DOC. 25 SOLVAY
DISCUSSION REMARKS
393
V.
KNUDSEN
Knudsen had reviewed
the
available evidence in favor
of
the kinetic
theory
of
gases, emphasizing
the
good
agreement
between
theory
and
experiment
in the
limiting case
that the
mutual interaction
between
the
molecules of
a gas
is
small in
comparison
to
the
interaction between the
gas
and its container. In
the
first
comment
during
the
discussion
of
Knudsen's
contribution,
Nernst claimed
that
Maxwell's law
of
the distribution
of molecular velocities
might
have
to
be
changed
because
the
quantum hypothesis implies a change
of
the law
of molecular
collisions. (For
the
implications
of
the quantum
hypothesis
for molecular
collisions, see
Einstein's
lecture Einstein 1914
[Doc.
26],
p.352.)
In his
response
to
Nernst's
comment,
Einstein shows himself convinced
of the
validity
of
the Maxwell distribution and hence
of the theorem of
the
equipartition
of
energy,
at
least for
the linear motion
of
gas molecules, a
conviction
that
also underlies his
contemporary
studies
of
radiation in
interaction with
a gas (see
Einstein and
Hopf 1910b
[Doc.
8]).
If the
mean length
of
the
path
of
a
molecule
is
small, however,
Einstein
argues
that the
validity
of
the
equipartition
theorem
is
no longer
assured. Einstein's
first
comment is
followed
by a
remark
by Warburg on
the
Krakatoa
eruption
of
1883,
which showed
that
the
motion of dust
particles
in
the
higher atmosphere
deviates from Stokes's
law.
The discussion thus
turned
to
the
problem
of small
spheres
suspended
in
a
medium.
This
problem,
touched
upon
in
Knudsen's
talk,
was
at
that
time
particularly important
because
of
its role in Millikan's oil
drop
experiments on
the
value
of the
elementary charge,
and
quickly
became the focus of
the
discussion
(see
Holton 1978 for
a
historical
study
of
Millikan's
experiments).
Perrin and Brillouin
suggested
possible
deformations of
spherical droplets
in
a
medium
as
the
cause
for
the
deviation
of
their motion from Stokes's
law.
In his second remark
during
this discussion
Einstein refuted the
conjecture
that
thermodynamic
fluctuations could
give
rise
to
such
deformations
by arguing
that
the work
to
produce
these deformations exceeded
the
energy
transferred
to
the
drops by collisions; see
Einstein 1907b
(Vol.
2,
Doc.
39).
No.
114
(Knudsen
et
al. 1914,
p. 121;
Knudsen
et
al.
1912,
p. 147)
5)
Even
though
it
is
certain that
our
mechanics fails with
regard
to
the
oscillatory
thermal motions of
atoms and
molecules,
it
can
not
hardly
be
doubted that
Maxwell's
distribution
law
is
valid for
the translational motion of
gas
molecules
involving
sufficiently
large
free
paths.
For
Maxwell's law
assumes
only
the
momentum
and
energy conserva-
tion
laws
for
individual
collisions;
these
will
certainly
remain
valid
even
if
our
mechanics
does not
hold
during
individual collisions.
However,
Maxwell's law
presumably
does not
hold
when,
at
a given
temperature,
the free
path length
becomes much too small.
For
in
that
case
the molecule
describes
a
zigzag
line,
that
is,
a
kind of
oscillatory motion,
for
which,
according
to
our
present
knowledge,
the
law
of the
equipartition
of
energy
does
not hold.
No.
127
(Knudsen
et al.
1914, p.
123;
Knudsen
et al.
1912, p. 150)
6)
A
noteworthy
deformation of
small
droplets
owing
to
irregular
thermal motion
must
be ruled
out
because of
the
considerable
capillary
forces.
Only
such deviations from
thermodynamic equilibrium
take
place
whose
average
value is such
that the
mechanical
work
necessary,
according
to
thermodynamics,
for
producing
the
deviations is
equal
to
RT
-2N,
i.e.,
to
a
third of the
average
kinetic
energy
of
a
monatomic
gas
molecule.