kinetic theory of gases – · experimental physics 4a - molecular-kinetic theory of gases 36 Ø...
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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!
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