1.3
2
Brownian motion
By the end of this spread, you should be able to …
A
1 Describe the differences in the motion of molecules in solids, liquids and gases.
1 Describe a simple kinetic model for solids, liquids and gases.
1 Describe an experiment that demonstrates Brownian motion.
The speed of molecules
B
7HENEVERYOUDESCRIBEANYPHENOMENONABOUTTHESPEEDOFMOLECULESYOUMUST
REMEMBERTHATTHELAWOFCONSERVATIONOFENERGYISALSOINVOLVED)FSOMEMOLECULESHAVE
ANAVERAGEKINETICENERGYHIGHERTHANSOMEOTHERMOLECULESTHENWHENTHEYCOLLIDETHOSE
WITHTHEHIGHERKINETICENERGYWILLLOSEKINETICENERGYANDTHEOTHERSWILLGAINANEQUAL
AMOUNTOFKINETICENERGY4HEPROCESSWILLSTOPWHENTHEAVERAGEKINETICENERGYOFBOTH
SETSOFMOLECULESARETHESAME4HISISACOMMONOCCURRENCE)FYOUPOURCOLDMILKINTO
HOTTEATHETEMPERATUREOFTHEMILKRISESANDTHETEMPERATUREOFTHETEAFALLS)FLOSSESTOTHE
SURROUNDINGSARENOTTAKENINTOACCOUNTTHEKINETICENERGYTHATTHEMOLECULESINTHEMILK
GAINWILLEQUALTHEKINETICENERGYTHEMOLECULESINTHETEALOSEANDALLTHEMOLECULESINBOTH
THEMILKANDTEAWILLEVENTUALLYHAVETHESAMEAVERAGEKINETICENERGY
4HETEMPERATUREOFTHEMOLECULESISDIRECTLYPROPORTIONALTOTHEIRKINETICENERGY4HISWILLBE
EXPLOREDFURTHERINLATERSPREADSBUTATTHISSTAGEITISCRUCIALTOUNDERSTANDTHATMOLECULESIN
ICEATª#HAVETHEsameAVERAGEKINETICENERGYASMOLECULESINWATERATª#4HEFREEZING
POINTOFANYSUBSTANCEISTHETEMPERATUREATWHICHBOTHSOLIDANDLIQUIDPHASESCANCO
EXIST4HESAMEPRINCIPLEAPPLIESATTHEBOILINGPOINTATª#MOLECULESINTHELIQUIDPHASE
WATERHAVETHEsameAVERAGEKINETICENERGYASMOLECULESINTHEGASPHASESTEAM
Pattern of movement in solids, liquids and gases compared
C
!SASOLIDISHEATEDITSTEMPERATURERISESANDTHEKINETICENERGYOFITSMOLECULES
THEREFOREINCREASES(OWEVERBECAUSEITISSOLIDTHEPOSITIONOFEACHMOLECULECANNOT
CHANGE4HEINCREASEINKINETICENERGYTHEREFORERESULTSINGREATERVIBRATIONAROUNDITS
EQUILIBRIUMPOSITION
)NALIQUIDTHESAMEEFFECTTAKESPLACE"UTTHISTIMEASMALLAMOUNTOFTRANSLATIONAL
KINETICENERGYWILLBEADDEDTOTHEINCREASEINVIBRATIONALKINETICENERGYSINCETHE
MOLECULESARENOWABLETOMOVEFROMPLACETOPLACE
4HINGSAREVERYDIFFERENTINAGAS(ERETHECHAOTICMOVEMENTOFTHEGASRESULTSIN
ALMOSTALLOFTHEKINETICENERGYBEINGTRANSLATIONAL
&IGURESAFORASOLIDBFORALIQUIDANDCFORAGASSUMMARISETHEPATTERNOF
MOVEMENTANDTHEPOSITIONOFMOLECULESINTHETHREEPHASES
Figure 1 4HESTRUCTUREANDPATTERNOF
MOVEMENTFORMOLECULESIN(a) ASOLID
(b)ALIQUID(c)AGAS4HOUGHTHEREARE
FARFEWERGASATOMSINANYGIVENVOLUME
COMPAREDTOVOLUMESOFLIQUIDORSOLID
GASATOMSDOSTILLCOLLIDEWITHONEANOTHER
Brownian motion
4HEMOTIONOFMOLECULESINAGASISINVISIBLETOTHE
NAKEDEYE)FHOWEVERSOMESMOKEISINTRODUCED
INTOASMALLGLASSCONTAINERANDTHECONTAINERIS
WELLILLUMINATEDANDVIEWEDTHROUGHAMICROSCOPE
THEEFFECTOFMOLECULARMOTIONCANBESEEN4HIS
SETUPISSHOWNIN&IGURE4HEMICROSCOPENEEDS
TOBEFOCUSEDONTHESMOKEWHICHYOUWILLSEEAS
TINYDOTSOFLIGHT)FYOUCANNOTSEEANYTHINGITIS
PROBABLYBECAUSEEITHERTHEMICROSCOPEISNOT
FOCUSEDINTHEPLACEWHERETHEILLUMINATIONIS
STRONGORMORELIKELYYOUWEREEXPECTINGTOSEE
SOMETHINGMUCHLARGERTHANITACTUALLYIS4HEDOTS
WILLBEONLYJUSTVISIBLE
Microscope
Cover slip
Particles of
smoke dust
Filament Glass rod
lamp
for focusing
Smoke cell
Figure 2 4HEEXPERIMENTALSETUPFOR
VIEWING"ROWNIANMOTION
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Module 3
Thermal physics
4HEMOTIONKNOWNAS"ROWNIANMOTIONWASlRSTOBSERVEDINBY4HOMAS"ROWN
WHENHEWASEXAMININGPOLLENGRAINSINWATER(ENOTICEDTHATTHEYNEVERREMAINED
ABSOLUTELYSTILLBUTALWAYSSHUDDEREDAROUND(EPUTTHISDOWNTOCONTINUOUSMOLECULAR
BOMBARDMENT)TWASTHElRSTDIRECTEVIDENCETHATMOLECULESAREINPERPETUALMOTION
7HENYOULOOKATTHESMOKEPARTICLESINTHEWAYDESCRIBEDABOVEYOUSHOULDBEABLETO
SEETHISSHUDDERINGMOVEMENT)TONLYHAPPENSWITHVERYSMALLPARTICLESBECAUSETHE
MOLECULESAROUNDTHEMDONOTHITTHEMEQUALLYFROMALLDIRECTIONSSOTHEIMPULSEGAINED
BYTHEPARTICLESISNOTZERO)FALARGEPARTICLEISUSEDTHEINDIVIDUALIMPULSESTENDTO
AVERAGEOUTTOZEROANDTHEINCREASEDMASSOFTHEPARTICLECHANGESITSVELOCITYLESS
Brownian motion
STRETCH and CHALLENGE
On the vertical axis the percentage of all the molecules in a particular
speed range is given. On the horizontal axis the speed is divided into
ranges. For example, 10% of the molecules in the gas travel with speed
between 350 and 400 m s–1.
Question
11
10
9
8
Percentage
In any gas with millions upon millions upon millions of molecules, there is
a wide variety of speeds at any one point in time. Having some idea of
the range of speeds is useful to explain the different properties of gases.
For this reason, the histogram (bar chart) shown in Figure 3 is given. The
histogram has been constructed for nitrogen gas (basically air) at a
temperature of 300 K, about room temperature.
7
6
5
4
3
2
1
Most people know that if you want to find the distance you are from a
0
0
250
500
750
1000
1250
lightning flash, you count the number of seconds between the flash and
Speed/m s 1
the thunder. Then you divide by five to get the distance in miles.
(a) What value does this give for the speed of sound in air?
Figure 3 !HISTOGRAMSHOWINGTHERANGEOFSPEEDSIN
(b) The value of the speed of sound in air using SI units is 340 m s–1. How
NITROGENGASAT+
does this value give evidence for the speed of molecules quoted above?
(c) Why do smells travel through the air slowly if molecules are moving so fast?
Questions
1 4HESPEEDOFTHESMOKEPARTICLESINTHEAIRINTHESMALLGLASSCELLCANBEMEASUREDBY
OBSERVING"ROWNIANMOTION!LTHOUGHTHEDIRECTIONOFMOTIONOFTHESMOKEPARTICLES
CHANGESMANYTIMESPERSECONDTHEYMOVEATABOUTMMSn
)NTHECELLTHEAVERAGEAIRMOLECULEANDTHEAVERAGESMOKEPARTICLEHAVETHESAME
KINETICENERGY4AKETHEMASSOFASMOKEPARTICLETOBE™nKGANDTHEMASSOF
ANAIRMOLECULETOBE™nKG%STIMATETHEAVERAGESPEEDOFAIRMOLECULES
BETWEENCOLLISIONSATROOMTEMPERATURE
2 !TYPICALSPEEDINFACTTHERMSSPEEDSPREADOFANAIRMOLECULEATROOM
TEMPERATUREISMSn7HENANAIRFRESHENERSPRAYISUSEDTHESCENTGRADUALLYlLLS
THEROOM4HEMOREMASSIVESCENTMOLECULESTRAVELATABOUTMSn
(a) (
OWLONGWOULDITTAKEASCENTMOLECULETOTRAVELMACROSSAROOMIFTHERE
WERENOOTHERMOLECULESALONGITSPATH
(b) )NFACTITWILLTAKEATLEASTTIMESLONGER%XPLAINWHY
(c) 3
UGGESTHOWTHERATEOFDIFFUSIONTHATISTHECONTINUOUSMOVEMENTOFMIXINGOF
SCENTMOLECULESTHROUGHTHEROOMCOMPARESWITHTHATOFTHEAIRMOLECULES
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