材料热力学习题答案2

Theproblemsofthesecondlaw1Thesolarenergyfluxisabout4Jcm2/min.innofocusingcollectorthesurfacetemperaturecanreachavalueofabout900℃.Ifweoperateaheatengineusingthecollectorastheheatsourceandalowtemperaturereservoirat25℃,calculatetheareaofcollectorneedediftheheatengineistoproduce1horsepower.Assumetheengineoperatesatmaximumefficiency.(2.1)Solution)(664.0)(74660104273900)25900(24mSWtWPStQTTTWHHLH2Arefrigeratorisoperatedby0.25hpmotor.Iftheinterioroftheboxistobemaintainedat-20℃ganisteramaximumexteriortemperatureof35℃,whatthemaximumheatleak(inwatts)intotheboxthatcanbetoleratedifthemotorrunscontinuously?Assumethecoefficientofperformanceis75%ofthevalueforareversibleengine.(2.2)Solution:)(114474625.02035202733475.0%75WPPTTTPQTTTWLLLLHHHLH3supposeanelectricalmotorsuppliestheworktooperateaCarnotrefrigerator.Theinterioroftherefrigeratorisat0℃.Liquidwateristakeninat0℃andconvertedtoiceat0℃.Toconvert1goficeto1gliquid.△H=334J/gisrequired.Ifthetemperatureoutsidetheboxis20℃,whatmassoficecanbeproducedinoneminutebya0.25hpmotorrunningcontinuously?Assumethattherefrigeratorisperfectlyinsulatedandthattheefficienciesinvolvedhavetheirlargestpossiblevalue.(2.3)Solution:)(4576033474625.020273gmMmPPTTTPLLLLH4under1atmpressure,heliumboilsat4.126K.Theheatofvaporizationis84J/molwhatsizemotor(inhp)isneededtorunarefrigeratorthatmustcondense2molofgaseousheliumat4.126ktoliquidatthesametemperatureinoneminute?Assumethattheambienttemperatureis300Kandthatthecoefficientofperformanceoftherefrigeratoris50%ofthemaximumpossible.(2.4)Solution:)(52.0)(393'60284216.4216.4300'5.0%50hpWPPTTTPPQTTTWLLLHLLLH5ifafossilfuelpowerplantoperatingbetween540and50℃providestheelectricalpowertorunaheatpumpthatworksbetween25and5℃,whatistheamountofheatpumpedintothehouseperunitamountofheatextractedfromthepowerplantboiler.(a)assumethattheefficienciesareequaltothetheoreticalmaximumvalues(b)assumethepowerplantefficiencyis70%ofmaximumandthatcoefficientofperformanceoftheheatpumpis10%ofmaximum(c)ifafurnacecanuse80%oftheenergyinfossilfoetoheatthehousewoulditbemoreeconomicalintermsofoverallfissilefuelconsumptiontouseaheatpumporafurnace?dothecalculationsforcasesaandb(2.5)solution:1,2,2,1,212,2,2,2,21,1,1,1,198.82527352527354050540)(HHHHHHLHHHLHPPPPPPPTTTPPTTTPa.,)(6286.0)(1,2,notisbokisacPPbHH6calculate△Uand△Swhen0.5moleofliquidwaterat273Kismixedwith0.5molofliquidwaterat373Kandthesystemisallowedtoreachequilibriuminanadiabaticenclosure.AssumethatCpis77J/(molK)from273Kto373K(2.6)Solution:)/(933.0)273323ln(5.0)373323ln(5.0)ln()ln()(02211KJCCTTCnTTCnSJUPPEPEP7Amoderncoalburningpowerplantoperateswithasteamoutletfromtheboilerat540℃andacondensatetemperatureof30℃.(a)whatisthemaximumelectricalworkthatcanbeproducedbytheplantperjouleofheatprovidedtotheboiler?(b)Howmanymetrictons(1000kg)ofcoalperhourisrequirediftheplantoutputistobe500MW(megawatts).Assumethemaximumefficiencyfortheplant.Theheatofcombustionofcoalis29.0MJ/kg(c)Electricityisusedtoheatahomeat25℃whentheoutdoortemperatureis10℃bypassingacurrentthroughresistors.Whatisthemaximumamountofheatthatcanbeaddedtothehomeperkilowatt-hourofelectricalenergysupplied?(2.7)Solution:)(3.69)(6937136005000.29)()(89.013054030540)(tonkgmTTTmbJQTTTWaLHLHHLH)(9.191102525273)(JQQTTTWcHHHLH8anelectricalresistorisimmersedinwaterattheboilingtemperatureofwater(100℃)theelectricalenergyinputintotheresistorisattherateofonekilowatt(a)calculatetherateofevaporationofthewateringramspersecondifthewatercontainerisinsulatedthatisnoheatisallowedtoflowtoorfromthewaterexceptforthatprovidedbytheresistor(b)atwhatratecouldwatercouldbeevaporatedifelectricalenergyweresuppliedattherateof1kwtoaheatpumpoperatingbetween25and100℃dataforwaterenthalpyofevaporationis40000J/molat100℃;molecularweightis18g/mol;densityis1g/cm3(2.8)solution:)(23.2,2510027310010004000018)()(45.0,10004000018)(gmmbgmma9somealuminumpartsarebeingquenched(cooledrapidly)from480℃to-20℃byimmersingtheminabrine,whichismaintainedat-20℃byarefrigerator.Thealuminumisbeingfedintothebrineatarateofonekilogramperminute.Therefrigeratoroperatesinanenvironmentat30℃;thatistherefrigeratormayrejectheatat30℃.whatisthemminuspowerratinginkilowatts,ofmotorrequiredtooperatetherefrigerator?Dataforaluminumheatcapacityis28J/molK;Molecularweight27g/mol(2.9)Solution:)(5.102)(102474202732030)20480(28271000kWWPPTTTPPLLLLHWL10anelectricpowergeneratingplanthasaratedoutputof100MW.Theboileroftheplantoperatesat300℃.Thecondenseroperatesat40℃(a)atwhatrate(joulesperhour)mustheatbesuppliedtotheboiler?(b)Thecondenseriscooledbywater,whichmayundergoatemperatureriseofnomorethan10℃.Whatvolumeofcoolingwaterincubicmetersperhour,isrequiretooperatetheplant?(c)Theboilertempetureistoberaisedto540℃,butthecondensedtemperatureandelectricoutputwillremainthesame.Willthecoolingwaterrequirementbeincreased,decreased,orremainthesame?Dataheatcapacity4.184,density1g/cm3(2.10)Solution:)(109.7)(102.21040300273300)(1188JtPQWPTTTPaHHLHHH)(1003.1184.41010)(103.4)(34611mVQVJQbLL