DOC.
32
183
§2. Examples
of
application
of the equation
derived in
§1
We
consider
a body
whose
center
of
gravity
can
move
along
a
straight
line
(the
X-axis of
a
coordinate
system). The
body
shall
be
surrounded
by a
gas,
and
there shall
be
thermal and
mechanical
equilibrium.
According
to
the
molecular
theory,
the
body
will
move
back and
forth
along
the straight line in
a
random
fashion
due
to
the
nonuniformity
of molecular
collisions,
such
that
none
of
the
points of
the straight
line
will
be
preferred in this
motion
-
provided
that
no
forces other than those of molecular collision
are
exerted
on
the
body
in
the direction of the straight line.
Hence,
the abscissa
x
of
the
center
of
gravity
is
a
parameter
of
the
system,
which
possesses
the
properties stipulated above
for the
parameter
«.
We
will
now
introduce
a
force
K
=
-Mx
that
acts
on
the
body
in the
direction of the straight line.
According
to
the molecular
theory
the
center
of
gravity
of
the
body
will then also
carry
out
random
motions,
but without
deviating
too
far
from
the
point
x
=
0,
whereas according
to
classical
thermodynamics
it
must be at rest at
the
point
x
=
0.
According
to
the
molecular
theory
(formula
I),
JL
u*L
dV
=
Ve K1
z
dx
equals
the
probability
that
at
a
randomly
chosen
instant the value of the
abscissa lies
between
x
and
x
+
dx.
From
this
we
find the
mean
distance
of
the
center
of
gravity from the
point
x
=
0,
N
Mx2
r+oo
~
-
x2A'e
RI
2
dx
-00
N
Mx
*
'+00
-
A'e
RT 2
dx
RT [11]
m
-oo
For
\x2
to
be
large
enough
to
be
accessible
to
observation, the force
that determines the
body's equilibrium
position
must
be
very
small. Putting
x2^
=
10-4
cm as
the
lower limit of observability,
we
get
M
=
about
5.10-6
[12]
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