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

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• Useatleasta24-pointfontsoeveryoneintheroomcanreadyourmaterial.

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Startwith:PV=nRT

Showderivationto:𝑝 = 𝜌𝑅𝑇