DOC.
32
181
latter
theory.
We
will
then have
to apply
these laws
to
the
following
special
cases:
1.
a
is the x-coordinate of
the center
of gravity of
a
spherically
shaped
particle
suspended
in
a homogeneous
liquid
(which
is
not subject to
gravitation).
2.
a
is the
angle
of rotation that determines the position
of
a
spherical
particle
suspended
in
a
liquid and
capable
of
rotating
about
a
diameter.
§1.
On a case
of
thermodynamic
equilibrium
In
an
environment
of absolute
temperature
T
let there
be
a
physical
system
in thermal interaction with this
environment and
in
a
state
of thermal
equilibrium.
This
system,
which hence
also
possesses
the absolute
temperature
T,
shall
be completely
determined
by
the
state
variables
P1...Pn
according
to
the molecular
theory
of heat.1 In the
special
cases
to be considered,
we
can
choose
for the
state
variables
P1...Pn
the coordinates
and velocity
components
of all
atoms constituting
the
system
under
consideration.
The
probability that
at
a
randomly
chosen
instant of time all
state
variables
P1...Pn
will
lie
in the n-fold
infinitesimally
small
region
(dp1....dpn)
is
given
by
the
equation2
(1)
dw = Ce
dp1...dp~,
where
C
denotes
a
constant,
R
the universal
constant
of the
gas
equation,
N
the
number
of
true
molecules
per
gram-molecule,
and
E
the
energy.
Suppose
that
a
is
an
observable
parameter
of the
system
and
that
to
each
system
of values
P1...Pn
there
corresponds
a
definite value
a.
We
denote
by
Ada
the
probability that
at
a
randomly
chosen
instant the value of
the
parameter
a
will lie
between
a
and
a
+
da.
We
then
have
1Cf. Ann.
d.
Phys.
17 (1905):
549.
2Loc.
cit.,
§§3
and 4.
[7]
[8]
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