148
DOC.
4
KINETIC THEORY LECTURE NOTES
c
5
Since
ci
obviously
increases
with
increasing
molecular
size,
-
is
here
-
and
c
3
v
approaches unity
with
increasing
ci.
[p. 3]
Approximate Theory
of Heat
Conduction,
Viscosity,
and
Diffusion
To
simplify
the
calculation, we
shall
assume
that
at
the
same
location
all molec. have
the
same velocity
\C2.
We
designate by
X
the
mean path length
of
a
molecule
on
which
the
quantities
to be
calculated
depend.
Transport
of
Any
Molecular
Quantity through
the
Gas[12]
n
number of
molecules in
unit
volume.
ndK
number
" " " " "
of
spec.
ndkc
cos Udt
During
time
dt, v
=
4ir
fly
from
top
to
bottom
dK
sinUdUdw
/
4tz 4tc
Each
molecule
carries
along
a
certain
quantity
of
something,
with this
amount
depending
only on
where the molecule's
last collision
took
place.
traveled
freely
the
distance
X
up
to
the
layer comes
from
the
3G0
layer
z
= z0
-
X
cos
U
There the
value
G(z0
-
Xcos0)
= G0
--zXcosü
obtains
permanently.
Thus,
the
v
molecules
carry along
during
dt the
quantity
G"
Xcosö3Gn
o
dz
In
the
same
way,
we
find
that the
amount
delivered
in
the
opposite direction, charac-
terized
by
the
opposite cone,
is
-v
/ G"
+
-ÜXcosü
0 dz
Here
v
=
v',
so
that
we
have in all
(for
k + k')