DOC. 26 THEORY OF TETRODE AND SACKUR
261
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©
=
\h2
...(7)
87C
I
Diese
Gleichung ergibt
das
Trägheitsmoment
des Wasserstoff-Moleküls.
AD.
[2
075].
The
manuscript
consists
of
thirteen
pages.
Page
numbers that
appear in
the
orig-
inal
in
the
upper-right
hand
corner
of each
page
are
here
placed
in the
margin
in
square
brack-
ets.
[1]This document
is
dated
on
the
assumption
that it
is
related
to
a
lecture entitled "Zur
Begründung
der Tetrode-Sackurschen
Bestimmung
der
Entropiekonstanten,"
which Einstein
delivered
at
the
meeting
of
14
January 1916
of the Deutsche
Physikalische
Gesellschaft
(see
Deutsche
Physikalische Gesellschaft. Verhandlungen
18
(1916): 41).
[2]During
the
years
1911
to
1913,
Otto Sackur
(1880-1914) in
Breslau
and
Hugo
Martin
Tetrode
(1895-1931) in
Amsterdam
independently developed
a
quantum theory
of the ideal
gas
and succeeded
in determining
the
explicit
value of its
entropy
constant (see
Sackur
1911,
1912,
1913a,
1913b,
and
Tetrode 1912).
The
lecture mentioned
in
the
previous
note-and thus
this
manuscript-seems to
be
inspired
by
Einstein's
reading
of
Tetrode 1915,
a
later
paper
on
the
same
subject
(see
Einstein
to
Paul
Ehrenfest,
17 January 1916,
and Einstein
to
H. A.
Lorentz of the
same
date, in
which he
expresses
his admiration for Tetrode's work and
men-
tions
having
lectured
on
it).
Sackur's earlier work had elicited Einstein's enthusiasm
as
well
(see
Einstein
to
Heinrich
Zangger,
after
5
June
1912
[Vol. 5,
Doc.
406]).
See also Desalvo
1992
for
a
historical review of this
work,
including
a
discussion of
its
controversial
status at
the
time.
[3]For
discussions of Nernst's theorem written
shortly
before and after this
time,
see
Nernst
1911,
1918. See
also Einstein's critical discussion of Nernst's theorem
in Einstein 1914n
(Doc.
5), §2,
where
he
concludes that the theorem
is
only
valid for
pure crystals.
[4]See Stern
1913.
[5]At
this
point
in the
original
text
Einstein indicates
a
note
he has
appended at
the foot of
the
page:
"Soweit nämlich diese
Frage überhaupt
klar
gestellt
werden
kann. Nicht die Abso-
lutwerte der
Entropiekonstanten
sind
thermodynamisch definiert,
sondern
stets
nur
die Diffe-
renz
der
Entropiekonstanten
zweier
Zustandsbereiche eines und desselben materiellen
Systems!"
[6]Einstein had
long emphasized
the
possibility
that results
might be
valid
more widely
than
their
derivations
suggested
and
might
well
not depend
on
the
particular
features of the model
on
which
they
seemed
to
be based.
See, e.g.,
Einstein
1902b,
1903, 1904,
1909b.
[7]The
inapplicability
of
classical mechanics
to a
variety
of
physical
situations
was
another
recurrent
theme in Einstein's
early writings. See, e.g.,
Einstein
1905i, 1909c,
1914a.
[8]Einstein
refers
to
Arnold Eucken's
experimental
results
on
the
specific
heat of
molecular
hydrogen
(see
Eucken
1912); in
collaboration with Otto
Stern,
Einstein had later
attempted
a
theoretical
explanation
(see
Einstein and Stern
1913; see
also
Vol.
4,
the editorial
note,
"Ein-
stein and Stern
on
Zero-Point
Energy,"
pp.
270-273,
for historical
background).
[9]The dimension
should be
(ML2T-1)n
[10]"MLT-2" should be "ML2T-1."
[11]The dependence
of
the
entropy
on
the numbers of
atoms
of various kinds
in
the
system,
discussed
on [pp.
5-6],
was
the
most
controversial
aspect
of the Sackur-Tetrode
equation.
As
Einstein
points
out,
there
is
an
arbitrariness
in
the introduction of the
factorials,
although they
are
needed if
the
result
is
to
be
an
entropy
that
is
an
extensive
quantity.
This
point
was
clarified
a
few
years
later
by
Paul Ehrenfest and Viktor
Trkal,
who
emphasized
that the
N-dependence
of
the
entropy
is
only
relevant and
meaningful
for
processes
in
which N
can
be changed
revers-
ibly.
See
Ehrenfest
and Trkal
1920;
see
also
Klein
1959
and
Desalvo
1992
for
historical dis-
cussions.
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