70
GENERAL MOLECULAR THEORY OF HEAT
If the
system
considered
has been
in that
environment
for
an
infinitely
long
time,
the
probability
W
that the value
of
the
system's
energy
lies
between
the limits
E
and E+1 at
an
arbitrarily
chosen
instant
(§3,
loc.
cit.)
will
be
E
[9]
u
2KT{
V =
Ce
A#V1° u(E)
where
C
is
a
constant.
This value is different
from
zero
for
every
E
but
has
a
maximum
for
a
certain
E
and
-
at
least for all
systems
accessible
to
direct investigation
-
is
very
small
for
any
appreciably
larger
or
smaller
E.
We
call the
system
"heat reservoir"
and
assert
in
brief: the
above
expression
represents
the
probability
that the
energy
of
the heat reservoir in
question
will have
the value
E
in the
environment mentioned.
Using
the
result
of
the
previous
section,
we
can
also write
1
V
^
Ce
2/c
S
-
E
T0
where
S
denotes the
entropy
of
the heat reservoir.
Let
there
be
a
number
of
heat
reservoirs,
all
of them
in the
environment
at
temperature
T0.
The
probability that
the
energy
of
the first
reservoir
will
have
the
value
E1,
the
second
the value
E2...,
and
the last the
value
El,
is, then, in
an
easily
understood notation,
[10]
[11]
(a)
arr
=
vvvr..vt
i
2/c
C^.
?2
* **
^
£
E S
i
£
£
E
i
IT
Let
these reservoirs
enter
into interaction with
an
engine
that
passes
through
a
cyclic
process.
Assume
that
during
this
process
no
heat
exchange
takes
place
either
between
the
heat
reservoir
and
the
environment
or
between
the
engine
and the
environment. After the
process
considered, let the
energies
and entropies
of the
systems
be, respectively,