DOC.
1
PHENOMENA OF CAPILLARITY
21
the
molecular
force
was
much
greater
than the
molecular
radius.
However, by
the
end
of
the
nineteenth
century
there
were reasons
to ques-
tion this
assumption.
For
a
historical review of
this mean-field
approximation
in
capillary
the-
ory, see
Rowlinson
and
Widom
1982,
pp.
17-
21. See also note 7.
[9]
O
denotes the surface
area.
The
sign
of
the
last term in this
equation
should be
positive.
[10]
This
expression
for K'
is incorrect,
as
is
clear
even
from dimensional considerations.
Einstein
1911a, without
mentioning
the
present
paper, gives
the correct
expression
(see
the for-
mula
for
K2 on p.
167).
[11]
This
expression
is
actually
the surface
po-
tential
energy
per
unit
area.
[12]
See
Ostwald
1891,
pp.
528-530, for
Schiff's data
on
surface
tension;
pp.
376-385
list
values
for
the molar volumes
of
a large num-
ber
of
chemical
compounds
at
their
boiling
point.
[13]
Boltzmann 1898a,
pp.
59-60, calculates
an
expression
for
the heat
of
vaporization
of
a
liquid,
based
on
the intermolecular force
law, to
which
Einstein's
is
equivalent.
In
calculating
the
external work done
against atmospheric pres-
sure,
Einstein
neglected
the volume
of
the
liquid
in
comparison
with that
of
the
vapor.
[14]
Ostwald
1891,
pp.
354-356,
gives
values,
due to
Schiff,
for
the heat
of
vaporization
of
a
number of
compounds; pp.
376-385
lists molar
volumes
at
the
boiling point.
Einstein
uses
the
molar,
not the
molecular
values for both
D'm
and
v;
the external work is
put equal
to
RT
=
1.991
T
cal/mol
(see,
e.g.,
Nernst
1898,
p.
61).
[15]
Here
2,51
is the
average
of
the
quotients
given
in the
table,
and
4,17
.
107 is
the value of
the
mechanical
equivalent
of
heat used
by
Ein-
stein.
[16]
For the
meaning
of
"Wärmeinhalt,"
see
note 5.
[17]
Here,
K
and
a
denote the standard coeffi-
cients
of
isothermal
compressibility
and isobaric
thermal
expansion.
[18]
The
terms pK
and pa
should be
pvK
and
pva,
respectively.
[19]
The
right-hand
side
of this
equation
should
be
multiplied by v.
[20]
The
right-hand
side of
this
equation
should
be
multiplied by v.
[21]
P
here is the
potential energy
per
mole,
given
on
the last line
of
p.
518. This
expression
should be
multiplied by v.
[22]
The numerator
of
the left-hand side should
be
Ta.
[23]
See
Landolt and
Börnstein
1894,
pp.
107-
109. The
values
for
v
are
again
taken from Ost-
wald
1891, pp.
376-385
(Einstein
uses
the
mo-
lar,
not the molecular
volume).
[24]
The two results
are thermodynamically
equivalent, however.
If
the volume
of
the fluid
is neglected,
the
Clausius-Clapeyron equation
for
vaporization
is
m
\dT)v
Tv
with
v
the volume
of
the
vapor
and
Dm
the heat
of
vaporization. Neglecting
the
atmospheric
pressure,
as
did Einstein,
we may
set
Dm =
D'm.
The
identity
(dp/dT)v(dv/dp)T(dT/dv)p=-1
then gives
D'm
=
Tva/k
.
The existence
of
a
thermodynamic
relation be-
tween
Einstein's
two
results
is
suggested
in
a re-
view
of Einstein's
paper (Wiedeburg 1901).
[25]
See Ostwald
1891,
pp.
279,
398-399, for
a
discussion
of Mendeleev's
formula.
[26]
Possibly a
reference to
Ostwald's
use
of
Schiff's
data
to test
Eötvös's
law
(Ostwald
1891,
pp.
541-543).
[27]
See
note
6.
[28]
See
note
7.
[29]
See
note 8.
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