Mean Free Path

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Lecture 21
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• Mean Free Path
• Collision Frequency

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Molecular air traffic is fairly busy
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450 m/s
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O2 molecules
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P 1 atm T 25C
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Diffusion
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Collision frequency O2 order of magnitude A) 100
times per sec B) 100.000 times per sec C)
10.000.000 times per sec D) 1000.000.000 times
per sec
Make your choice ..
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Equilibrium velocity distribution
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non-equilibrium
?S gt 0
equilibrium
PV nRT
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The velocities have a certain distribution in
equilibrium the Maxwell-Boltzmann distribution
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Why are velocities different, even in
equilibrium?
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In equilibrium, both types of collisions occur.
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Summary of Statistics of distributions
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Slow molecules
P(v)
particles with very high speed
v
dv
dv
P(v) dv Probability to find a value for v in
the range v, v dv

distribution function
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Average kinetic energy
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continuous
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discrete
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Boltzmann
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Distribution function P(v)
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v
Maxwell-Boltzmann distribution
low T, high M
v
high T, low M
speed v
average
typically 500-1000 m/s
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? Collision frequency z
? Collision frequency z
(see Ball p 665)
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Collision frequency z on ONE particle
d
d
Hit
pd2
Miss
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Number of collisions in t seconds
in t sec
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Mean Free Path ? (1)
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Mean Free Path ? (2)
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? 7 x 10-8 m for O2 at P 1 atm
O2 molecule in the atmosphere travels many times
its own diameter before it hits another molecule.
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Lecture 22
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Diffusion
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Molecules find each other in a solution by
diffusion
Collision only
Fe2
Diffusion coefficient D0
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S2-
collision reaction
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gas
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liquid
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In a liquid with viscosity ? the diffusion
coefficient of a sphere with radius R is
Stokes friction factor
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Translation x by diffusion
x3
x1
x2
x
-x
etc.
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Average displacement
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Quadratic displacement
(Einstein 1905)
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Ficks first law
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Particle flux
x
Diffusion flux through surface area
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concentration c
flux J
concentration gradient
x
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Spontaneous ?G -T?S ?S gt 0 ?G lt 0
total
entropy increases
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Do-it your-self slides
In a stationary diffusion process the diffusion
flux J is constant in time. The following two
slides show a practical example of stationary
diffusion, and how to evaluate the stationary
diffusion flux from Ficks first law.
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Application of Ficks first law
c1, c2 are constant
c2
c1
porous disk
?x
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D constant . J constant (in stationary
state)
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Units