24 DOC.
5
CONTRIBUTIONS TO
QUANTUM
THEORY
[16]
[17]
[p.
826]
separate
index
system).
Under
this
limitation,
1)
remains
valid*
not
only
for
a
"molecule" in the
ordinary sense,
but
also for
a
physical system
looked at
quantum-
theoretically
in the
sense
of Jeans-Debye.
In this
manner
one stays safely
within
the
bounds of
experimentally
verified
quantum theory.
Energy
ea
is
referred
to
the
gram-mole.
The
quantity
ea/N
= e*a
for
an
individual
molecule will
always
be introduced when the "molecule" is
a
system
to
be treated
as
a
single
structure accessible
to experience.
In
this
case
one
has
to set
Via
n~o
-
N
tv
eJ
~~
e0
RT
1b)
§2.
Entropy.
The
NERNST
Theorem. We
now
think of
a physical system
to
play
the
role
of
the "molecule"
of
the
previous paragraph.
For this
purpose
it is
necessary
to
imagine
the
system
not in isolation but rather linked with
an
infinitely large
heat
reservoir. We
assume
the
system
to be
thermodynamically
determined
by temperature
and
one parameter
A.
(e.g.,
volume),
or by
several
parameters.
The
possible
states
of
the
system
and, therefore,
its realizable
energy
values
e*
will then
depend upon
the
parameter
values
A.
Under constant
X
we
will have to
accept
equation
3b)
as
valid.
The
mean
energy
of
the
system
is then
given
by
Ne
o
lehva
_Zs*"e RT
ItC
a
le
V £*
£t
Iff
*?
fi
-NA.
£r_
T2
_
lots*
RT\
N
clT.
g{~e
'*
3)
From this follows
the
entropy
at constant
X as a
function
of
T:
S
-
S,
els
To
_
T
*
+
T
2
clT,
To
To
or
with suitable choice of the value
of
S0:
8
£
+
ylg{26
Ne
a
RT 4)
If
the
system
has
a large
number of
degrees
of
freedom,
1b)
implies
in
a
well-
known
manner
that
only
those
states
of the
system
have to be considered which
correspond
to
a
small
range
of
e*a.
With the evaluation
of
the
sum
in
4)
one can
confine oneself to this
narrow range
within which
ea
is
set
constant. One then
gets
S
=
R/NlgZ,
4a)
where Z is the number of
elementary
states
possible
under
quantum theory;
and the
*Translator's
note.
The
word
"gelten"
=
valid
is
missing
in the German
original.