4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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HW10:Chap17.5,17.7,Chap.18.418.6Due:11:59pmonThursday,April16,2015
Youwillreceivenocreditforitemsyoucompleteaftertheassignmentisdue.GradingPolicy
HeatversusTemperature
Thespecificheatcapacityofaluminumisabouttwicethatofiron.Considertwoblocksofequalmass,onemadeofaluminumandtheotheronemadeofiron,initiallyinthermalequilibrium.
PartA
Heatisaddedtoeachblockatthesameconstantrateuntilitreachesatemperatureof500 .Whichofthefollowingstatementsistrue?
Hint1.Howtoapproachtheproblem
Heatisaddedtobothblocksatthesameconstantrate.Thatis,thesameamountofheatisaddedtoeachblockperunittime.Therefore,theblockthatreachesthefinaltemperatureinthesmallestamountoftimeistheblockthatrequiresthesmallestamountofheattoundergothegiventemperaturechange.Sincebothblockshavethesamemassandundergothesametemperaturechange,youcanrelatetheamountofheatabsorbedbyeachblocktotheblock'sspecificheatcapacity.
Hint2.Specificheatcapacity
Givenasampleofmass ofacertainsubstance,theamountofheat neededtochangeitstemperaturebyanamount isgivenby
,
where isthespecificheatcapacitycharacteristicofthatsubstance.Itfollowsthatthespecificheatcapacity ofasampleistheamountofheatrequiredtoraisethetemperatureofonegramofthesampleby1 .
Hint3.Identifywhichmaterialrequiresmoreheat
Considerseveralonegramsamplesofdifferentmaterials.Heatisaddedtoeachsampletoincreaseitstemperatureby1 .Whichmaterialwillabsorbthemostheat?
Hint1.Definitionofspecificheatcapacity
Thespecificheatcapacity ofasampleistheamountofheatrequiredtoraisethetemperatureofonegramofthatsampleby1 .
ANSWER:
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Thematerialwiththesmallestspecificheatcapacitywillabsorbthemostheat.Thematerialwiththelargestspecificheatcapacitywillabsorbthemostheat.Allthematerialswillabsorbthesameamountofheatbecausetheyallhavethesamemass.Allthematerialswillabsorbthesameamountofheatbecausetheyallundergothesamechangeintemperature.
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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ANSWER:
Correct
PartB
Whenthetwomaterialshavereachedthermalequilibrium,theblockofaluminumiscutinhalfandequalquantitiesofheatareaddedtotheironblockandtoeachportionofthealuminumblock.Whichofthefollowingstatementsistrue?
Hint1.Howtoapproachtheproblem
Sincethesamequantitiesofheatareaddedtosamplesthathavedifferentmassesanddifferentspecificheatcapacities,thismayresultindifferentfinaltemperaturesforeachsample.However,youmustkeepinmindthateachsmallerblockofaluminumnowhashalfthemassoftheironblock,butabouttwicethespecificheatcapacity.Tosolvethisproblemuseproportionalreasoningtofindarelationbetween , ,and .
Findthesimplestequationthatcontainsthesevariablesandotherknownquantitiesfromtheproblem.Writethisequationtwice:oncetodescribe , ,and andagaintorelate , ,and ,wherethesubscriptireferstoironandatoaluminum.Writeeachequationsothatalltheconstantsareononesideandthevariablesareontheother.Inthisproblemthevariableis sowriteyourequationsintheform .Finally,comparethetwocasespresentedintheproblem.Forthisquestionyoushouldfindtheratio .
Hint2.Findthetemperaturechangeoftheironblock
Whenanamountofheat isabsorbedbytheblockofiron,whatisitschangeintemperature ?Useand forthemassoftheironblockandthespecificheatcapacityofiron,respectively.
Expressyouranswerintermsof , ,and .
Hint1.Specificheatcapacity
Givenamass ofacertainsubstance,theamountofheat neededtochangeitstemperaturebyanamount isgivenby
,
where isaconstant,calledspecificheatcapacity,characteristicofthatsubstance.
ANSWER:
Theirontakeslesstimethanthealuminumtoreachthefinaltemperature.Thealuminumtakeslesstimethantheirontoreachthefinaltemperature.Thetwoblockstakethesameamountoftimetoreachthefinaltemperature.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Hint3.Findthetemperaturechangeofthesmalleraluminumblock
Whenanamountofheat isabsorbedbytheblockofiron,whatisitschangeintemperature ?Expressthemassoftheblockintermsofthemassoftheironblock andthespecificheatcapacityofaluminumintermsofthespecificheatcapacityofiron .
Expressyouranswerintermsof , ,and .
Hint1.Specificheatcapacityofaluminum
Recallthatthespecificheatcapacityofaluminumisabouttwicethespecificheatcapacityofiron.
ANSWER:
ANSWER:
Correct
UnderstandingHeatConduction
LearningGoal:
Tounderstandtheheatconductionformulaandthevariablesinit.
Conductiontheflowofheatfromahotterobjecttoacoolerobjectorfromahotterregiontoacoolerregionofthesameobjectisthemostcommonmechanismofheattransfer.Theformulagoverningthisis
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PartA
Thisformulaappliesto________________.
ANSWER:
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 4/21
Correct
Thisformulagivestheheatconductedatsteadystatebyanyobjectofuniformheatconductivityandcrosssectionalarea,whosehotandcoolerendsareat and ,respectively.Typicalexamplesareawire,rod,oraninsulatinglayer,thelatterofwhichwilltypicallyhavealargearea andrelativelyshortlength(thickness) .
Imaginethatyouareapplyingtheheatconductionformulatoarodthatisheldatahightemperatureononeendandatalowtemperatureontheotherend.Indicatewhetherthefollowingstatementsaretrueorfalse.
PartB
Thequantity istherateofheattransferfromthehottothecoldendoftherod.
ANSWER:
Correct
PartC
Thequantity istherateofheataddedtothehotendoftherodtomaintainitstemperature.
ANSWER:
Correct
PartD
Thequantity istherateofheatremovedfromthecoldendoftherodtomaintainitstemperature.
ANSWER:
anyobjectofcrosssectionalarea length andthermalconductivityanyobjectofcrosssectionalarea length andthermalresistivityaplateofsurfacearea longdimension andthermalconductivityaplateofsurfacearea longdimension andthermalresistivity
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 5/21
Correct
PartE
Thequantity isthetotalamountofheattransferredfromthehottothecoldendoftherod.
ANSWER:
Correct
Theflowofheatinto,through,andoutoftherodareequalundersteadystateconditionsinwhichthetemperatureofeachendoftherodisconstant.Theheatconductionformulaappliesonlyinsteadystateitdoesnotapplytothesituationinwhichoneendofabarissuddenlyplacedinaflamewhiletheotherendisheldatfixedtemperature(asinanicebath)theformulawouldonlyapplyafterthetemperatureateverypointinthebarhadreachedasteadystatevalue.
PartF
IntheSIsystemofunits,whataretheunitsofthequantity ?
ANSWER:
Correct
HeatFlowingthroughaSectionedRod
Alongrod,insulatedtopreventheatlossalongitssides,isinperfectthermalcontactwithboilingwater(atatmosphericpressure)atoneendandwithanicewatermixtureattheother.Therodconsistsofa1.00 sectionofcopper(withoneendintheboilingwater)joinedendtoendtoalength ofsteel(withoneendintheicewater).Bothsectionsoftherodhavecrosssectionalareasof4.00 .Thetemperatureofthecoppersteeljunctionis65.0 afterasteadystatehasbeenreached.Assumethatthethermalconductivitiesofcopperandsteelaregivenby
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 6/21
PartA
Howmuchheatpersecond ( )flowsfromtheboilingwatertotheicewatermixture?
Expressyouranswerinwatts.
Hint1.Howtoapproachtheproblem
Becausethelengthofthesteelsectionoftherodisunknown,theequationfortheheatconductioncannotbesetupdirectlybetweentheboilingwaterandtheicewater.Instead,sincethejunctiontemperatureisknown,calculatetheheatflowingthroughthecoppersectiononly.Becauseasteadystatehasbeenreached,theheatflowingoutoftheboilingwatermustbeequaltotheheatflowingthroughthecoppersection,whichisequaltotheheatflowingthroughthesteelsection,whichisfinallyequaltotheheatflowingintotheicewater.
Hint2.Equationforheatconduction
Theheatcurrentthrougharodis,
where and are,respectively,thelengthandcrosssectionalareaoftherodincontactwitheachsideand isthethermalconductivityoftherod,whichdependsonthematerialusedtomaketherod.
ANSWER:
Correct
Becausethesystemisassumedtohavereachedasteadystate,theheatflowingoutoftheboilingwatermustbeequaltotheheatflowingthroughthecoppersectionoftherod.
PartB
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 7/21
Whatisthelength ofthesteelsection?
Expressyouranswerinmeters.
Hint1.Howtoapproachtheproblem
InPartA,youfoundtheheatcurrentthroughthecopperrod,whichisthesameastheheatcurrentthroughthesteelrod.Youalsoknowthetemperaturesofbothendsofthesteelrod.Usethesevaluesintheheatcurrentequationtocalculatethelengthofthesteelrod.
ANSWER:
CorrectExtendingtheanalysisfromthefirstpart,weseethat,sinceasteadystatehasbeenreached,theheatflowingthroughthecoppersectionmustbeequaltotheheatflowingthroughthesteelsection,whichisalsoequaltotheheatflowingintotheicewater.
UnderstandingHeatRadiation
LearningGoal:
Tounderstandtheformulaforpowerradiatedintheformofelectromagneticenergybyanobjectatnonzerotemperature.
Everyobjectatabsolute(Kelvin)temperature willradiateelectromagneticwaves.Thisradiationistypicallyintheinfraredforobjectsatroomtemperature,withsomevisiblelightemittedforobjectsheatedabove1000 .Theformulagoverningtherateofenergyradiationfromasurfaceisgivenby
,
where isthethermalpower(alsoknownastheheatcurrent ).
PartA
Thisformulaappliesto_______________.
ANSWER:
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Correct
Intheformulagiven, isthethermalemissivity.Theemissivityis1.0foratrulyblackobjectandvariesdowntoabout0.02forashinygoldplatedobject.
TheStefanBoltzmannconstantis
andisaconstantofnature.Itspredictionfromfirstprincipleswasthefirstmajortriumphofquantummechanics,giving
where isBoltzmann'sconstant, isPlanck'squantumofangularmomentum(orPlanck'sconstant),andisthespeedoflight.
PartB
Ifyouwantedtofindtheareaofthehotfilamentinalightbulb,youwouldhavetoknowthetemperature(determinablefromthecolorofthelight),thepowerinput,theStefanBoltzmannconstant,andwhatpropertyofthefilament?
ANSWER:
Correct
PartC
Ifyoucalculatethethermalpowerradiatedbytypicalobjectsatroomtemperature,youwillfindsurprisinglylargevalues,severalkilowattstypically.Forexample,asquareboxthatis1 oneachsideandpaintedblack(thereforejustifyinganemissivity nearunity)emits2.5 atatemperatureof20 .Inrealitythenetthermalpoweremittedbysuchaboxmustbemuchsmallerthanthis,orelsetheboxwouldcooloffquitequickly.Whichofthefollowingalternativesseemstoexplainthisconundrumbest?
ANSWER:
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Theboxisblackonlyinthevisiblespectrumintheinfrared(whereitradiates)itisquiteshinyandradiateslittlepower.Thesurroundingroomisnearthetemperatureoftheboxandradiatesabout2.5 ofthermalenergyintothebox.Bothofthefirsttwofactorscontributesignificantly.Neitherofthefirsttwofactorsistheexplanation.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Correct
PartD
Asaroughapproximation,thehumanbodymaybeconsideredtobeacylinderoflength andcircumference .(Tosimplifythings,ignorethecirculartopandbottomofthecylinder,andjustconsiderthecylindricalsides.)Iftheemissivityofskinistakentobe ,andthesurfacetemperatureistakentobe
,howmuchthermalpower doesthehumanbodyradiate?
Expressthepowerradiatednumericallygiveyouranswertothenearest10 .
Hint1.Findtheareaoftheperson
Findthearea oftheperson.
Expresstheareaintermsof , ,andanyconstants.
ANSWER:
Hint2.Findasymbolicexpressionforthepower
Findthetotalpower radiatedbytheperson.
ExpressyouranswerintermsoftheStefanBoltzmannconstant ,thebodyarea ,thebodytemperature ,andtheemissivity .
ANSWER:
ANSWER:
Correct
Exercise17.26
Inanefforttostayawakeforanallnightstudysession,astudentmakesacupofcoffeebyfirstplacinga200Welectricimmersionheaterin0.300 ofwater.
PartA
Howmuchheatmustbeaddedtothewatertoraiseitstemperaturefrom21.5 to86.0 ?
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 10/21
ANSWER:
Correct
PartB
Howmuchtimeisrequired?Assumethatalloftheheater'spowergoesintoheatingthewater.
ANSWER:
Correct
DegreesofFreedom
Thermodynamicsdealswiththemacroscopicpropertiesofmaterials.Scientistscanmakequantitativepredictionsaboutthesemacroscopicpropertiesbythinkingonamicroscopicscale.Kinetictheoryandstatisticalmechanicsprovideawaytorelatemolecularmodelstothermodynamics.Predictingtheheatcapacitiesofgasesataconstantvolumefromthenumberofdegreesoffreedomofagasmoleculeisoneexampleofthepredictivepowerofmolecularmodels.
Themolarspecificheat ofagasataconstantvolumeisthequantityofenergyrequiredtoraisethetemperatureofonemoleofgasbyonedegreewhilethevolumeremainsthesame.Mathematically,
,
where isthenumberofmolesofgas, isthechangeininternalenergy,and isthechangeintemperature.
Kinetictheorytellsusthatthetemperatureofagasisdirectlyproportionaltothetotalkineticenergyofthemoleculesinthegas.Theequipartitiontheoremsaysthateachdegreeoffreedomofamoleculehasanaverageenergyequalto
,where isBoltzmann'sconstant .Whensummedovertheentiregas,thisgives
,where istheidealgasconstant,foreachmoleculardegreeoffreedom.
PartA
Usingtheequipartitiontheorem,determinethemolarspecificheat, ,ofagasinwhicheachmoleculehasdegreesoffreedom.
Expressyouranswerintermsof and .
Hint1.Howtoapproachtheproblem
ThemolarspecificheatofasubstanceistheamountofenergyrequiredtoincreasethetemperatureofonemoleofthesubstancebyonedegreeCelsius.Usingtheequipartitiontheorem,determinebyhowmuchthetotalenergyofagasincreaseswhenitstemperatureincreasesbyonedegree.Thenapplytheformulagiven
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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intheproblemintroductionfor .
Recallthatachangeintemperaturereflectsachangeintheamountofenergyassociatedwitheachdegreeoffreedom.
Hint2.Monatomicgas:anexample
Themolarspecificheatforamonatomicgasis .
Amonatomicgashasthreedegreesoffreedom,oneforeachofthethreeCartesiandirections.Bytheequipartitiontheorem,whenthetemperatureofthegaschanges,theenergyineachdegreeoffreedomchangesbyanamount .
ANSWER:
Correct
Experimentally,kinetictheoryandtheequipartitiontheoremdoagoodjobofpredictingthespecificheatofmanygasesatroomtemperatureasshowninthechartbelow.
Molecule DegreesofFreedom
Argon(Ar) 12.5 1.50 3
Helium(He) 12.5 1.50 3
CarbonMonoxide(CO) 20.7 2.49 5
Hydrogen(H2) 20.4 2.45 5
NitricOxide(NO) 20.9 2.51 5
HydrogenSulfide(H2S) 25.92 3.12 6
WaterVapor(H2O) 25.24 3.03 6
Foramonatomicgas,thereareonlythreetranslationaldegreesoffreedom,so isabout .Diatomicmoleculesandlinearmoleculeshavethreetranslationaldegreesoffreedomandtworotationalcomponentstothemotion(rotationabouttheaxisofthemoleculedoesnotcontributemuchexceptathightemperatures),giving avalueofabout .Nonlinearmoleculeshavethreetranslationalandthreerotationaldegreesof
freedom,whichgives .
Polyatomicmoleculesalsohavevibrationaldegreesoffreedom,wherethebondsbetweenatomscanvibratebackandforthlikeaspringbeingcompressedandreleasedaswellaspossiblesidetosideswingingmotionfromthebondsbending.Thevibrationalmotiondoesnotnormallycontributetothedegreesoffreedomuntilahightemperatureof400degreesCelsiusormoreisreached.
PartB
Giventhemolarspecificheat ofagasatconstantvolume,youcandeterminethenumberofdegreesoffreedom thatareenergeticallyaccessible.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Forexample,atroomtemperaturecis2butene, ,hasmolarspecificheat .Howmanydegreesoffreedomofcis2buteneareenergeticallyaccessible?
Expressyouranswernumericallytothenearestinteger.
Hint1.Howtoapproachtheproblem
InPartA,youderivedanequationfor intermsofthenumberofdegreesoffreedom .Substituteknownquantitiesintothatequationandsolvefor .
ANSWER:
Correct
TheSpeedofNitrogenMolecules
Thekinetictheoryofgasesstatesthatthekineticenergyofagasisdirectlyproportionaltothetemperatureofthegas.Arelationshipbetweenthemicroscopicpropertiesofthegasmoleculesandthemacroscopicpropertiesofthegascanbederivedusingthefollowingassumptions:
Thegasiscomposedofpointlikeparticlesseparatedbycomparativelylargedistances.Thegasmoleculesareincontinualrandommotionwithcollisionsbeingperfectlyelastic.Thegasmoleculesexertnolongrangeforcesoneachother.
Oneofthemostimportantmicroscopicpropertiesofgasmoleculesisvelocity.Thereareseveraldifferentwaystodescribestatisticallytheaveragevelocityofamoleculeinagas.Themostobviousmeasureistheaveragevelocity
.However,sincethemoleculesinagasaremovinginrandomdirections,theaveragevelocityisapproximatelyzero.Anothermeasureofvelocityis ,theaveragesquaredvelocity.Sincethesquareofvelocityisalwayspositive,thismeasuredoesnotaveragetozeroovertheentiregas.Athirdmeasureistherootmeansquare(rms)speed, ,equaltothesquarerootof .Thermsspeedisagoodapproximationofthethetypicalspeedofthemoleculesinagas.
Thishistogramshowsatheoreticaldistributionofspeedsofmoleculesinasampleofnitrogen( )gas.Inthisproblem,you'llusethehistogramtocomputepropertiesofthegas.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 13/21
PartA
Whatistheaveragespeed ofthemoleculesinthegas?
Expressyouranswernumericallytothreesignificantdigits.
Hint1.Howtousethehistogram
Thehistogramshowsthefractionofmoleculesthathavespeedswithineachofasetofranges.Eachspeedrangeiscalledabin.Takethecentralspeedvalueofeachbinasanestimateofthespeedofallthemoleculesinthatbin.Computetheweightedaveragespeed,usingthepercentageofmoleculesinabinastheweightingfactorforthatbin.
Hint2.Moreoncomputingtheaverage
Tofindtheweightedaverage,taketheaveragespeedofthemoleculesineach"bin"(forexample,theaveragespeedofmoleculesinthe0200rangeis100),andmultiplythatvaluebythefractionofmoleculesinthatbin.Repeatthisprocessforeachbin,addingtheresults.Thiswillgiveyoutheaveragespeedofthemoleculesinthegas.
ANSWER:
Correct
PartB
Becausethekineticenergyofasinglemoleculeisrelatedtoitsvelocitysquared,thebestmeasureofthekineticenergyoftheentiregasisobtainedbycomputingthemeansquaredvelocity, ,oritssquareroot .Thequantity ismorecommonthan becauseithasthedimensionsofvelocityinsteadofthelessfamiliarvelocitysquared.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Whatisthermsspeed ofthemoleculesinthenitrogengas?
Expressyouranswernumericallytothreesignificantdigits.
Hint1.Howtoapproachtheproblem
Thermsspeedofasystemofmoleculesisthesquarerootoftheaverageofthesquaresofthevelocities.Takethecentralspeedvalueofeachbinasanestimateofthespeedofallthemoleculesinthatbin.Computetheweightedaveragesquaredspeed,usingthepercentageofmoleculesinabinastheweightingfactorforthatbin.Thentakethesquareroot.
Hint2.Findthemeansquarevelocity
Whatisthemeansquarevelocity forthegivendistributionofmolecules?
Expressyouranswernumericallyinmeterssquaredpersecondsquaredtothreesignificantfigures.
Hint1.Understandingmeansquarevelocity
Themeansquarevelocityisgivenby ,wherethesumistakenoverallthemoleculesinthegasand isthetotalnumberofmolecules.Ifyoutakethecentralspeedvalueofeachbinasanestimateofthespeedofallthemoleculesinthatbin,thisequationreducesto
,wherethesumisnowoverthenumberofdiscretebinsand isthenumberofmolecules(orequivalentlythepercentageofmolecules)inaparticularbin.
ANSWER:
ANSWER:
Correct
Aspeedof519 iscomparabletothatofabulletshotfromahandgun.Incontrast,aBoeing747jetairlinerhasamaximumairspeedof270 andthespeedofsoundinairisonlyabout330 .Thespeedofsoundinairmustbeslowerthantheaveragespeedofthemoleculesbecauseitisthemovementofthemoleculesthattransmitssound.
PartC
Whatisthetemperature ofthesampleof gasdescribedinthehistogram?
ExpressyouranswerindegreesCelsiustothreesignificantfigues.
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Hint1.Howtoapproachtheproblem
Usingtheassumptionsofkinematics,theidealgaslaw,andtheformulaforkineticenergy,itcanbeshownthat ,where istheidealgasconstant, isthetemperatureinkelvins,and isthemolarmassinkilograms.
Solvethisequationfor .Use .
Hint2.FindthemolarmassofN2
Tothreesignificantfigures,theweightofnitrogenis14.0 .Whatisthemolarmass ofthemolecule?
Expressyouransweringramspermoletothreesignificantfigures.
ANSWER:
ANSWER:
Correct
PartD
Thehistogramusedinthisproblemisobviouslyonlyanapproximationofthetruedistributionofvelocitiesinagas.Inreality,themoleculesspanacontinuousrangeofvelocities.Foragiventemperature,themajorityofthemoleculeshaveaspeedneartheaveragespeed,withafewmoleculestravelingveryfastorveryslow.Togoodapproximation,thespeedsofmoleculesinagasfollowwhatisknownastheMaxwellBoltzmanndistribution.ThisappletallowsyoutoseethecurvesfortheMaxwellBoltzmanndistributionatmanydifferenttemperatures.Italsoletsyoumoveasmallintervalaroundonthehistogramtohighlightallofthemoleculeswithinthespeedrangeofthatpartofthehistogram.
WhichofthefollowingdescribesthequalitativebehavioroftheMaxwellBoltzmanndistributionastemperatureincreases?Youwillhavetopressthe"reset"buttonontheappletbeforeyoucanchangethetemperatureusingthethermometerontherightside.
ANSWER:
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Thepeakmovestotheright,whilethedistributionbecomesmorespreadout.Thepeakmovestotheright,whilethedistributionbecomeslessspreadout.Thepeakmovestotheleft,whilethedistributionbecomesmorespreadout.Thepeakmovestotheleft,whilethedistributionbecomeslessspreadout.
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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Correct
Atthehighertemperatures,thepeakofthecurveshiftstotheright,indicatingahigheraveragevelocity.Thepeaksofthehighertemperaturecurvesarealsobroader,indicatingthatagreaterpercentageofmoleculesaretravelingatahighervelocitythaninthelowtemperaturecase.
Exercise18.41
PartA
Howmuchheatdoesittaketoincreasethetemperatureof3.50molesofadiatomicidealgasbyanamount40.0ifthegasisheldatconstantvolume?Thegasmoleculescantranslateandrotatebutnotvibrate.
Expressyouranswerusingthreesignificantfigures.
ANSWER:
Correct
PartB
Whatistheanswertothequestioninpart(A)ifthegasismonatomic?
Expressyouranswerusingthreesignificantfigures.
ANSWER:
Correct
StoringAmmonia
Ammonia( )isacolorless,pungentgasatstandardpressureandtemperature.Itisanaturalmetabolicbyproduct,usuallygettingreleasedinrespiration,sweat,andurine.However,becauseammoniaiscaustic,exposuretolargequantitiesofitcancauseillnessandevendeath.Despiteitsinherentdangers,ammoniaisenvironmentallyfriendlyinsmallquantitiesandhasmanyapplicationsinoureconomy.Itcanbeusedasafertilizer,asasourceofhydrogengasforwelding,asarefrigerant,intheproductionofnitricacidandsodiumcarbonate,inmetallugy,andintheinfamoussmellingsaltsusedtoreviveunconsciouspeople.Ammoniatodaycanbemassproducedinexpensivelyinchemicalrefineries.
Tosafelyproduceandstoreammonia,itsphysicalandthermodynamicpropertiesmustbeunderstood.Physically,ammoniaisastrongbasethatreactswithacidsandmetals.Thethermodynamicpropertiesdescribingthephasesofammonia(solid,liquid,andgas)andthetransitionsbetweenthephasesarejustasimportant.Therelationshipofthese
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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 17/21
phasestopressureandtemperatureisquantitativelydescribedbyammonia'spTphasediagram.Notethat,inthisdiagram,thepressureaxisisnottoscale.
Fromthediagram,themeltingtemperature,boilingtemperature,andotherquantitiescanbedeterminedforanypressure.Thepressureandtemperaturerangeforeachofthephasesisshownbyitsownuniqueareaofthegraph.Thelinesboundingeachofthephasesonthediagramrepresentthetemperaturesandpressuresatwhichtwostatescancoexist.
Forthisproblem,anysectionofcurveonthediagramcanbenamedusingtwolettersontheboundaryinalphabeticalorder.Otherpointsnotlyingontheboundarycanalsobeusedtohelpidentifyvariousthermodynamicprocesses.
PartA
Onthephasediagram,whichsectionofcurverepresentsthepressureandtemperaturevaluesatwhichammoniawillboil?
Expressyouranswerastwolettersthatlieonasectionoftheappropriatecurve.
Hint1.Describeboilingintermsofphasechanges
Boilingisthetransitionfromonephasetoanotherwithbothphasesexistingtogether.Thephasesanddirectionofchangeinvolvedinboilingare__________to__________.
Expressyouranswerastwowordsseparatedbycommasintheordertheyappearinthesentence.Choosefromthefollowinglist:gas,liquid,orsolid.
ANSWER:
ANSWER:
Correct
PartB
Thelinebetweenwhichtwopointswoulddescribeaprocessofliquidammoniaboilingcompletelyaway?
Expresstheanswerastwolettersrepresentingtheendpointsofthelineinordersothatgoingfromthefirstlettertothesecondletterwouldshowaprocessofboiling.Becarefultoputthelettersinthecorrectorder.
ANSWER:
liquid,gas
boilingcurve=CE
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 18/21
Correct
PartC
Onthephasediagram,whichsectionofcurverepresentsthepressureandtemperaturevaluesatwhichammoniawillsublimate?
Expresstheanswerastwolettersthatlieonasectionoftheappropriatecurve.
Hint1.Describetheprocessofsublimation
Thephasesanddirectionofchangeforsublimationare__________to__________.
Expressyouranswerastwowordsseparatedbyacommaintheordertheyappearinthesentence.Choosefromthefollowinglist:gas,liquid,orsolid.
ANSWER:
ANSWER:
Correct
PartD
Thelinebetweenwhichtwopointswoulddescribeaprocessofsublimationforammonia?
Expressyouranswerwithtwolettersorderedinthedirectionofsublimation.Becarefultoputthelettersinthecorrectorder.
ANSWER:
Correct
Theheataddedtoasubstanceundergoingsublimationmustbeequaltotheheatoffusionplustheheatofvaporization.
PartE
Onthephasediagram,whichsectionofcurverepresentsthepressureandtemperaturevaluesatwhichammonia
HG
solid,gas
sublimationcurve=BC
AF
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 19/21
willmelt?
Expresstheanswerastwolettersthatlieonasectionoftheappropriatecurve.
ANSWER:
Correct
PartF
Thelinebetweenwhichtwopointswoulddescribetheprocessofcompletemeltingofammonia?
Expressyouranswerastwolettersorderedinthedirectionofmelting.Becarefultoputthelettersinthecorrectorder.
ANSWER:
Correct
PartG
Oneofthemostimportantpointsonaphasediagramisthetriplepoint,wheregas,liquid,andsolidphasesallcanexistatonce.Whatarethecoordinates( , )ofthetriplepointofammoniainthediagram?
Expressyouranswerasanorderedpair.Determinethetemperaturetothenearest5 andthepressuretoonesignificantdigit.
Hint1.Determinetheletternameforthetriplepoint
Giventhatthetriplepointisthepressureandtemperatureatwhichallthreephasescancoexist,whatistheletternameforthetriplepointofammonia?
Expresstheanswerasasingleletter.
ANSWER:
ANSWER:
meltingcurve=CD
AH
USJQMF
,
USJQMF
,
triplepoint=C
, = 195,0.05USJQMF
,
USJQMF
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 20/21
Correct
Temperaturescaleswereoriginallybaseduponthemeltingandboilingpointsofasubstance,butthesevaluesvarywithpressureasseeninthephasediagramofammonia.Soifonedidnotcontrolandmeasurethepressureprecisely,themeasurementusedtocalibratethetemperaturescalewouldbeinaccurate.
Tocircumventthisproblem,moderntemperaturescalesarebasedonthetriplepointofwater.Thetriplepointtemperatureofwateris0.01 at0.006 .Thethreephasesofwaterwillnotcoexistatanyothertemperature,regardlessofthepressure,sothetemperaturecanbecalibratedwithoutanadditionalpressuremeasurement.Thetriplepointsofmercuryandothersubstancesarealsousedasstandardsforcalibratingthermometers.
PartH
Atoneatmosphereofpressureandtemperaturesabove ,ammoniaexistsasagas.Fortransportation,ammoniaisstoredasaliquidunderitsownvaporpressure.Thismeansthattheliquidandgasphasesexistsimultaneously.Ifacontainerofammoniaistransportedinantemperaturecontrolledtruckthatismaintainedatnogreaterthan330 ,whatmaximumpressure mustthesidesofthecontainerbeabletowithstand?
Expresstheanswernumericallyinatmospherestoonesignificantfigure.
Hint1.Howtoapproachtheproblem
Becausetheliquidandvaporformsbothexistinthecontainer,findthepointonthegraphwherethegiventemperatureintersectsthecurverepresentingthephasechangeofliquidtogas.
ANSWER:
Correct
Exercise18.49
Solidwater(ice)isslowlywarmedfromaverylowtemperature.
PartA
Whatminimumexternalpressure mustbeappliedtothesolidifameltingphasetransitionistobeobserved?
ANSWER:
Correct
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= 8 , BUN
,
= 610 ,
1B
4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6
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PartB
Aboveacertainmaximumpressure ,noboilingtransitionisobserved.Whatisthispressure?
ANSWER:
Correct
ScoreSummary:Yourscoreonthisassignmentis102%.Youreceived50.8outofapossibletotalof50points.
,
= 2.21107 ,
1B