工程热力学第三版答案英文第4章.docx

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