242
DOC.
4
KINETIC THEORY
LECTURE NOTES
AD.
[3 003].
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[P.
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[pp. 53-54].
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of which
has
an upside-down
text
presented
as
[p.
52].
The
verso, containing
a
fragment
of unrelated
calculations
in
pencil,
is
omitted.
All
other omitted material contains calculations
that
seem
to
be
related
to
the
quantization
of the motion of
a
rigid
rotator.
The notebook also contains
a
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of another loose sheet of
plain
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paper presented
here
at
the end of the
note-
book
as [p.
55].
On the back
cover
of the notebook
the
following
formula
is
written
in
pencil:
[1]Dated
on
the
assumption
that Einstein
prepared
these notes
for his
course
in the
summer
semester 1910 at
the
University
of
Zurich, 19
April
to
5
August 1910
(see
Zürich
Verzeichnis
1910a,
title
page).
[2]These
notes,
written
on
the
back of the
flyleaf
adjacent
to
[p.
1],
contain
the
two
deriva-
tions
of
the ideal
gas law
that
are
hinted at in
the
first sentence
of [p.
1].
The law
is derived
directly
from the kinetic
theory
and with
the
help
of the
virial theorem, respectively.
Here and
in
the
following,
L
denotes the
mean
kinetic
energy
of
the
gas
and
X
the
x-component
of
the
force acting
on
the
molecules. For
a
more
detailed discussion
of the
two derivations
see
Boltzmann
1896,
§2,
and
Boltzmann
1898,
§§49,
50;
for
a
historical discussion
see
Brush
1976,
§11.4.
The
notes presented
below
as
[p.
52] seem
to
be
an
extension of the derivation
via the
virial theorem, taking
into
account
intermolecular forces and
finite
molecular dimensions.
[3]Dalton's
law states
that
the total
pressure
exerted
by a
mixture
of
gases
is
equal to
the
sum
of the
partial
pressures
of
its constituents.
For
a
contemporary
discussion of this
law in
the
framework of kinetic
theory,
see, e.g.,
Meyer, O.
E.
1899,
part
1,
§17.
[4]In
Eichelberg's notes
the
equation pV
=
(2/3)L
is characterized
by
the
term "Theorie,"
the
ideal
gas equation pV
=
RT
by
the
term
"Erfahrung"; a
similar characterization
is
made
in
Einstein
1915a,
pp.
255-256.
[5]Here
and
in
the
following
material,
the
mass
of
a
molecule
is
denoted
by
m
and the
mass
of
a
mole
by
M.
N
is
the number
of molecules
per mole,
and
n
the number
density.
The
mass
density is
denoted
by p.
[6]See
[p.
31].
[7]The word "mittleren"
is
interlineated
in
the
original.
Calculating
the
mean
thermal veloc-
ity
of
a
molecule
directly
from the
mean
kinetic
energy
of
a
gas is
a
simplification
made
in
the
first
part
of these
notes
when
compared
to
Boltzmann
1896. A
more
sophisticated
calculation
from the Maxwellian
velocity
distribution will be
given on
[p. 32].
[8]While
the factor
3/2
should
be
3,
both
in
the formula and in the numerical
example,
the
value of
1840 m/sec
for the
mean
velocity
of
hydrogen
is
correct.
[9]The
words "der fortschreitenden
B[ewegung]"
are
interlineated in
the
original.
The theo-
rem
that the kinetic
energy
of
a
molecule
depends only
on
temperature
is derived
on [p.
30].
[10]cxv
is expressed
in
calories.
[11]See
Kundt and
Warburg 1876
for
a very
accurate
experimental
determination of the ratio
of the
specific
heats of
mercury vapor.
These authors found
a
value of
1.666
with
an
uncertainty
of
roughly
0.1%.
This
experimental
verification
was widely seen as an
important
success
for
kinetic
theory; see,
e.g.,
Meyer, O.
E.
1899,
part
1,
§54,
and Einstein 1914
(Doc. 26), p.
330.
[12]Einstein's
treatment
below follows
Boltzmann
1896,
§11;
see,
however, note
7.
In the
following
formulas
c
or
c
denotes the
mean
thermal
velocity
of
the
molecules
as
calculated
above,
i.e., c
=
Jc2;
K
denotes
a
solid
angle.
[13]In
the
following
equation sin3g
should
be cos3g.
The
final
result
for F
is
correct.
4F2
F-
-~/5q
A.
RT
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