DOC.
9
CRITICAL OPALESCENCE
237
part
of the
parameters
A
in
the
preceding section,
which
determine the
state
of
our
system
in
the
phenomenological
sense.
In accordance
with
the
preceding section, we
obtain these
statistical
laws
by
determining
the
work A
as
a
function of the
quantities B.
This
can
be
done
in
the
following
way.
If
p(p)
denotes the
work
one
must
do
to bring
a
unit
mass
isothermally
from the
mean density
p0
to
the
density
p,
then
this work has
the
value
pp
dx
for the
mass
pdx
contained
in
the volume element
dx,
and
hence the
value
A
=
J
p.
ip.dx
for the
whole fluid cube.
We
will have to
assume
that the
deviations
A
of the
density
from the
mean
value
are very small,
and
will set
P =
Po +
A,
*
'
*(Pc)
+
($"A
*
5
a2p
{dp2}0
A2
+
• •
From
this it follows
that,
because
p(p0) =
0
and
/Adz
=
0,
A
=
5cp
+
I
d2»
dp
2
dp2
ftfdx,
where the index
"0" has
been omitted for the
sake
of
simplicity.
The fourth-order and
higher
terms
have
been omitted from the
integrand,
which
is
obviously only
permitted
if
£P
+
1
d2P
dp
2
dp2
is
not too
small,
and the
terms
multiplied
by
A4
etc.
are
not too
large.
But
according
to
(5) we
have
fA2dv
=`jEEEB~~
because the volume
integrals
of the double
products
of the Fourier summation
terms
vanish.
Hence
we
have
A
=
3p
+
1
d2P
3p 2
dp2
V
8
EEE*
2
par.
a
x
If
the work
per
unit
mass
that needs
to be
done
to
attain
a
state with
a
certain
p
from
the
state
of
thermodynamic equilibrium
is
expressed as a
function of
the
specific
volume
1/p
= v,
i.e.,
if
we
thus
put