DOC.
16
125
§2.
Osmotic
pressure from
the
standpoint
of
the
molecular-kinetic
theory of
heat1
If
P1P2...Pe
are
state
variables of
a
physical
system
that determine
completely
the
system's
instantaneous
state
(e.g., the
coordinates and
velocity
components
of all the
atoms of
the
system), and
if
the
complete
system
of
the
equations
of
change
of
these variables is
given
in the
form
dPv
(v
=
1,2,...l),
dtp
where
^
=
0,
then the
entropy
of
the
system
is
given
by
the
expression
[6]
E
E
S
=
-j
+
2/c
lg
e dp^..
.dpg.
Here
T
denotes the absolute
temperature,
E
the
energy
of
the
physical
system, and
E
the
energy
as a
function of the
pv's.
The
integral
is
to be
extended
over
all combinations
of
values
of
pv
consistent with the condi-
tions of the
problem.
k
is connected with the
constant
N
mentioned above
[8]
by
the relation
2kN
=
R.
We
therefore
get
for
the free
energy F
EN
R
RT
^
.
RT
F
=
-
-N
T
lg
e
dp1un~i
a
• •
-dp
=
-
T
-tst
lg
B.
Let
us now
imagine
a
liquid enclosed in the
volume
V;
let the partial
volume
V*
of
V
contain
n
dissociated molecules
or suspended
bodies,
which
are
retained in the
volume
V*
by a
semipermeable
wall;
this will
affect the
integration
limits
of
the
integral
B
entering the
expressions
for
S
and F. Let
the total
volume
of the
dissolved molecules
or
suspended
bodies
1In
this section it is
assumed
that the reader is familiar with the author's
papers
on
the foundations of
thermodynamics
(cf.
Ann.
d.
Phys.
9 (1902): 417
and
11
(1903): 120).
Knowledge
of
the
papers
cited
and
of this
section of
the present
paper
is
not
essential for the
understanding
of
the
present
paper's results.
[7]
[5]