普通物理英语课件31_KineticTheoryGases.pdfVIP

KineticTheoryofGases

Physics1425Lecture31

MichaelFowler,UVa

Bernoulli’sPicture

•DanielBernoulli,in1738,was

thefirsttounderstandair

pressureintermsofmolecules—

hevisualizedthemshooting

aroundveryrapidlyinaclosed

container,supportingaweight

asshownbyconstantlybouncing

offtheundersideofthepiston.

•Givenmoreroom,theywould

rushintofillthenewspace,just

asagasisobservedtodo.

•No-onebelievedhim.

OneDimensional,OneMoleculeGas

•Themoleculeroundtripsintime•V

2L/v,soitbouncesoffthepiston

v/2Ltimespersec,eachtime

deliveringmomentum2mv,sothe

pistonwillpickupmomentumfrom

this“gas”atrate2mvxv/2LperL

second.v

•Forcefromgasonpiston:

F=rateofchangeofmomentum=

2

mv/L.Anequaloppositeforcemust

besuppliedfromoutsidetokeepthe

pistonatrest.1-Dgas:moleculebounces

•Animation!betweenendsofcylinder.

MoleculeinaTwo-DimensionalBox

•Assumeperfectlyelastic

•a

collisionswithallwalls.

y

•Themoleculewillfollowa

zigzagpath,thetimebetweenv

y

collisionswiththesameend,

v

saytheendatx=L,isnowx

2L/vx,andthemomentum0x

transferredpercollisionis

L

2mvx,sotheaveragefor