268 DOC. 22 SOLVAY DISCUSSION REMARKS
that
is
to
say,
in other
words, to
elevate the assertion of Nernst's
argument
to
the
status
of
a postulate.
In this
way one
arrives
at
a
very
intuitive formulation of
Nernst's theorem but also
again, unfortunately,
at
consequences
that
engender
mistrust
on
account
of
their
oddity.
Let
us
first draw the
general thermodynamic consequence
from
the
assumption
of the nonexistence of such adiabatics! We
consider
a system
whose
state
is
determined
by
the absolute
temperature
T and
an
arbitrary parameter
v.
For
an
adiabatic
process,
we
have
0
=
dq
=
TdS
=
T(ds-dT
+
-dv).dv
dt
But,
as
follows from this
equation,
Tds is the heat
capacity
C
of
the
system
at
constant
v,
so
that
we can
also write this
equation
for the adiabatic in the form
dS
_
C dt
3v T
d\
'
But
according
to
experience,
C/T
vanishes
in
the
limit
as
it
approaches
absolute
zero;
it is
therefore certain
a
fortiori that this
quantity
does
not
tend to
infinitely large
values. For it
to
be
impossible
to reach absolute
zero
by
the adiabatic
process
considered,
dT/dv
must
tend with T toward the value
0.
Thus,
our equation
teaches
us
that the
equation
ds/dv
=
0
must
hold
at
absolute
zero.
Since
v
denotes
an arbitrary parameter
of
the
system,
we
conclude:
If
the heat
capacity
of
a system
does
not
vanish less
rapidly
than T
as
it
approaches
absolute
zero,
and if there
are no
adiabatics that intersect the T-axis in the
finite,
then the
entropy
has the
same
value
S
for all
states
of
the
system
at
T
=
0.
Thus,
Nernst's heat theorem in Planck's formulation holds
not
only
for
systems
with
chemically homogeneous
phases
but also for
arbitrary
mixtures in the condensed
state.
By
the
way,
it should also be noted
that,
according
to
this
conception,
it
seems
very
improbable
that the theorem has
to
be restricted
to
condensed
systems,
because
the
zigzag
motion
of
the
gas
molecules also has
a
quasi-oscillatory
character,
so
that
it
hardly seems
doubtful
that,
at
a given
volume,
the heat
capacity
of
a
gas
vanishes
toward absolute
zero
in
a
manner
similar
to
the heat
capacity
of condensed
systems.
If
Nernst's
hypothesis
of
the
unreachability
of
absolute
zero
by
adiabatic
processes
proves
correct,
then
we are
confronted with
one
of the
most
fundamental