforthisstationaryclosedsystemcanbeexpressedas
Thepropertiesofsteaminbothtanksattheinitialstateare(TablesA-4throughA-6)
Thetotalvolumeandtotalmassofthesystemare
Now,thespecificvolumeatthefinalstatemaybedetermined
whichfixesthefinalstateandwecandetermineotherproperties
(b)Substituting,
or
4-60
Theairinarigidtankisheateduntilitspressuredoubles.Thevolumeofthetankandtheamountofheattransferaretobedetermined.
Assumptions1Airisanidealgassinceitisatahightemperatureandlowpressurerelativetoitscriticalpointvaluesof-221Fand547psia.2Thekineticandpotentialenergychangesarenegligible,
.3Constantspecificheatsatroomtemperaturecanbeusedforair.Thisassumptionresultsinnegligibleerrorinheatingandair-conditioningapplications.
PropertiesThegasconstantofairisR=0.3704psia.ft3/lbm.R(TableA-1E).
Analysis(a)Thevolumeofthetankcanbedeterminedfromtheidealgasrelation,
(b)Wetaketheairinthetankasoursystem.Theenergybalanceforthisstationaryclosedsystemcanbeexpressedas
Thefinaltemperatureofairis
Theinternalenergiesare(TableA-17E)
Substituting,
Qin=(20lbm)(186.93-92.04)Btu/lbm=1898Btu
AlternativesolutionsThespecificheatofairattheaveragetemperatureofTavg=(540+1080)/2=810R=350Fis,fromTableA-2Eb,cv,avg=0.175Btu/lbm.R.Substituting,
Qin=(20lbm)(0.175Btu/lbm.R)(1080-540)R=1890Btu
DiscussionBothapproachesresultedinalmostthesamesolutioninthiscase.
4-64
Astudentlivinginaroomturnsher150-Wfanoninthemorning.Thetemperatureintheroomwhenshecomesback10hlateristobedetermined.
Assumptions1Airisanidealgassinceitisatahightemperatureandlowpressurerelativetoitscriticalpointvaluesof-141Cand3.77MPa.2Thekineticandpotentialenergychangesarenegligible,
.3Constantspecificheatsatroomtemperaturecanbeusedforair.Thisassumptionresultsinnegligibleerrorinheatingandair-conditioningapplications.4Allthedoorsandwindowsaretightlyclosed,andheattransferthroughthewallsandthewindowsisdisregarded.
PropertiesThegasconstantofairisR=0.287kPa.m3/kg.K(TableA-1).Also,cv=0.718kJ/kg.Kforairatroomtemperature(TableA-2).
AnalysisWetaketheroomasthesystem.Thisisaclosedsystemsincethedoorsandthewindowsaresaidtobetightlyclosed,andthusnomasscrossesthesystemboundaryduringtheprocess.Theenergybalanceforthissystemcanbeexpressedas
Themassofairis
Theelectricalworkdonebythefanis
Substitutingandusingthecvvalueatroomtemperature,
5400kJ=(174.2kg)(0.718kJ/kgC)(T2-15)C
T2=58.2C
DiscussionNotethatafanactuallycausestheinternaltemperatureofaconfinedspacetorise.Infact,a100-Wfansuppliesaroomwithasmuchenergyasa100-Wresistanceheater.
4-69
Carbondioxidecontainedinaspring-loadedpiston-cylinderdeviceisheated.Theworkdoneandtheheattransferaretobedetermined.
Assumptions1CO2isanidealgassinceitisatahightemperaturerelativetoitscriticaltemperatureof304.2K.2Thekineticandpotentialenergychangesarenegligible,
.
PropertiesThepropertiesofCO2areR=0.1889kJ/kgKandcv=0.657kJ/kgK(TableA-2a).
AnalysisWetakeCO2asthesystem.Thisisaclosedsystemsincenomasscrossestheboundariesofthesystem.Theenergybalanceforthissystemcanbeexpressedas
Theinitialandfinalspecificvolumesare
Pressurechangeslinearlywithvolumeandtheworkdoneisequaltotheareaundertheprocessline1-2:
Thus,
Usingtheenergybalanceequation,
Thus,
4-76
Airataspecifiedstatecontainedinapiston-cylinderdevicewithasetofstopsisheateduntilafinaltemperature.Theamountofheattransferistobedetermined.
Assumptions1Airisanidealgassinceitisatahightemperaturerelativetoitscriticaltemperatureof304.2K.2Thekineticandpotentialenergychangesarenegligible,
.
PropertiesThepropertiesofairareR=0.287kJ/kgKandcv=0.718kJ/kgK(TableA-2a).
AnalysisWetakeairasthesystem.Thisisaclosedsystemsincenomasscrossestheboundariesofthesystem.Theenergybalanceforthissystemcanbeexpressedas
Thevolumewillbeconstantuntilthepressureis300kPa:
Themassoftheairis
Theboundaryworkdoneduringprocess2-3is
Substitutingthesevaluesintoenergybalanceequation,
4-85
Aneggisdroppedintoboilingwater.Theamountofheattransfertotheeggbythetimeitiscookedistobedetermined.
Assumptions1Theeggissphericalinshapewitharadiusofr0=2.75cm.2Thethermalpropertiesoftheeggareconstant.3Energyabsorptionorreleaseassociatedwithanychemicaland/orphasechangeswithintheeggisnegligible.4Therearenochangesinkineticandpotentialenergies.
PropertiesThedensityandspecificheatoftheeggaregiventobe=1020kg/m3andcp=3.32kJ/kg.C.
AnalysisWetaketheeggasthesystem.Thisisaclosessystemsincenomassentersorleavestheegg.Theenergybalanceforthisclosedsystemcanbeexpressedas
Thenthemassoftheeggandtheamountofheattransferbecome
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