DOC.
9
CRITICAL OPALESCENCE
247
temperature
is
the
state
of
greatest entropy,
and thus the
greatest
statistical
probability,
at
a given
total
energy.
If
the
substance
in
question is
an
ideal
gas,
then
we can
set
c +
2 = 3.
For
this
case
we
obtain
(17c)
S
a
e
N
RT0
(e
_1)2
p
4
(4~)2
c0s2
(p~
As
a
rough
calculation
shows,
this
formula
might very
well
explain why
the
light given
off
by
the irradiated
atmosphere
is
predominantly
blue.8
In
this
connection
it
is
worth
noting
that
our
theory
does not make
any
direct
use
of the
assumption
of the discrete
distribution of
matter.
§
6. Liquid
Mixtures
[21]
The derivation
according
to
equation
(17a)
is
also valid in
the
case
of
a
liquid
mixture
if
one
sets
v
=
specific
volume
of the unit
mass
of the
first
component,
y
=
work needed
to
bring
the unit
mass
of the
first
component along
a
reversible
path
from
the
specific
volume
it
has in
thermal
equilibrium
to
some
other
given specific
volume
along a
reversible
path
at constant
temperature.
If the
vapor
coexisting
with
the
liquid
mixture
under consideration
can
be
regarded
as a
mixture
of
ideal
gases,
and the
mixture
can
be
regarded as
incompressible,
then the
quantity
y
can
be
replaced
by
quantities
accessible to
experience.
We
then
find y
by
the
following
elementary argument.
Let the
mass
k of the second
component
be mixed with
the unit
mass
of the
first
component.
In that
case,
k
is
a measure
of the
composition
of the
mixture,
the total
mass
of
which is
1
+
k.
Let
this mixture have
a
vapor phase,
and let
p"
be
the
partial
pressure,
and
v"
the
specific
volume of
the
second
component
in
the
vapor phase.
Let
this
system
be enclosed
in
a
container
with
a
semipermeable
section of
wall
through
which
the
second,
but
not
the first
component
can
be taken
in
and
out in
gaseous
form.
Let
a second, relatively
infinitely large
container
enclose
a
relatively
infinitely large
amount
of the
mixture with
that
composition (characterized
by
k0)
for
which
we
wish to
calculate
the
opalescence.
This second mixture shall also
occupy a
vapor
space
with
a
semipermeable wall,
and the
partial pressure
and
specific
volume
of the
second
component
in
the
vapor
space
shall
be denoted
by p0"
and
v0",
respectively.
Let the
temperature
inside
both containers be
T0.
We
shall
now
calculate
the
work dy
that
is
necessary
to
increase the
concentration
measure
k
in
the
first
container
by
dk
by
transporting,
in
gaseous
form
and
in
a
reversible
way,
the
mass
dk of the second
8 Equation
(17c) can
also be
obtained
by summing
the radiations of the
individual
gas molecules,
which
are
considered
to
be
completely randomly
distributed.
(Cf. Rayleigh,
Phil
Mag.
47
[1899]:
375,
and
Papers 4, p. 400.)
[20]