44
THEORY OF
THERMAL
EQUILIBRIUM
[28]
dQ=dpv=dpv-dpv+dt{dldv}
v
dt
[29]
[30]
[31]
[32]
However,
since
and,
further,
we
have
Since,
further
we
will
have
I
n-
d
pv
Tt
dL
V
dL
Jp
r
pl
=
2Z,
v
«
=
lKw-l
dL
dp
v
v
\
fo
Jn
x
V
dL
wV
dpv
+
LTpv
r
dp*
=
dL
,
dv
Jp
r rfp
+
dL
v
T
=
1
4/cA
UK
[33]
(1)
dO dL
-f
=
nKj-
+
4/cA
^
dV
dp
v
v
We
will
now concern
ourselves with
the expression
lwd'
v
v
[34]
This
represents
the increase
of
potential
energy
in the
system
that
would
take
place
during
time
dt
if
V
were
not
explicitly
dependent
on
time.
The
time
element
dt shall
be chosen
so
large
that
the
sum
indicated
above
can
be
replaced
by
its
average
value for infinitely
many
systems
S
of
equal temper-
ature, and
at
the
same
time
so
small that the explicit
changes
of
h
and
V
with time
be infinitesimally
small.
Suppose
that infinitely
many
systems
S
in
a
stationary state, all
of
which have
identical
h
and
Va,
change
to
new
stationary
systems
which
are
characterized
by
values h+Sh,
V+SV
common
to
all.
Generally,
"6"
shall
denote the
change
of
a
quantity
during
transition of the
system
to
a new
state; the
symbol
"d"
shall
no
longer
denote the
change
with time but differ-
entials
of
definite integrals.
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