DOC.
9
CRITICAL
OPALESCENCE
235
The
terms
entering
in
the
exponent appear multiplied
by
the
very large
number
N/R.
For
that
reason
the
exponential
factor
will,
in
general,
practically
vanish
already
for such
values
of
A
which,
because of their
smallness,
do not
correspond
to states
of the
system
that
deviate
significantly
from
the
state
of
thermodynamic
equilibrium.
For
such small
values
of
A,
the
factor
f
can always
be
replaced
by
the
value
f0
that
it has in
the
state
of
thermodynamic
equilibrium.
Hence,
in all
those
cases
in which
the
variables deviate
only slightly
from their
values at
the
ideal
thermal
equilibrium,
the
last
formula
can
be
replaced
by
(S-S
)
(2)
dW
=
const.e
*
°d\v
.
.dkn.
[11]
For
deviations
from the
thermodynamic equilibrium as
small
as
those considered
in
our
case,
the
quantity
S
-
S0
has
an
intuitive
meaning.
If
we
imagine
that
the
states
of
interest to
us
in
the
vicinity
of
thermodynamic equilibrium
are
produced
in
a
reversible
manner by
external
influences,
then,
according
to
thermodynamics, every
elementary
process
obeys
the
energy equation
dU
=
dA
+
TdS,
if
one
denotes
by
U
the
energy
of the
system,
and
by
dA
the
elementary
work
applied
to it.
We
are
interested
only
in
those
states
that
an externally
closed
system can
assume,
namely
states
belonging
to
the
same energy
value.
For the transition of
such
a
state to
a
neighboring state,
we
will have
dU
=
0. Further,
we
will
cause
only
a
negligible error
if
we
substitute the
temperature
T0
of the
thermodynamic equilibrium
for
T in
the
above
equation.
The latter
will
then
have
the form
dA
+
T0dS =
0
or
(3)
p5=5-50
=
^,
"o
where
A
denotes the
work
that
has to
be
expended,
according
to
thermodynamics,
in
order to transfer the
system
from the
state
of
thermodynamic equilibrium
to
the
state
under consideration. We
can
therefore
write
equation (2)
in
the
form
»A
(2a)
dW
=
const.
e °
dk1...
dkn.
Let
us now
imagine
that the
parameters
A
are
chosen
so
that
they
vanish
just
at
thermodynamic
equilibrium.
In
a
certain
region
it will
then be
possible
to
expand
A in
terms
of
A
according
to
the
Taylor
theorem,
and, given an
appropriate
choice
of
A's,
this
expansion
will have
the form
A
+ ViSa,
A.J
+
terms
of
higher
than the
second
power
in
the
A, [12]
where
all
of the
av
are
positive.
Further,
since
the
quantity
A enters
the
exponent
of
equation
(2a)
multiplied
by
the
very large
factor
N/RT0,
the
exponential
factor
will,
in