328
DOC.
12
COMMENT
ON
EÖTVÖS'S
LAW
Doc.
12
Comment
on
Eötvös's
Law
[1]
by
A.
Einstein
[Annalen
der
Physik
34
(1911): 165169]
Eötvös
established
empirically
the
following
lawlike
regularity
for
liquids,
which,
as we
know, proves
to be correct to
a
remarkable
approximation:
(1)
yv2/3 =
k(x

T).
Here
y
is
the
surface
tension,
v
the molecular
volume,
k
a
universal
constant,
T
[2]
the
temperature,
and
x
a temperature
that deviates
only slightly
from the
critical
temperature.
Y
is
the free
energy
per
unit
surface
area,
hence
Y
T*L
dT
is
the
energy
per
unit
surface
area.
Taking
into
account
that,
in
comparison
with
y,
v
depends
only slightly on
the
temperature,
one can
write in
similarly good approximation:
(1a)
y

v™
=kx
But
according
to
the rule of
corresponding states,
the
boiling
temperature
at
atmospheric
[3]
pressure
is
approximately
equal
to
a
fixed
fraction of
the critical
temperature,
and
on
the
[4]
other
hand,
the
boiling
temperature
is
proportional
to
the heat of
evaporation (Trouton's
rule).
From
this it follows
that
equation
(1a)
also entails
the
approximate
validity
of the
equation
[5]
(lb)
fy
T^v? =k(DsRTs).
[6]
Since
y
is
to
a
high
degree
of
approximation a
linear function of the
temperature,
the
bracket
on
the lefthand
side
does
not
need
to
be calculated for the
boiling
temperature
[7]
at
atmospheric pressure.
The lefthand
side
of the
equation
equals
the
energy
Uf
necessary
to
increase the
surface
of the substance
by an area
equal
to
a
lateral
surface
of
a grammolecular
cube.
Ds

RTS
is
the internal
energy
Ui
to be
expended
in
the
evaporation
of
one
grammolecule.
Equation
(1b)
can
therefore be written
in
the form