46
THEORY OF THERMAL
EQUILIBRIUM
V
and
L
denote the
mean
values of the
potential and
kinetic
energies
of
the
N
systems.
Adding
(3)
and
(4),
one
obtains
[38]
or,
because
4/cA ^
dV*
wv
dp

4K,S[hV]
+
4kL.6h
,
h
=
n
4
L
Sh
=
n
4P
6L
,
[39]
4k1i
I
dpv
= 4K6[hY]

riK^f
If
we
substitute this formula in
(1),
we
obtain
if
=
S[4KhV*]
=
6
y*
T
Thus,
dQ/T
is
a
complete
differential.
Since
L
1 UK
thus
6
one
may
also
set
I
T
=
0
,
f
=
6
E*'
T
Thus,
apart
from
an
arbitrary
additive
constant,
E*/T
is the
expression
for
the
entropy
of the
system,
where
we
have
put
E*
=
V*+L.
The second
law
thus
appears as
a
necessary consequence
of
the
mechanistic
world
picture.
S9.
Calculation
of
the
entropy
The
expression
e
=
E*/T
that
we
obtained
for the
entropy
e
only
appears
to
be
simple,
because
E*
remains
to be
calculated
from
the
conditions of the mechanical
system.
I.e.,
we
have
E*
=
E
+
E0
,