DOC. 26 THEORY OF TETRODE AND SACKUR
121
Doc. 26
On
the
Theory
of Tetrode and
Sackur
for the
Entropy
Constant
[p.
1]
[about
February 15,
1916][1]
The
following
considerationswithout
offering anything substantially
newshould
facilitate
a
better
understanding
of
the
theory
of Tetrode and
Sackur.[2]
In order to
achieve this
goal,
I
have removed all
confusing paraphernalia.
It is worthwhile to
give
some thought
to
this
important theory
because it contains Nernst's theorem
as
applied
to
crystallized
solid
bodies[3]
and also Stern's formula of
vapor
pressure.[4]
§1.
Entropy
and Statistical Mechanics
The
probability
dW
of
the "micro"state
of
a
physical system (assumed
to be
connected to
a
heat reservoir
of
a
relatively, infinitely large
thermal
capacity)
is,
according
to
Gibbs,
given by
the wellknown law
of
the canonical distribution
i)t 
E
dW
=
e
0
dq1...dqndp1...dpn
(1)
{1}
or
in shorter form
i»

E
dW
=
e
0
dr.
(1a)
We
assume preliminarily
that the
system can
be viewed
as a
mechanical
system as
understood
by
classical mechanics.
©
is the absolute
temperature,
measured in
suitable
units;
E the
energy
as a
function of the
ql...pn;
\[f
a
quantity
that is constant
with
respect
to molecular
movements, i.e.,
a quantity independent
of
q1...
qn,
p1...pn,
which,
as
Gibbs has
shown,
is
equal
to
the free
energy
of
the
system.
Considering
that the total
phase integral
of
(1)
must
equal unity,
one
has
I
if
=

Ees
=
_eig~5e
edtt
(la) (2)
or
for the
entropy
S
the
expression
Translator's
note.
The
typographical errors
in the
original
have been corrected here
according
to editorial notes
[9], [10], [14],
and
[19].