DOC.
9
CRITICAL OPALESCENCE
231
Doc.
9
The
Theory
of the
Opalescence
of
Homogeneous
Fluids and
Liquid
Mixtures
near
the Critical State
by
A.
Einstein.
[Annalen
der
Physik
33
(1910): 1275-1298]
In
an important
theoretical
paper,1
Smoluchowski has shown
that the
opalescence
of
fluids
near
the
critical state
as
well
as
the
opalescence
of
liquid
mixtures
near
the
critical
mixing
ratio and the
critical
temperature
can
be
explained
in
a
simple way
from
the
point
of
view
of the molecular
theory
of heat.
This
explanation
is
based
on
the
following
[2]
general
implication
of Boltzmann's
entropy-probability
principle:
In the
course
of
an
infinitely long
period
of
time, an externally
closed
system passes
through
all
the
states
that
are
compatible
with
the
(constant)
value of
its
energy.
However,
the
statistical
probability
of
a
state
is
noticeably
different from
zero only
when
the
work
that
would
have to be
expended
according
to
thermodynamics
to
produce
the
state in
question
from
the
state
of ideal
thermodynamic equilibrium is
of the
same
order of
magnitude
as
the
kinetic
energy
of
a
monatomic
gas
molecule
at
the
temperature
under consideration.
[3]
If
such
a
small amount
of
work suffices to
bring about,
in volumes
of
fluid
of the
order of
magnitude
of the
cube
of
a wavelength, a
density
that
deviates
markedly
from
the
average density
of
the fluid
or a
mixing
ratio that
deviates
markedly
from
the
average,
then,
obviously,
the
phenomenon
of
opalescence (the
Tyndall
phenomenon)
must
take
place.
Smoluchowski has shown
that
this
condition
is
actually
fulfilled
near
the
critical
[4]
state; however,
he
did not
provide
an
exact calculation
of the
quantity
of
light given
off
laterally
through opalescence.
This
gap
shall
be
filled in
the
following.
§1.
General Remarks
about
the Boltzmann
Principle
[5]
Boltzmann's
principle
can
be
expressed
by
the
equation
(1)
S
= ^lg
W
+
const.,
where
R
is
the
gas
constant,
N
is
the
number
of
molecules in
one gram-molecule,
S
is
the
entropy,
W
is
the
quantity
customarily designated as
the
"probability"
of the
state with which
the
entropy
value S
is
associated.
1
M.
v. Smoluchowski,
Ann.
d.
Phys.
25
(1908):
205-226.
[1]