Experimental Physics II - Molecular-kinetic theory of gases 28

Experimental Physics EP2 Thermodynamics

– Kinetic theory of gases –Collisions

https://bloch.physgeo.uni-leipzig.de/amr/

Experimental Physics II - Molecular-kinetic theory of gases 29

Collision frequency

A

yv

yv

v!

tvAnN iyii D××= å=D

ºi

iivnAtNz yyy dvvfvA )(

0ò¥

=

Experimental Physics II - Molecular-kinetic theory of gases 30

Collision frequency

A

yv

yv

v!

tvAnN iyii D××= å=D

ºi

iivnAtNz yyy dvvfvA )(

0ò¥

=

yy

y dvkTmv

vkTmnAz

þýü

îíì-= ò

¥

2exp

2

2

0p

{ }21

exp 2

0

=-ò¥

xxx d

mkTnA

mkT

kTmnAz

pp 2212

2==

mkTvp8

=

vnAz41

=Compare to what

you will getwithout distribution

of velocities.

Experimental Physics 4a - Molecular-kinetic theory of gases 31

Reservoir with a hole

T

V

S

zSdtdN -=

SdtvndN41

-=

dtVSv

ndn

41

-=

tt

enn-

= 0 SvV4

=t

0v 0n

Conservation of particle number: vnvn 41

00 =

Conservation of energy: ®=× kEmvvn 2

021

00

pmkTnEk

3)(2=

®

The average kinetic energy of a particle escaping a small hole in the reservoir

3

161 vnmEk p=

®

kT2=e

02 vvp

= p80nn =k

mvT4

20=

Experimental Physics 4a - Molecular-kinetic theory of gases 32

Molecular collisions

d2

tvV ×=s2dps =

tvnnVN s==

Volume explored by a molecule

Number of molecules collided with

Collision frequency vntNz s== /

Mean free-path- length

ssl

ntvntv

NL

21

2===

‘Maxwellian’ correction vnz s2=

nm145)103.0(14.31001.1

3001038.1295

23

»´×××

×´= -

-

nl

Experimental Physics 4a - Molecular-kinetic theory of gases 33

Crooks radiometer

Thermal creep

Momentum conservation in stationary state:

Very low pressures (~P)

Higher, but still low pressures (~1/P)

Experimental Physics 4a - Molecular-kinetic theory of gases 35

Viscosity and heat conduction

u

nmv ×= lh31

particlencv ×= lk31

sl

n21

=

Momentum transfer

Energy transfer

Experimental Physics 4a - Molecular-kinetic theory of gases 36

Ø The Boltzmann distribution describes variation of

particle densities in external potential fields.

Ø The Boltzmann and Maxwell distributions are

intimately related and follow from each other.

Ø Molecular collisions play important

role in establishing distribution of

molecular velocities.

Ø Viscosity is related to momentum transfer,

heat conduction – energy transfer,

diffusion – mass transfer.

To remember!