DOC. 26 THEORY OF TETRODE AND SACKUR
127
S
=
0.
(3a)
This is the
expression
of
Nernst's theorem insofar
as
it
applies
at all
according
to this
[p.
9]
theory;
it
holds for
crystallized, chemically
uniform substances.
For mixed
crystals
the
theory
allows for deviations from Nernst's
theorem.[17]
For
example,
let the
spatial
lattice
hold two kinds
of
atoms,
a
and
ß,
which
can
replace
each other
arbitrarily.
The number
of
permutations
of
equal
valuation is then
(Na
+
Nß)!
For the
entropy
S at
absolute
zero,
after
an argument analogous
to
the
one just given,
results
a
value
of
S
lg
* ;
v.
(3b)
NJ
NJ
The
Ideal Gas
with
a
Rigid
Type
of Molecule
We
imagine a
chemically
homogeneous gas
made
up
of N molecules. Let there be
Na
atoms
of the
a-th
kind in
it; i.e.,
Na/N
per single
molecule.
First,
we
imagine
the
gas
at such
high temperature
that
we are
in
a
normal
area
where
we
are
allowed
to
assume
all
degrees
of freedom
of
a
molecule to be effective. We
now
apply
the
fundamental formula
(2b)
to this
gas.
Then
one
has
to
insert for
n
the threefold
number of atoms in the
system.
The
phase integral
in the
numerator
of the second
term
splits again
into
separate partial areas
of
equal valuation,
which
correspond
to
the various
possibilities
to distribute the atoms
among
the molecules that
are
to
be
formed.
Again, one can
calculate the
integral by extending
it
over just one
of
these
partial
areas, i.e.,
the
integration
is carried
out
as
if the molecule
compound
were
indestructible,
and
afterwards the
integral
is
multiplied by
the number of
possible
distributions
Z.
I
imagine a
coordinate
system rigidly
connected with each
one
of the
N
molecules such that the fixed locations of
corresponding
atoms
of
these molecules
have the
same
coordinates in
all
these coordinate
systems;
and
we
think of these
coordinate
systems as being
numbered. It is clear that there
are
II(Na!)
=
C
different
ways
to distribute
our
atoms in the
prescribed
manner
among
the coordinate
[p.
10]
systems.
I
now imagine
all these
C
(possible)
distributions to be realized
separately,
whereby
I obtain for the
gas £
models that
are only
distinct
by
the
way
the molecules
are
distributed
among
the coordinate
systems.
In each
one
of
the (
models,
I
now