材料科學(xué)與工程專業(yè)課程總結(jié)

朽木易折，金石可鏤。千里之行，始于足下。第④findthecorrespondingcardofthisnumber,onwhichthereistheparametersofthisphase.ThequantitativeanalysisThediffractionintensityinthepatternincreasewiththecontentofthephase,ifwewanttoknowthecontentofonephase,wecanusetheKvaluemethod.IA,ISarethediffractedintensityofphaseAandS,wA,wSarethemassfractionofphaseAandS.AddtheknowncontentwSofphaseSintothesample,getthepatternfromthediffractometer,wecanreadtheIAandISfromthepattern,thenwecancalculatewA.WecangetthevalueofKbymeansofexperiment:mixthesamequantityofphaseAandphaseS,thatistosay,mA=mS,hereK=Othermethod:internalstandardmethod,externalstandardmethodIntheanalysismethodbyelectronmicroscopewehavelearnedtransmissionelectronmicroscope.Itscoreisimagingsysteminlenscone.Itconsistsofobjectivelens,intermediatelensandprojectivelens.Thediffractionpatternisfirstlymagnifiedbyobjectivelens,ifthemagnificationfactorofintermediatelensisgreaterthan1,thenthepatternwillbemagnifiedagain,ifthemagnificationfactorofintermediatelensislessthan1,thepatternwillbeshrank.Thefunctionofprojectivelensistomagnifythepatternintheintermediatelensandcastitsshadowonthenegativepicture.Physicalchemistryofsilicate1.Silicatematerialsismainlymadeupofpottery,cementandglass.Inthiscoursewehavemainlylearnedglass.Theproductionofglassisaconversionprocessofmeltsandvitreum.Meltsandvitreumarethetwostateofaggregationofsubstanceexceptsolid,gasandliquid.Theconversionprocessofmeltsandvitreumisagradualchange,itfinishesinatemperaturerange,sotheglasshavenofixedmeltingpoint.Forexampleinthispicture,theordinateistheinternalenergyandthevolume,thehorizontalordinateisthetemperature,whenthemeltsiscooleddown,whenitmeetspointf,thismomentthetemperatureisTgandhavefinishedthetransmissiontothesolidglass,thedynamicviscosityis1012pas,usuallywedefinedthetemperatureasTfwhenthedynamicviscosityis108pas,withtheincreaseoftemperature,thedynamicviscositydecrease,sotheTfisontheright.WhenthetemperatureishigherthanTf,allismelts,thatistosay,whenitmeetspointb,itbegintoturntothesolidglass.TheconversionprocesstakesplaceinthetemperaturerangebetweenTgandTf,sotheglasshavenofixedmeltingpoint.(dynamicviscosityshowstheobstructionwhenthefluidflows,thefluidisasubstancethatchangeitsshapeunderasurfaceparalleledforce).Diffusionisacommonphenomenoninourdailylife,thediffusionofsolidsisthefoundationofreactionsbetweensolids.Forexamplethereisapileofcoalinthecorner,afterlongtime,thecornerwillbecomeblacklikethecolorofcoal,thatisthediffusionofsolids,thisprocessisveryslowandthepathoftheparticlehavenorule,forexamplelikethis.Whenwewanttoknowhowmanyparticlestakepartinthisdiffusion,thenwecanusethefirstlawofFick,Jisthequantityofatomswhentheypassthecrosssectioninunittime,Disacoefficient,**isthechangeofconcentrationinunitlength,theminussignrepresenttheparticlespreadalongthedirectionofdecreaseofconcentration.Forasolid,itsconcentrationisnotuniform,likethis,onthelefttheconcentrationofasubstanceishigherthanontheright,thenthissubstancewillspreadfromlefttoright,atlasttheconcentrationwillbeequal,forexampleinthischart,thisistheoriginalconcentrationofleftandright,afterthediffusionprocess,thelastconcentrationisbetweenC1andC2.FundamentalsofmetallicmaterialsengineeringInthiscoursewehavelearnedshapingmethod.Therearemanymetalproductsinourdailylife,likemetalbuckets,metalhammers,theyaremadeofrawmaterialsthroughacertainshapingmethod.Actuallyintheproduction,themostcommonmethodisliquidforming.Thatistosay,meltthemetalfromsolidtoliquid,thenpourtheliquidmetalintoamouldwithacertainshapeandsize,afterthecoolingandsolidificationprocesswegettheproductweneed.Forexample,wewanttoproduceabatchofartworkswithashapeofgourds.FirstlyjustlikeIsaid,meltthemetalfromsolidtoliquid,thenputtheliquidmetalintoamould,aftercoolingandsolidification,openthemouldandgettheworkwithashapeandsizeweneed.Thismethodislowcost,manyobsoletingelementscanbeusedagain.Ontheotherwordwecangetallkindsofshapeandsizeofelementsbythismethod.Buttheproductionmaybehaveafewholesonthesurfaceorinside,itwillaffecttheuseandpropertiesoftheproducts,thetechnologyisoldandtheefficiencyislow.Wehavelearnedanothermethod,forexamplethereisametalrod,wewanttoturnitintoashapeofcuporU-shape.Weputthemetalrodonthemachineandopentheswitch,therolleronthemachinewillbringtobearonthemetalrod,thenthemetalwillbeoutofshape.Whenwecontroltheheightthattherollerdropandchooseasuitableradiusoftheroller,thenwecangettheproductwithashapeandsizeweneed.Actuallyinthedailylifetherearemanyelements,theymustbeartorsion,bendingandchangingcurrentandvoltage,forexampletheroller,itssurfacewithstandgreaterforcethanthecore,ifthereisafrictionforce,thesurfacewillgraduallywearaway.Itcausesagreatdamagetotheelementanddecreasetheusefullife.Sowemusthaveaseriesoftreatmentsonthesurface,makeithasahigherhardnessandstrength,buttheinsidematerialskeeptheoriginaltoughness.Thetoughnessistheabilitytonottobreakoff,whentheelementbeartheappliedforce.Thatisthesurfacemodificationofmaterials.Themostcommonmethodofsurfacemodificationisasfollows,puttheelementintoaheatingstoveandinletcarbonincludedgas,suchascoalgas,liquefiedpetroleumgas,thegaswillconductaseriesofreactionssuchasAandB,andgaincarbonatoms.Thesefreecarbonatomsspreadfromsurfaceoftheelementtoinside,thuschangethecomponentandthepropertiesofsurface.PhysicalmetallurgyInthiscourse,Ithinkthemostimportantpartistheiron-carbonphasediagram,itisthemostprimaryknowledgeofiron-carbon-alloy.Itislikethat,theordinateisthetemperature,thehorizontalordinateisthecontentofcarbon,thislineistheliquidus,thislineisthesolidus,thatistosay,whentheliquidwithahightemperaturecooldownandmeetstheliquidus,itwillbegintogrowsolid,whenitmeetsthesolidus,theliquidwilldisappear.Firstlyappeartheaustenite,becauseinahightemperature,theinnerstructureofironisγ-Fe(gamaphaseiron),austeniteissolidsolutionofiron,thatistosay,carbonenterthestructureofiron.CanIuseanexampletoexplainthephasediagram?Thereisasteel,itscarboncontentis0.77%,correspondtohereinthehorizontalordinate,justlikeIsaid,whenthesteelcooldownandmeetstheliquidus,theliquidbegintoappearaustenite,whenitmeetsthesolidus,thereisnoliquidandallisaustenite,whenthetemperaturecontinuetofallandmeetthepointP,theaustenitewillbecometopearlite,itisamixtureofferriteandcementite,becauseinalowtemperature,theinnerstructureofironisα-Fe,cementiteisacompoundofcarbon,thepointEisthemaximalsolubilityofcarboninaustenite,thepointBisthemaximalsolubilityofcarboninferrite,thesolubilityofpointEisgreater,sowhentheausteniteturntotheferrite,whentheausteniteturntotheferrite,thereisasmallsurplusofcarbon,thentherestofcarbonexistinthestateofcementite,theultimacomponentispearlite.Throughthephasediagramweknowthechangeofcomponentduringthecoolingprocessandtheultimacomponentofanalloy,wecanalsoseethat,ifthecarboncontentisdifferent,thecomponentofsteelisdifferent,thenthepropertiesisdifferent.Sowemustchoosematerialswithasuitablecarboncontentaccordingtotherequirement.Inourdailylife,wefindthattheusefullifeofmanythingsisshorterthanintheory,incontrastthepropertiesisnotsogood.Becausetherearedefectsintheinnerstructureofmaterials.Intheory,wethinktheatomicarrangementinthecrystalisregular,butundertheinfluenceofoutsidefactors,suchasradiation,theatomicarrangementinthecrystalisnotregular,thisisdefect.Thecrystalisasolidwhoseinnerparticlesrepeatedarrangeinthespace.Forexamplepointdefect,thetheoreticalarrangementislikethis,theatom1transfertothisstate,thentheatomicarrangementisdisarranged.Otherdefectslikelinedefect,therearethreeatomicplanes,theyarrangeregularly,ifbetweenthesetwoplanesgrowanewplaneABCD,resultintheatomnexttoABCDplanedeviatetheoriginalstate.PropertiesofmaterialsIntheengineeringtherearemanyelements,theymustbearchangingappliedforce,suchasgearandbridge.Accordingtostatistics,thereare80%ofelementsandinstallationsloseeffectivenessbecauseoffatigue.Whentheelementsworkunderchangingforcebothindirectionandmagnitudeofforce,suchasthepartsofcars,tractorsandairplanes,theforcewillchangeasfollowswhentheywork.Inthissituationtheinnerstructureofmaterialswillchangeandemergecracks,astimegoeson,thecrackswillspreadandgrowup,toacertainextenttheelementswillbreakoff.Thatisfatiguefailure.Thetemperatureandthemagnitudeoftheforcewilleffectthetime,thatthefatiguefailureemerge.Generallyhighertemperatureandforceadvancedtheemergencyoffatiguefailure.Thematerialshavemanypropertiessuchasfatigueproperties,wearpropertiesandthermalproperties.Thewearpropertiesisthat,whenthemachinework,theelementswillbewornbecauseofthefriction,thatiswear-outfailure.Thethermalpropertiesisthat,thevolumeandlengthwillchangewhenheated,forexamplethechooseofglazeinprocessofinorganicmaterials.Manymaterialshaveelectricconductivity,suchasthetungstenwireinthelampbulb,butthesematerialshavearesistancewhentheyconductelectricity,thatistosay,theywillhaveafeverwhenacurrentpassthroughit,thenapartofenergywilllose.Butthereisamaterials,whoseelectricresistancewillbesolowthatcan'tbemeasuredwhenthetemperatureislowenough,forexamplearound0kelvin,thismaterialiscalledsuperconductor.CanIuseanexampletoexplainthisprocess?Firstlymakeasuperconductorintoaringandputinamagneticfieldatroomtemperature,justlikethis,collofftoaround0kelvin,thentakethemagneticfieldaway,becauseofthemagneticinduction,alongtheringemergeacurrent,theelectricresistanceoftheringis0,sotheenergyisnotconsumedandexistforever.Magneticinductioncanbeexplainedasfollows,inaclosedcircuitwillproduceainductionelectromotiveforcewhenthequantityofmagneticlineofforcechange,theelectromotiveforcewillproduceacurrent.FundamentalsofinorganicmaterialsengineeringThetwoobjectswithdifferenttemperaturesincontractwitheachother,orthedifferentpartsofoneobjecthavedifferenttemperatures,thenthereisaheattransfer,theheatflowsfromthewarmertothecoolerbody,thisistheheatconduction.Itisanimportantheattransfermode.Allobjectshaveaheattransferability,butthequantityisdifferent,thequantityofheattransfercanbecalculatedaccordingtothisformular:***Qisthequantityofheattransfer,kshowstheabilityofheattransfer,Aisthecontractarea,theminussignrepresenttheheatflowsfromthewarmertothecolderbody.CanIuseanexampletoexplaintheprocessofconductionofheat?Ibelieveallofushaveairedquilts,wefindthattheairedquiltsareverywarm,becauseagreatdealofairwillenterthegapofcotton,inthenarrowspacethewayofheattransfermainlyistheheatconduction,theabilityofheattransferofairnamelykairislow,sothequantityofheattransferislow,thustheinsolatingeffectisgood,ifthequiltisbeaten,moreairentersandtheeffectisbetter.Anotherimportantheattransfermodeisheatradiation,itisaprocess,thattheobjecttransfertheheatthroughtheelectromagneticwave.Thequantityofheattransfercanbecalculatedaccordingtothisformular:***Qisthequantityofheattransfer,Aisthecontractarea,εshowstheabilitytoradiate,T1andT2arethetemperatures.CanIuseanexampletoexplaintheprocessofheatradiation?Onthewinterevening,theuppersurfaceoftheleaveshaveasheetoffrost,nottheundersurface.Becausetheundersurfacehaveaheatradiationwithground,theuppersurfacewithspace,thetemperatureofgroundishigherandissimilarwiththetemperatureofleaves,butthetemperatureofspaceislow.SoQupperismorethantheQunder,itwillfrostwhenthetemperatureisminus0centigrade.Fluidisasubstancethatchangeitsshapeunderasurfaceparalleledforce,ithasnofixedshapeandcanflow.Gasesandliquidsareallcalledfluid.Themostimportantpropertiesoffluidisthethermalexpansion,thatistosaywhenthetemperaturechange,thevolumeanddensitywillchange.Themostcommonexampleisthehotballoon,whentheairintheballoonisheated,becauseofthethermalexpansionthevolumewillincreaseandthedensitywilldecrease,(themassoftheairisfixed,whenthevolumeincrease,thenthedensitywilldecrease.)whenthedensityissmallerthanthedensityofairinsurroundings,theballoonwillfloat.Justlikeputanobjectonthesurfaceofthewater,whosedensityissmallerthanthewater,itfloats.PrincipleandprocessofheattreatmentHeattreatmentisthat,heatthesteeltoacertaintemperatureasitissolid,keepwarmforatime,thencoolofftotheroomtemperature.Itsprincipleisthechangeofcomponentinthesteel.Inordertohavethepropertiesandcomponentweneedaftertheheattreatment,weusuallyfirstlygaintheaustenite,thencooloffinanappropriatewaytogettheneededcomponent.Theestablishmentofausteniteisasfollows,theoriginalcomponentofsteelisacombinationofferriteandcementite,thewhiterepresentsferriteandtheblackrepresentthecementite,whenheated,ontheedgeofcementitegrowsseveralaustenites,continuetobeheated,theaustenitewillgrowupandthecementitewillgradualdissolve,afterawhiletheferritedisappearandtheausteniteismature,butthereisasmallsurplusofcementite,becauseitsdissolutionisaprocessofdiffusion,it'sslow,thedissolutionofferriteisatransformationbetweenferriteandaustenite,bothofthemareinnerstructuresofironindifferenttemperatures.Withtheincreaseoftemperaturethecementitewilldisappearandtheaustenitebecomeuniform.Anothertechnologiesofheattreatmentaresurfacemodificationinfundamentalsofmetallicmaterialsengineering,andannealing.Annealingisthat,heatthemetaltoacertaintemperature,keepwarmforatime,cooloffslowlytogetthecomponentclosetoequilibrium.Bythismeansmakethecomponentofthesteeluniformandreducetheforcebetweenthedifferentparts,andthenimprovethefunctionalperformance.Thewindowsofcarsafterheattreatmentbecometoanorbicularpiecewhenbreakoff,theyaresafetothehumanbody,butthegeneralglassbecometoapointedpiece,becausetheforcecentralizedpartsfirstlybreak.PetrographyofsilicateWecanobservemanypropertiesofcrystalundersinglepolarizingmicroscope,forexampleatthecontractoftwoobjectswithdifferentrefractiveindexeswecanseeadarkedge,nearthedarkedgeisabrightline,whenriseandfallthelenscore,thebrightlinewillmove.Theemergencyofthislineisattributedtothedifferencesofrefractiveindexofthecontiguousobjects.Justlikethis,therefractiveindexofrightisgreater,whenthelightshineonthecontractsurface,fromopticallythinnermediumtoopticallydensermedium,accordingtotherefractionlaw,thelightwillbepartialtonormal,resultinmorelightatoneside,lesslightatanotherside,thusemergethedarkedgeandbrightline.n=c/v,cisthespeedoflightinspace,nistherefractiveindex,visthespeedoflightinthecrystal,whenthenissmaller,thenthevisgreater,thatistheopticallythinnermedium.Therefractionlaw:sini/sinr=nr/niInthiscoursewehavealsolearnedportlandclinkerasinprocessofinorganicmaterials.Exceptusemicroscopetoanalysisthestructureofcrystal,wecanmeasurethephysicalandchemicalprocessbymeansofdifferentialthermalanalysis.Firstlyheatthesampleandreferencematerialunderthesamecondition,measuretherangeoftemperaturebetweensampleandreferencematerialandtherelationshipwithtemperature,thenmakeadiagram,thatisDTAcurve.Theordinateisrangeoftemperature,thispartrepresenttheexothermicreaction,theareaofthispeakrepresentthequantityoftheenergy.MechanicsofsilicateindustryThedevelopmentallevelandtheefficiencyofafactorytoagreatextentdependontheintegrityandprogressivenessoftheequipments.Everyproductionlinemustbefinishedbymechanicalequipments.Intheproduction,massivematerialsandsuppliesmustbebrokentopiecesinvariousdegree,thenputintotheproduction.Theneededequipmentisthesizereductionmachinery,itisthemostelementaryintheproductionline,soIwanttoshowyouonekindofthesizereductionmachinery.Whentheradiusofthematerialsandsuppliesisrequiredtobebetween30-100millimeter,weusuallyusejawcrasher.CanIuseapicturetoexplaintheprinciple?1and2aretwoboards,1isfixedand2canmove,thisisanaxel,whenitrevolvestherod3willmoveupanddownlikethis,therodandtheboard2areconnectedatthispoint,whentherodmove,thisanglewillchangeandthenmovetheboard.Whentheboard2isclosetotheboard1,thematerialsaresqueezedandbroken,whentheboard2isaway,thebrokenmaterialswilldropbygravity.Sometimestherawmaterialsisdistantfromtheworkshop,soweneedtransportmachineries,suchashorizontalandobliqueconveyerband.Thisisahorizontalconveyerband,theprincipleisthefrictionforcebetweenthematerialsandtheband.Thisoneisoblique,whenthematerialsistransported,differentsizesandkindsofmaterialshaveamaximalangleβ,ifthisangleexceedβ,thenthematerialswillslipandleadstodecreasedefficiency.ThermodynamicsofmaterialsInthiscoursewehavemainlylearnedthefirstlawandthesecondlawofthermodynamics.Thefirstlawcanbedescribedbythisformular:U=Q+W,thesystemabsorbheatfromsurroundings,theamountisQ,Q>0,atthesametimethesystemdoworkonthesurroundings,theamountisW,W<0,Ushowsthechangeofinternalenergy,itdependsontheoriginalandtheultimaconditions,ithasnothingtodowiththeprocess.ButQandWhaveacloserelationshipwiththeprocessofthereaction.CanIuseanexampletoexplainthefirstlawofthermodynamics?Asystemchangefromstate1tostate2throughtheline1-a-2,itobserves314Jouleheatfromthesurroundings,andsimultaneouslydo117Jouleworkonthesurroundings.Ifthesystemreactsthroughtheline1-b-2,itdo44Jouleworkonthesurroundings,howmuchheatitobservesfromthesurroundings?Wecanusetheformularofthefirstlawofthethermodynamicstocalculate,thegeneralinternalenergyisfixedwhatevertheprocessis,fromthe1-a-2line,wecanknowthatUequalsQ1addsW1,thenintheprocess1-b-2,wecancalculateQ2.Thattisthefirstlawofthermodynamics.Innaturewefindthat,theamountofheatwilltransmitfromthewarmertothecoolerbodyautomatically,untilthetemperatureofthetwoobjectsisunanimous.Whendifferentgasesmeeteachother,theyusuallytendtointerminglewitheachother,untilthegasesistotallyuniform.Theseprocessesarespontaneous,buttheycan'trecovertheoriginalstatespontaneously.Forexamplethevacuumexpansionofidealgasinadiabaticcondition,itisaspontaneousprocess,Q=0,W=0,so*U=0,thentherangeoftemperatureis0,becausethetemperatureistheonlyinfluencingfactorofinternalenergy.Ifwewanttorecovertheexpandedgastotheoriginalstate,wemustthroughanisothermalcompression,butintheprocessofcompressionthesurroundingshavetodoworkonthesystem,theamountisW,atthesametime,thesystemwillgiveoutapartofheat,theamountisQ,andQ=W,onlyinthiswaycanthesystemrecover.Iftheamountofheatthatthesystemgiveoutcantranslateintotheworkcompletelyandleadtonootherchanges,thatistosayQequalstoW,thenwecansaythatisareversibleprocess.Actuallythatisimpossible.Thatisthesecondlawofthethermodynamics.Theinternalenergyisthecombinationofmolecularkineticandpotentialenergy,withregardtoidealgas,themolecularpotentialenergyistoosmallthatisignored,becausethedistancebetweenthetwomoleculesisgreaterthantenfoldoftheatomicradius.Thentheinternalenergyofidealgasisthemolecularkineticenergy,itdependsontemperature.PhysicalchemistryInthiscoursewehavealsolearnedthefirstandthesecondlawofthermodynamics,inadditionwehavelearnedtheelectricchemistry,suchasprimarybattery.ForexamplethereisaCu-Zn(copper-zinc)primarybattery,itsstructureislikethis.Theammeteristomeasurethesizeofthecurrent.Thereactionsofpolesarelikethis,zinclosetwoelectronandbecometozincion,copperiongainthetwoelectronsandbecometocopper,electronsaredeliveredfromthezincpoletothecopperpole,thedirectionofcurrentisopposite,thenthezincpoleisnegativeelectrode,thecopperpoleisthepositiveelectrode.TheelectromotiveforceofthisprimarybatterycanbecalculatedbyNernstequation,forthenegativepole,theelectromotiveforceisthat,thisistheelectromotiveforceofstandardstate,RandFareconstants,nistheamountofthetranslatedelectrons,Tisthetemperature,thisistheconcentrationofzincions.ThegeneralelectromotiveforceequalsEpositiveminusEnegative.Whenthereactantsaresolids,theyarenotinvolvedintheNernstequation.FundamentalsofmaterialsscienceAllsubstancesareformedbycountlessparticles,theseparticlescanbeatoms,moleculesandions,whentheycombinetosolids,whatkindofcombiningpowermakethemgatheredtogether?Formetals,theatomsinteractdependsonthefreeelectronsandmetallicpositiveionsinthemetal,thesefreeelectronsarecommontoallpositiveions,theymakethemetalhavegoodelectricalandthermalconductivity.Theheatisdeliveredthroughthemovementoffreeelectrons,andtheelectronshaveaweakresistancetothecurrent.Whenthemetalisundertheappliedforce,thepositionofatomswillchange,buttheinnerstructurewillnotbedestroyed,thismakethemetalbarcanbeprocessedintothinsliceswithoutthechangingofstructureandproperties.DiffusionanddefectPhysicsInthiscoursewehavelearnedGausstheorem,itisthat,inanelectrostaticfieldinvacuum,theelectricfluxthroughanyclosedsurfaceequalsthegeneralchargenumbersurroundedbythissurfacemultiply1/ε0.Electricfluxisthenumberofelectricfieldline.Theformulaisasfollows:***Emultiplydsistheelectricflux,Eistheelectricfieldintensity,Sisthearea,thisisthegeneralchargenumber,ε0isaconstant.CanIuseanexampletoexplaintheGausstheorem?Thereisauniformlychargedstraightline,thelinedensityis+λ,theelectricfieldaroundthelineissymmetrical,wefindapointP,thedistancebetweenthelineandthepointisr,thedirectionofelectricfieldofpointPcanonlyalongtheradialdirection,otherpointsonthesamecylindricalsurfacewithPhaveaequalelectricfieldstrengthbothinquantityanddirection.Thenwesupposeacylindricalsurface,theelectricfluxistheproductofEandS,Sconsistsoftheside,uppersurfaceandundersurface,weusuallythinkthat,theelectricfluxisnegativewhentheelectricfieldlinethroughthesurfacefromtheoutsidein,itispositivewhentheelectricfieldlinethroughthesurfacefromtheinsideout,thenthesummationoftheelectricfluxofupperandundersurfacesis0,thenthegeneralelectricfluxdependsontheside,theareaofthesideis2πrl,Ecanberegardedasaconstanthere,sowecanwriteitoutoftheintegral.Thegeneralchargenumberoftheclosedsurfaceisλl.FromtheGausstheoremwecansaythat.ProbabilityandmathematicalstatisticsInthiscoursewehavelearnedthecompleteprobabilityformula,itisthat,Paistheprobabilityofincidenta,Pbiistheprobabilityofincidentb,P(a/bi)istheprobabilityofincidentaaftertheoccurrenceofincidentb.CanIuseanexampletoexplaintheformula?Therearethreesameopaquejars,thefirsthastwowhiteballsandoneblackball,thesecondhasthreewhiteballsandoneblackball,thethirdhastwowhiteballsandtwoblackballs.NowIrandomlychooseajarandchooseaballfromit,whatistheprobabilitythatgetawhiteball?Supposetheincidentaiswegetawhiteball,incidentbrepresenttheballisfromwhichjar.ThenPb1is1/3,Pb2is1/3andPb3is1/3.Pa/b1is2/3,Pa/b2is3/4,Pa/b3is1/2,fromthecompleteprobabilityformulawecancometo...Mathematicalstatisticsisthat,afterarepeatedobservationsandexperimentsoftheobjectswewanttosearch,wecanestimateandcheckoutaccordingtotheregularitiesofdistributionofdata.Forexamplewewanttoresearchtheusefullifeofabatchoflampbulbs,thelifeofeverybulbisdifferent,someis1200hours,someis1600hours,butthelivesofbulbshaveacertainpercentageateachinterval,forexamplethepercentagebetween1000hoursand1600hoursis80%ofallthebulbs,butthepercentagebetween1600hoursand2000hoursisonly8%.Accordingtotheregularitiesofdistributionoftheknowndatawecanestimatetherangeoflivesofthenottestedbulbs.Forthesebulbs,wecansaythelivesarebetween1000hoursand1600hours.Materialsmechanics1.Inthiscoursewehavelearnedtorsionaldeflection,itisakindofmodeoftexturingwhenthematerialsundertheappliedforce.Inourdailylifewecanalsofindthetorsion,fore