138
REVIEW
OF LANGEVIN
Doc. 22
Review
of
P.
LANGEVIN,
"On
a
Fundamental Formula
of the Kinetic
Theory"
("Sur
une
formule fondamentale
de
la theorie
cinetique,"
Academie
des
Sciences (Paris).
Comptes
rendus
140 (1905): 35-38)
[Beiblätter
zu
den
Annalen
der
Physik 29 (1905):
640]
The
author
reports
that,
assuming
arbitrary
laws
of action
between
[1]
molecules
as
well
as
external forces
acting
upon
the
molecules,
he has
solved
[2]
exactly
the
problem
of
diffusion
of
two gases
by
the Maxwell-Kirchhoff
method,
[3]
requiring
only
a
graphic
integration. For
the
case
that the molecules
are
elastic
spheres
which
are
only
infinitesimally deformable,
and
that external
forces
do
not
act
on
the
molecules,
the author obtains for the diffusion
of
one
gas
(molecular
mass
m1)
in the other
gas
(molecular
mass
m)
[4] B
=
16
a2M
ihm
l
m+
m1
Here
D
denotes the diffusion
constant,
a
the
sum
of the radii
of
two
unlike molecules,
M
the
number
of
molecules
"m" per
unit
volume,
h
three-quarters of
the
reciprocal of
the
mean
value
of the
energy
of
the
translational
motion
of
one
molecule.
Boltzmann found
by
the Clausius
[5] approximation method
[6]
D
=
3ia2M\
ih(m+
)
The two
formulas differ
especially strongly
when
m
and
m1
are
very
different. It is further
reported
that
at constant
pressure
the diffusion
coefficient varies
as
T3/2 + 2/n
when two
unlike molecules
repel
each
other
with
a
force that
is inversely proportional to
the
n
+
1st
power
of
the
distance
between
the
centers
of the molecules.
The
author
has also
applied
the
theory to
changes
in
position of
electric
charges
in
gases. He
found
that
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