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Lecture3
PhysicalPropertiesofAir• IntroductiontoKineticTheoryofGases• Boyle’sLaw• Charles’Law• Avogadro'sLaw• DefinitionofaMoleandMolecularWeight• IdealGasLaw
ATMOS5130
KineticTheoryofGases
Fourbasicpostulates:• Gasesaremadeupofmolecules
• moleculesaspointmassesthatareperfectspheres.• Separationofmoleculesislargecomparedtomolecularsize
• Moleculesareinconstantrandommotion• Withadistributionofspeedthatdoesnotchange.
• ThemovementofmoleculesisgovernedbyNewton’sLaws:• movesinastraightlineatasteadyvelocity,notinteractingwithanyoftheothermoleculesexceptinacollision.Moleculesexertequalandoppositeforcesononeanotherwithcollision.
• Molecularcollisionsareperfectlyelastic:• Moleculesdonotloseanykineticenergywhentheycollidewithoneanother.
Studyofthemicroscopicbehaviorofmoleculesandtheinteractionswhichleadtomacroscopicrelationshipsliketheidealgaslaw
CHAPTER2:Statevs.ProcessVariables
StateVariablesUniquelydeterminedbythecurrentstateofthesystemPropertiesofasystemareatapointintime,nothowitarrivedatthatstate.
• Pressure• Temperature• Density
ProcessVariablesAssociatedwithaprocess,Exchangeofenergybetweensystemandenvironmente..g.heatenergy(Q)addedtoairsampletobringittocurrenttemp
CHAPTER2:Extensivevs.IntensiveVariables
ExtensiveVariablesDependsonthesizeofthesampleorsysteme.g.volume
IntensiveVariablesDoesnotdependonthesizeofthesampleorsysteme.g.volumepermass
Chapter3:EquationofState
Forahomogeneousparcelofair,thestatevariables(intensiveform)wewillconsiderfirstare:p=pressureT=temperatureα=specificvolume𝜌 =density
𝛼 ≡1𝜌
Variableforallequations
VisthevolumeofgasPisthepressureofgasTisthetemperatureofgaskisaconstantM=Mole
Boyle’sLaw
Atconstanttemperatureforafixedmass,theabsolutepressureandthevolumeofagasareinverselyproportional.
Video
CharlesandGay-Lussac’sLaw(alsoknownasthelawofvolumes)isanexperimentalgaslawthatdescribeshowgasestendtoexpandwhenheated.
Video
Avogadro’sLaw
Equalvolumesofallgases,atthesametemperatureandpressure,havethesamenumberofmolecules.
Definitionofamole(M)Mole=6.02214179× 1023,
OnemoleofanidealgasatStandardTemperatureandPressure(STP)occupies22.4liters.
Standardtemperature:0°C=273.15KStandardpressure=1atm =1013hPa
Definitionofamole(M)Mole=6.02214179× 1023,
Numberofatomsfoundin12gramsofCarbon-12.
Carbon-12waschosenarbitrarilytoserveasthereferencestandardofthemoleunitfortheInternationalSystemofUnits(SI).
ThenumberofunitsinamolealsobearsthenameAvogadro’snumber,orAvogadro’sconstant.
MolecularWeight=massofonemoleofsubstance
ExploringEarthfundedbyNSF
Element AtomicWeight(g/mol)
Ba 137.327
C 12.0107
Ca 40.078
Cr 51.9961
H 1.00794
Mg 24.3050
N 14.0067
Na 22.989770
O 15.9994
P 30.973761
Usethedatafromtheperiodictabletoanswerthefollowingquestions.
CalculatethemolecularweightofCa3 (PO4)2 [CalciumPhosphate]
Element AtomicWeight(g/mol)
Ba 137.327
C 12.0107
Ca 40.078
Cr 51.9961
H 1.00794
Mg 24.3050
N 14.0067
Na 22.989770
O 15.9994
P 30.973761
Usethedatafromtheperiodictabletoanswerthefollowingquestions.
CalculatethemolecularweightofCa3 (PO4)2 [CalciumPhosphate]
Answer:
Themolecularweight=
3(40.078)+2(30.973761)+8(15.9994)=
120.23+61.947522+127.9952=310.18g/mol.
Question:Threeballoonsarefilledwithdifferentamountsofanidealgas.Oneballoonisfilledwith3molesoftheidealgas,fillingtheballoonto30L.
a)Oneballooncontains2molesofgas.Whatisthevolumeoftheballoon?b)Oneballoonenclosesavolumeof45L.Howmanymolesofgasareintheballoon?
Question:Threeballoonsarefilledwithdifferentamountsofanidealgas.Oneballoonisfilledwith3molesoftheidealgas,fillingtheballoonto30L.
a)Oneballooncontains2molesofgas.Whatisthevolumeoftheballoon?20Lb)Oneballoonenclosesavolumeof45L.Howmanymolesofgasareintheballoon?4.5moles
Dalton’sLawofPartialPressures
Totalpressureexertedbyamixtureofgasesisequaltothesumofthepartialpressurethatwouldbeexertedbyeachconstituentaloneifitfilledtheentirevolumeatthetemperatureofthemixture.
𝑝 ='𝑝(
)
(*+
GasConstants
R=NAkB
WhereNA =AvogadroConstantkB =Boltzmannconstant
AverageTranslationalKineticEnergyofamoleculeinanidealgasis:
KEavg =(3/2)kBT PERMOLECULE
Keavg =(3/2)RTPERMOLE
kB =Boltzmannconstant=1.38066x10-23 J/K
UniversalGasConstantR=8.3145J/mol K
Inourtextbook,theuniversalgasconstantiswrittenasR*
CompositionofaDRYAtmosphere:Troposphere
WaterVaporVaries0– 5%
0.041%
GasConstantsforDryAirUniversalGasConstantR=8.3145J/mol K
Inourtextbook,theuniversalgasconstantiswrittenasR*
Massofdryair:
𝑚- ≈ 0.7808 ∗ 28 + .2095 ∗ 32 + .00093 ∗ 40 + 0.000405 ∗ 44 = 28.96𝑚- ≈ Nitrogen(N2)+Oxygen(O2)+Argon(Ar)+CarbonDioxide(CO2)
𝑅- ==∗
>?= 8314.472( A
)>BC∗ 𝐾)/28.9655(kg/kmol)=287.047J/(kg*K)
NOWcanbeusedwithIntensiveVariables
IdealGasLaw
PV=nR*Twhere:
Pisthepressureofthegas,Visthevolumeofthegas,nistheamountofsubstanceofgas(alsoknownasnumberofmoles),Ristheideal,oruniversal,gasconstant,equaltotheproductoftheBoltzmann
constantandtheAvogadroconstant,Tistheabsolutetemperatureofthegas.
IdealGasLaw– Meteorologist
𝑝 = 𝜌𝑅𝑑𝑇R=Gasconstantfordryairp =pressure𝜌 =density
Boyle’sLaw
Charles’Law
CLASSPresentation• Formgroupof2students• Present~20minutepresentation(~10minuteeachperson)• Focusontopicsfoundwithin“InPractice”sectionofyourtextbook.• Yourresearchshouldgobeyondthetextbook.• BeCreative!Props
Examplesofmaterialtopresent• Hygrometer• WindChill• Radiosonde• Skew-Tdiagram• Psychrometer• HeatIndex• AneroidBarometer• Altimeter• Subsidenceinversion
Suggestionsforeffectivedisplay• Keepitsimple! Fancydesignsorcolorshiftsmakeimportantmaterialhardtoread.Lessismore.
• Useatleasta24-pointfontsoeveryoneintheroomcanreadyourmaterial.
• Trytolimitthematerialtoeightlinesperslide,andkeepthenumberofwordstoaminimum.Keepitsimple.
• Limitthetablestofourrows/columnsforreadability.Sacrificecontentforlegibility.Largetablescanbedisplayedmoreeffectivelyasagraph.
• Useeasilyreadfonts.• Don'tfilluptheslide- theperipheralmaterialmaynotmakeitontothedisplayscreen.
• Identifythejournalwhenyougivereferences.• Finally,alwayspreviewyourpresentation.YouwilllookfoolishifsymbolsthatlookedOKinaWORDdocumentdidn'ttranslateintoanythingreadableinPOWERPOINT.
Startwith:PV=nRT
Showderivationto:𝑝 = 𝜌𝑅𝑇
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