DOCUMENT 18 JULY 1914 39
Besten
Gruss Ihr
W.
Nernst
N. B.
Auf
die Konfusion,
die dem
Obigen
entsprechend
bei Stern
bezüglich
sei-
nem
L0
u.
Ä0
-Modell
herrscht,
lohnt sich wohl
nicht
weiter
einzugehen.[8]
ALS. [18 440].
On the
verso,
Einstein has
written down
the
first
two
terms
of
the
high-temperature
(or low-frequency) expansion
of
the
expression
for
U
given
in this document.
[1]In
the
equations
below,
X
is
the heat of
evaporation,
which
for low
temperatures can
be
written
as
in the second
equation.
A version
of
this
expression
without
the terms
involving
U
was
derived
in
Nernst
1914;
see
Nernst
1918,
pp.
135-138, for
a
derivation
of
a
formula
very
similar to the
one
given
here.
[2]In
the
equation below,
M
is the molar
weight
and
log
denotes
the
common logarithm.
Sackur
1912
gives a
value
of
-1.18 for the
first
term
on
the
right-hand
side
if
the
pressure
is
expressed
in
atmospheres.
Nernst
1918, p. 152, gives
-1.6.
[3]See Stern, O.
1913. The
expression
for
U,
which
was
first derived
by
Einstein
(see
Einstein
1907a
[Vol.
2,
Doc.
38]),
is valid for
a
system
of
monochromatic harmonic oscillators
following
Planck’s law.
[4]In
fact,
as
Nernst
points
out
himself
in
Nernst
1918,
pp.
139-142, Stern’s
result
is in
complete
agreement
with the
expression
for
lnp
given
here.
Nernst
overlooks the fact
that,
in
the
notation
employed
here,
Stern’s C differs
from
that used here
precisely
by
the
amount
31nßv.
[5]Stern
arrived
at
his
result for
the
vapor pressure
in two different
ways:
from
thermodynamics
together
with Sackur’s and Tetrode’s
expression
for the
entropy
constant,
and from kinetic
theory.
The
model
used in the latter
approach was
that of
a system
of
particles moving
in
a space,
in which
a num-
ber
of
points
P
attract the
particles
with
a
force
proportional
to the distance but with
a
finite
range.
Thus,
each
point
P
is surrounded
by a sphere
in which
particles
vibrate
harmonically.
It
is
supposed
that
each
sphere
contains,
on average, one particle.
[6]In
the
thermodynamical part
of
his
paper,
Stern
assumed
the
existence
of
a
zero-point
energy
of
hv/2
per
degree
of
freedom.
[7]A
slight
variation in the
last
couplet
of
the first
prank
in Wilhelm Busch’s Max
und
Moritz.
At
this
point
in the
original
text,
Nernst
indicates
a phrase
that he has
appended
at the foot
of
the
page:
“Nämlich das
Diagramm
In the
diagram, A might
be
the
affinity
and
q
the reaction heat. One
of
the formulations
of
the heat
theorem
is that in the
limit of
low
temperatures
these
quantities
approach
each other in such
a way
that
dA/dT
=
dq/dT
=
0
(see,
e.g.,
Nernst
1918,
cha.p 1).
[8]In
Stern’s
paper,
L0
represents
the heat
of
evaporation
at absolute
zero,
and
X()
the
potential en-
ergy.
In accordance with the
hypothesis
of
zero-point energy,
the two
quantities
are
connected
through
L0
+
(3/2)Nhv
= X0
.
18. To
Max
Planck
Dahlem. 7. VII. 14
Lieber Herr
Kollege!
Auf
dem
Heimwege
ist mir
eine kleine Grille
zu unserer Besprechung aufge-
taucht,
die ich Ihnen
mitteilen
muss.
Setzen Sie den
Fall,
das
Institut käme
zu–