工程材料科学与基础-余永宁-答案.doc

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1、Chapter6-ProblemSolutions1.FIND:Comparethestructureofaglasstothatoftheliquid.GIVEN:Botharenoncrystalline.SOLUTION:Thestructureofaglassisessentiallythatofafrozenliquid.ThereisSRObutnoLRO.Sincetheglassisatalowertemperaturethantheliquidofthesamecompositionandmostmater

2、ialscontrastastheyarecooled,thedensityoftheglassisusuallylessthanthatoftheliquid.Thedensityoftheglassisusuallyconsiderablygreaterthanthatofthecrystal,however.Densityismassperunitvolume,andtheunitsweseemostoftenareg/cm3.Themostcommonunitsofreciprocaldensityarecm3/g.

3、Thisisvolumeperunitmass,orspecificvolume.Itisfrequentlyusedbychemicalphysicists,whostudynoncrystallinematerials.2.3.FIND:HowdoesCpofanamorphousmaterialchangeasthetemperatureisincreasedthroughtheglasstransitiontemperature?SOLUTION:Heatcapacityisanintensiveproperty,o

4、nethatdoesdependonthebulkpropertiesofthematerial.Mostthermodynamicintensivepropertiesbehaveexactlythesameas(molar)volumeinthevicinityoftheglasstransitiontemperature.Hence,heatcapacitychangesslopethroughtheTg.4.5.FIND:Estimatethevolumethermalexpansioncoefficientofag

5、lass.GIVEN:Itslinearthermalexpansioncoefficientinthemeltis10x10-6oC-1.ASSUMPTIONS:Thematerialbehavestypically,sothatthethermalexpansioncoefficientoftheglassisabout1/3ofthatofthemelt.SOLUTION:Thelinearthermalexpansioncoefficientisathandthevolumetricthermalexpansionc

6、oefficientisav.ath(glass)»ath(melt)/3andav(glass)»3ath(glass)Hence,av(glass)»3ath(melt)=10x10-6oC-16.FIND:Derivetherelationshipbetweenathandav:ath/av=1/3SOLUTION:consideracubeofmaterials,length1onaside.Withheat,thematerialsexpandsisotropicallytolength1+d1.Wedothepr

7、oblemfirstusingdifferentials.Nowwithdeltas:V=(i+di)3=13+3i2di+...ÞDV»3i2di.Therefore,9.FIND:IsTgatemperatureorrangeoftemperatures?SOLUTION:Althoughweoftenciteaglasstransitiontemperature,theglasstransitionoccursoverarangeoftemperatures.Tgisratesensitiveandstructures

8、ensitive;itdependsontherateofheatingorcoolingandonthelocalstructurewhichisstatisticallyvariableinaglassormelt.10.FIND:Thetemperaturerangefortrans