DOC. 20 THEORETICAL ATOMISM
241
According
to
the molecular-kinetic theory of heat, the laws of thermodynamics
are not exactly valid laws, but
are,
instead, merely average laws, from which
deviations must occur
all
the
time.
Thus, for example, the molecules bouncing off
the
unit surface of the wall enclosing
a
gas will produce
a
pressure of
a
determinate
average value. However, the actually exerted instantaneous pressure will not
be
exactly equal
to
that average value, but will undergo, instead, the most irregular
fluctuations,
in
accordance with the irregularity of the molecular motions that bring
about the pressure. An important question arises
here:
"Can
we
really observe such
irregular fluctuations, which have their origin
in
the disorderliness of molecular
motion, or are they necessarily inaccessible
to
observation because of their
smallness?" The amazing answer
is
that the theory really requires fluctuations of
this
kind that are observable by means available
to us,
and that such phenomena have
already been observed for almost
a
century.
We have
already
seen
that,
according
to
the
theory,
each molecule
moves as a
3N
whole
so quickly
that the
mean
kinetic
energy
L
of this
motion
equals
T.
2 R
However, according
to its
derivation,
this
result is valid
not
only
for
molecules,
but
also for
arbitrarily large
material
complexes capable
of
moving as a
whole. From
the
relation
given
above it
can
easily
be deduced that the
larger
the
mass
of the
structure
in
question,
the smaller the velocities of that motion. Particles with
a
diameter of
a
thousandth of
a
millimeter
can now
easily
be observed
by microscope.
Their
mass
is
-12
of the order of
magnitude
of
10
gram.
For
the
mean
velocity
of the molecular
motion
at
normal
temperature,
the relation
just
indicated
yields a
value
of
about
0.2
mm
per
second,
which is
a
huge
value for the
purposes
of
macroscopic
observation.
However,
this does
not
show
up directly.
The
particle
is
always
surrounded
by
a
medium,
for
example
by
a liquid.
If
at
one
moment
the
particle possesses
some
specific motion,
this
will
very
quickly
be slowed down due
to
friction with the
liquid.
On the other
hand, however,
the
particle always
receives
new
impulses
due
to
the
irregularity
of
molecular motion
of
the medium. The result of these
two
effects
is
a
motion of the
greatest irregularity,
the
velocity
and direction of which
change
most
rapidly,
and the
more
viscuous the medium that surrounds the
particle,
the faster the
change.
To calculate the
mean
value of
the
distance traveled
by a particle
in this kind
of motion
is
an easy
matter. A
particle
of the size
considered above that
is
surrounded
by
water
travels
on
average
about
one-thousandth of
a
millimeter
per
second.
Thus,
small
particles suspended
in
liquids
perform microscopically
visible
irregular
movements
under the influence of
irregular
molecular
motion;
actually,
these
have
already
been discovered almost
100
years
ago
("Brownian Motion," cf.
Article
11,
p.
242).
[14]
This Brownian motion
is
of
great
importance because,
for
one thing,
it
permits
Brownian
Motion.