Doc.
1
CONCLUSIONS
DRAWN
FROM
THE
PHENOMENA OF
CAPILLARITY
by
Albert Einstein
[Annalen
der
Physik 4 (1901):
513523]
If
we
denote
by
7
the
amount
of mechanical
work
that
we
have to
supply
to
a
liquid in
order
to
increase the free surface
by one
unit, then
7
is
not
the total
energy
increase
of
the
system,
as
the
following
cyclic
process
will
show.
Let
there
be
a
certain
amount
of
liquid of (absolute)
temperature
T1
and
surface
area
01.
We
now
increase
isothermally
the surface
01
to
02,
increase (at
constant
surface
area)
the
temperature to
T2,
then reduce the
surface
to
01
and
cool the
liquid
to
T1
again.
If
one assumes
that
no
heat is
supplied to
the
body
other than that received
on
account
of its
speci
fic heat, then the total heat
supplied
to
the substance
during
the
cyclic
process
will
be
equal to
the total heat
withdrawn.
According
to
the principle
of conservation of
energy,
the total mechanical
work supplied must
then also
be
zero.
Hence
the
following equation
holds:
(02
 
(02

0j)7j
=
0
or
?! =
?2
'
However,
this contradicts
experience.
We
have,
then,
no
other choice but
to
assume
that the
change
in the
sur
face is associated with
an exchange
of heat
as
well, and
that the
surface
has
a
specific
heat
of
its
own.
If
we
denote
by
U
the
energy,
by
S
the
en
tropy
of the unit surface
of
the liquid,
by s
the specific heat of the
surface,
and
by
w0
the heat
necessary to form
a
unit surface,
expressed
in
mechanical units, then
the quantities
[1]
[2]
dU
=
s.O.dT
+
{7 +
w0}dO
and
ds
=
+1
+
f
do
will
be
total differentials.
Hence
we
will
have