226
THERMODYNAMIC EQUILIBRIUM
or,
since the
change
in
question
is
infinitesimally
small
and
dE
=
0,
A =
-T(S-S0)
.
On
the other
hand,
however, according to
the connection between
entropy
and
probability
of
state,
we
have
S
-
S0
=
R/N
lg
W
W0.
From
the
last
two equations
it follows that
J
=
-
RT
l«r
v
7T
ig
7^
V =
V0e
N
IT
A.
or
The
result
involves
a
certain
degree
of
inaccuracy,
because
in
fact
one
cannot
talk about the
probability of
a
state,
but
only
about the probability
of
a
state
range.
If instead
of
the
equation
found
we
write
[3]
[4]
=
const.
e
then the latter
law
is
exact. The
arbitrariness
due
to
our
having
inserted
the differential
of
Y
rather than the differential of
some
function
of
Y
into the
equation
will
not
affect
our
result.
We
now
put
Y = A0+
e
and
restrict ourselves
to
the
case
that
A
can
be developed
in positive
powers
of
e,
and
that
only
the first
nonvanishing
term of
this series contributes
noticeably
to
the value of the
exponent
at
such
values
of
e
for
which
the
exponential
function is still
noticeably
different from
zero.
Thus,
we
put
A =
ae2
and
obtain
N
=
const.
e
at2