DOC.
1
9
potential
energy
is
correct),
I
decided
to
obtain the absolute
quantity
ca
in
one
more
way.
I
proceeded
from
the
following
idea:
If
we
compress
a
liquid isothermally
and
its
heat
content
does not
change
in the
process,
as we now
wish to
assume,
then the heat released
during
compression
equals
the
sum
of the
work
of
compression
and
the
work
done
by
the
molecular
forces.
We
can
therefore calculate the latter
work
if
we can
find
the
amount
of heat released
during
compression.
This
we
can
do
with the
help
of
Carnot's
principle.
Let
the
state
of the
liquid
be
determined
by
the
pressure
p
in
absolute units and
by
the absolute
temperature
T;
if the value of the heat
supplied to
the substance
during
an
infinitesimally small
change
of
state
is
dQ
in
absolute
units,
and
the
mechanical
work
done
on
the substance is
dA,
and
if
we
put
dQ = Xdp
+
S.dT,
dA
=
-
p.dv
=
-
p
Y3p
dv
dp
j
+ JT
dv
dT
i
m
p.v.Kdp
-
p.v.adT
,
[16]
then the condition that
dQ/T
and
dQ
+ dA
must be
total
differentials
yields
the
equations
and
d X d
zr
wr
7
Up
i
d d
+
pk)
=
-
pa)
;
[17]
[18]
here,
as
can
be
seen,
X
denotes the heat,
in mechanical
units,
supplied
to
the substance
during
isothermal
compression produced
by
pressure
p
=
1, S
is the specific heat
at constant
pressure,
k
is the coefficient of
compres-
sibility,
and
a
is the coefficient
of
thermal
expansion.
From
these
equations,
we
find
Xdp
=
-
T
a
+
Vfö da
rp
+
pjf
dK
dp.
[19]
One
has to remember
that for
any
phenomena
involving compression
of
liquids, the
atmospheric
pressure,
to which
our
bodies
are
usually subjected,