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:

,

)

)

,

,

,

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

.

PartA

Thisformulaappliesto________________.

ANSWER:

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Thethreeblocksarenolongerinthermalequilibriumtheironblockiswarmer.Thethreeblocksarenolongerinthermalequilibriumboththealuminumblocksarewarmer.Theblocksremaininthermalequilibrium.

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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6

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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

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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

and .

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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6

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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

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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:

= 0.242

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anyobjectoftotalsurfacearea ,Kelvintemperature ,andemissivity anyobjectofcrosssectionalarea ,Kelvintemperature ,andemissivity anyobjectoftotalsurfacearea ,Kelvintemperature ,andemissivity anyobjectofcrosssectionalarea ,Kelvintemperature ,andemissivity

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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.

L8

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

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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

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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.

2

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BWH

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

,

= 2910 +

= 1750 +

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4/15/2015 HW10:Chap17.5,17.7,Chap.18.418.6

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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

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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

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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

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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

$

BUN

$

, ,

= 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