40 DOC.
2
DIFFERENCE
IN POTENTIALS
Published in Annalen
der
Physik
8
(1902):
798
814. Dated
Bern,
April
1902,
received
30
April
1902, published 10 July
1902.
[1]
See
Planck
1891 for
a
general
discussion
of
the role
of
ideal
processes
in
thermodynamics.
Nernst
1898,
pp.
102103, discusses the
use
of
semipermeable
membranes in
thermodynamics.
Nernst
stresses that
processes
involving
semi
permeable
membranes must be
physically
real
izable
for
the second law to be
applicable
to
them.
Applying an
argument
first
developed by
Boltzmann
(Boltzmann 1878b),
he concludes
that the second law
can
be used in the
case
of
mixing or separation
of
any
two
chemically
dif
ferent
gases by means
of
semipermeable
mem
branes. There is
no
mention
of
external forces
mimicking
the membranes.
[2]
See Einstein 1902b
(Doc. 3)
for
Einstein's
proof
of
this
hypothesis,
based
on
the
"mechan
ical
theory
of heat."
[3]
The
symbols usually
denote the number
of
moles
per unit
volume.
[4]
"E"
is known
as
Faraday's
constant.
[5] Pm
and
Ps are actually
the
potentials per
mole.
[6]
The relation:
_
d
log
v0
dp0
RT

+
 =
0,
dz
dz
where
p0 = v0
RT.
[7]
In
1889
Nernst
developed a general
ther
modynamic
theory
for electromotive
phenom
ena
in
electrolytes (Nernst 1889);
Nernst
1898,
pp.
659678,
gives
a
"mechanical"
theory
for
these
phenomena,
based
on a
molecular
model
involving moving
ions. The
expression
for
the
electromotive force Einstein refers
to
is
RT
c2
E
=

log0
n
Cj
where
c1
and
c2
are
the concentrations
of
the salt
ions at the two
electrodes,
and
n
is the
valency
of
the
metal
ions.
Nernst
1898, pp.
667668,
cites
experimental
evidence
in
support
of
this
equation.
[8]
Einstein
1901
(Doc.
1).
[9] v
is
actually
the molar volume.
[10]
"E1",
etc., should be "e1", etc.
[11]
See
Einstein
1901
(Doc.
1), pp.
522523.
[12]
Note that
vm
and
vs
are
velocities
per
unit
force.
[13]
In the second term
of
the
righthand
side
of
this
equation a
factor "E"
is
missing.
[14]
The factor
"RT"
should be
"RT/E"
in
both
equations
on
this
page.
[15]
The reference is
to
equation
(a). Refer
ences to (2)
in the
following
are
to (ß).
[16]
There
are no
indications that
anyone per
formed
an experiment
based
on
Einstein's
work.