DOC. 26 THEORY OF TETRODE AND SACKUR
123
meaning
for
us
insofar
as
its results
are
largely independent
of
the
peculiarities
of
the
molecular
picture
chosen.[6]
b) Equation
(2a) presupposes
that molecular
processes can
be
perceived as
movements
within the framework
of
classical mechanics. But
we
know from
individual
results,
which
are presently only loosely
connected
by quantum theory,
that
this
postulate
does not hold in
nature.[7]
It
seems
therefore doubtful
if,
with this
equation,
one can
successfully
answer
such
general question impossible
to draw
{2}
exact
and valid conclusions from
our equation (2a);
and it is furthermore doubtful
if
the
equation
can
successfully
be used at
all
for the determination
of
the
entropy
constant.
We first address the consideration
of
the
last-mentioned
principal
objection.
§2.
Taking Quantum Theory
into Account
While
our
present knowledge
excludes
an
understanding
of
molecular
processes
within the laws
of
classical
mechanics,
we
also
know,
on
the other
hand,
that
molecular
mechanics
allows,
within
far-reaching areas
of
macroscopic (thermody-
namic)
variables
of
state
of
a
system,
to
give a representation as good as one can
wish. Such "normal"
areas
of state
are, however, separated by
others in which
molecular mechanics fails. For
example,
the thermal behavior of rarefied
hydrogen
[p. 4]
gas
above
a
certain
temperature 02
can
be described
by
molecular mechanics with
high accuracy, provided
the molecule is viewed
as
consisting
of
two
rigidly
connected
atoms;
whereas below
a
certain
temperature
01 a
molecular-kinetic
interpretation
is
possible
based
upon
the
hypothesis
that the molecule behaves
kinetically
like
a single masspoint.
Between
©1
and
©2,
however,
a
molecular-
mechanic
interpretation
is
impossible.[8]
This situation
brings
about that
equation
(2a)
can
be used for the calculation of
an entropy
difference
S2
-
S1
if
the
two states
belong
to
the
same
"normal"
area
of
state.
Similarly,
it is clear that
(2a)
cannot
be used
to
calculate
entropy
differences
if
at
least
one
state
belongs
to
a
non-normal
area.
The
question
is
now
whether
or
not
a bridge can
be built between
two
"normal"
areas
that
are
separated by
non-normal
areas, i.e.,
if
a
rule
can
be found
to
calculate
the
entropy
difference
S2
-
S1
in
case
S1
and
S2
belong
to
two
different normal
areas.
Of
course,
such connection
can only
be
established
by a hypothesis
outside the
domain of molecular mechanics.
The
simplest hypothesis
would be to
use equation (2a)
without
any scruples, even
in that
case.
But this
hypothesis
is
to be
rejected
for the
following reason.
Since
0
has the dimension
of
energy,
the
entropy
difference
AS
is
a
dimensionless
quantity,
i.e.,
independent
of
the choice
of
basic units. In
contrast,
the
integral
in the second