MFTAI-戴明凤

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1、Lab.12-Determinethevalueofair實驗12：空氣值的測定I.Object:MeasuretheratioofairusingClement&Desorms’method.目的：以克雷孟和德梭姆的方法測量空氣的值=cp/cv=定壓比熱及定容比熱比值,--氣體動力學中一個很重要參數Adiabaticprocess(絕熱過程)BroilgeLaw:atconstantT，anidealgaswiththefixedparticlesobeysPV=nRT=constant.Butrealgasisn’tagoodheatconducto

2、r,itneedtimetoreachanewthermalequilibrium.AsPandVchangetoorapidly,e.g.,thepropagationofsound,theenergiesbetweenthepartsofgascannotexchangewitheachotheratonce.Soitisimpossiblefortheisothermalprocess(等溫過程),therealizereactionshallbeanadiabaticprocess.Adiabaticprocess:Ifgasiscompressed(ex

3、panded),allworkdonebythesurroundingbecomes(dissipate)theinternalenergyofgas,thusthePandTofgaswillsimultaneouslyincrease(decrease).Theslopeofp(V)curveinadiabaticprocessmuststeeperthanintheisothermalprocess.熱力學第一定律(能量守恆)：系統能量U之微分dU(1stthermodynamicallaw:energyconservationlaw)吸/放熱+作正功(en

4、dothermic/exothermicreaction+dopositivework):dU=dQ+dW吸/放熱+作負功(endothermic/exothermicreaction+donegativework):dU=dQ–pdV摩爾定容比熱(molarheatcapacityatconstantvolume)摩爾定壓比熱(molarheatcapacityatconstantpressure)空氣在室溫(T~300K)可視為接近理想氣體(Airat300Kcanbeasideagas)pV=NkT,pV=nRTN=粒子數(Particlenumber)k=

5、1.38x10-23J/K=波茲曼常數(Boltzmanconstant)nN/NA=粒子摩爾數(Molarno.)NA=6.02x1023/mol=亞佛加德常數(Advogadroconstant)RkNA=8.31J/mol-K=氣體常數(Gasconstant)Principle(原理)DerivethevalueofideagasIdealgasespV=nRTpdV+Vdp=nRdTConstantPressuredp=0(定壓時)dQ=dU+pdV=dU+nRdT能量均分(EquipartitionofEnergy):kT/2perdegree

6、offreedom空氣主要為雙原子分子N2:78%,O2:21%，在室溫(T~300K)有3個自由度的平移，2個自由度的轉動，但不會振動。故每一分子共有5自由度，每自由度貢獻kT/2能量。總能量Total=U~5nRT/2定容比熱:cv~5R/2定壓比熱:cp=cv+R~7R/2定壓比熱及定容比熱比值:cp/cV~7/5cP=cv+R=cp/cv=(cV+R)/cv(19–11)InternalEnergyofanidealGas理想氣體的內能f=3f=5f=6Cv=3/2R=12.5J/mol.KCp=5/2R=20.8J/mol.KTheoreti

7、calvaluesofCV,CP,andareinexcellentagreementformonatomicgases.MolarSpecificHeatforanIdealgasSeveralprocessescanchangethetemperatureofanidealgas.SinceDTisthesameforeachprocess,DEintisalsothesame.Theheatisdifferentforthedifferentpaths.Theheatassociatedwithaparticularchangeintemperaturei

8、snotu