DOC. 22 SOLVAY DISCUSSION REMARKS 269
results
of
thermodynamics.
It is well known that
many consequences
drawn
from the
theorem had been confirmed
by experience.
On the other
hand,
it has
already
been
emphasized
that
our
physical
sensibilities
struggle against admitting
the existence of
the adiabatics
(ruled out
by
the
theorem)
of
type
BC in the above
figure.
But there is
a
theoretical
argument
that must
instill
some misgivings regarding
Nernst's
theorem, probably
the
same
argument
that induced Planck
to
restrict the
theorem
to
chemically homogeneous
bodies. To
wit,
there
are
terms in the
expression
for the
entropy
of certain
systems
that
depend only on
the
way
in which
things
are
arranged
and
not
on
the
temperature,
and it
is
uncommonly
difficult to
imagine
that
these
terms
would
drop
out
as we
approach
absolute
zero.
An
example:
a
gram-molecule
of
a
substance in dilute state is dissolved in the
partial
volume
v
of
a
solvent of total volume
v0.
The
entropy
of the
system
shows
a
dependence
on
the size
of
the
partial
volume
v
that
is
given
by
the
equation
S
= S0
+
R
log
v.
As
we
all
know,
the law
of
osmotic
pressure
follows from the
term R
log
v;
the
existence
of
this
term
is
connected with the
degree
of
order
of the
system,
which
consists in the fact that all of
the
dissolved molecules
are present
in the
part v
instead
of
being randomly
distributed
over
the entire volume
v0.
This
term
has
nothing
to
do
with
energetic
factors
(temperature, specific
heats,
molecular
forces,
etc.),
but
concerns
exclusively
the order
properties
with
respect to
the
geometric arrangement.
It is therefore
difficult
to
imagine
how this
term
could lose its
meaning
at
low
temperatures,
and this
difficulty by
no means
disappears
if
one
subjects
Van't Hoff's
and Planck's
thermodynamic
theories
of
dilute solutions
to
a
careful revision. It is
difficult
to find
a
reason
why
these theories should fail
at
low
temperatures.
In
any case,
it
is
practically hopeless
to
investigate
osmotic
pressures
at
temperatures
so
low that
we are sure
to find ourselves in
a thermally
abnormal
region,
where the dissolved substance
possesses
a
smaller value of the
mean
kinetic
energy
of
translatory
motion of the
molecules than that
prescribed by
statistical
mechanics.
However,
there is
a
second domain of
phenomena
in which
entropy
differences
also
play
a
role,
and in which this difference
rests
only
on a
change
of
order with
respect
to
the
geometric
arrangement, namely,
the domain
of
paramagnetic
phenomena.
Here the orientation of the molecule
plays
the
same
role
as
the
position
of its
center
of
mass
in osmotic
phenomena.
The
Curie-Langevin
law
expresses
the
resistance
put up by
thermal
agitation against
an
alignment
of the molecules in
just
the
same way
as
the law
of
osmotic
pressure
is determined
by
the resistance
put up
by
thermal
agitation against
a
restriction
of
the
space
available
to
the molecule
during
its diffusional
wandering.
It
is
therefore
of
the
utmost
importance
to learn
whether,
in
principle,
the
Curie-Langevin
law loses its
validity
at
low
temperatures.
To be
more precise,
the
question
arises: Is the
Curie-Langevin
law
connected to those