242 DOC. 20 THEORETICAL ATOMISM
a
completely
exact
calculation of the
number
N,
and
hence also
of
the absolute size
3
RT
of the molecules. For the
quantity
N determines the
mean
kinetic
energy
L
=
-
2N
of
the
translatory
motion of
the
particle,
and the
latter,
in
turn,
determines the
average
magnitude
of the
path
traveled
by
a
particle
in
one
second.
But the
great
fundamental
significance
of Brownian motion
lies,
as
already
mentioned,
in the fact that in this motion the
disordered
elementary
processes,
which
according
to
the kinetic
theory
constitute the heat
content
of
matter,
are
accessible
to
direct observation. Under the
microscope
one sees
directly,
so
to
speak,
a part
of
the thermal
energy
in
the form of the mechanical
energy
of
moving particles.
This
phenomenon
also shows
clearly
that the laws of
phenomenological
thermodynamics possess only approximate validity. According
to
the latter
theory,
if
one
of
our
particles initially possessed
a
translatory motion,
it
would have
to
come
quickly
to rest
due
to
friction with the
liquid,
and then
stay
at rest.
By generalizing
the
theory
of Brownian
motion,
one
obtains
precise
information
about
how
far,
on
average,
the
states
of
arbitrary physical systems
deviate from the
states
in which these
systems
would have
to
remain
at rest
according
to
the
phenomenological theory
of
heat because of the disorderliness of the
elementary processes.
These considerations lead
us to a
problem that has concerned theoreticians ever
since the formulation of the molecular theory, but that has been solved, in principle,
only
in
the seventies
by
Boltzmann. The mechanical processes to which we seek
to
reduce the thermal ones with the help of the kinetic theory of heat are reversible.
[15]
That
means:
for
every possible
motion there exists another motion
in which the
material
points
will
pass through exactly
the
same
positions
with
exactly
the
same
speed
but in
reverse
order.
However,
reversions of thermal
processes
have
never
been
observed.
If,
for
example, I
were
to
bring
into
contact two
pieces
of metal
possessing
the
same temperature,
they
would
never
assume
different
temperatures
on
their
own.
One would
be
inclined
to
conclude from this that
it is
on principle impossible
to
reduce thermal
processes
to
mechanical
ones,
because it
simply
seems
impossible
to
reduce irreversible
processes to
reversible
ones.
Using the special case of
the
suspended particle considered above,
we will
try
to
show how Boltzmann resolved
this
apparent contradiction.1 We envisage
a
suspended
particle that
is so
large that
its
Brownian motion
is so
weak
as to
be almost
imperceptible.
What
are
the maximal velocities such
a
particle
can assume as a
result
of the disorder of the molecular motion? The
theory gives
the
following answer
to
this
question: Despite
the fact that the Brownian motion
is
on
the
average very small,
1This
argument
is
rather
lengthy
and subtle. But the
importance
and
beauty
of the
subject richly
rewards
one
for the mental effort.
An
Old Objec-
tion Raised
against
the
Kinetic
Theory
of
Heat.
Answer to the
Objection
along
Boltzmannian
Lines.