74
GENERAL MOLECULAR THEORY
OF
HEAT
where
L
denotes the
mean
value
of
the kinetic
energy
of
motion
of
the
center
of gravity
of
a
molecule. If
one
also takes into
account
that
L
=
Lv
one
obtains
N.2K
=
R
.
Hence
the
constant
2K
equals
the quotient
of the constant
R
and
the
number
of molecules contained in
one
equivalent.
[20]
If, in accordance with
O.
E.
Meyer,
one
sets
N
=
6.4
x
1023,
one
gets
[21]
K =
6.5
x
10-17.
§4.
The general
significance
of
the constant
K
Let
a
given
system
be
in
contact
with
a
system
of
relatively infinitely
large
energy
and temperature
T.
The
probability
dW
that the value
of
its
energy
will lie
between
E
and
E
+
dE at
an
arbitrarily
chosen
instant is
E
[22]
W =
Ce
2kTME
For
the
mean
value
E
of
E
one
obtains
Since,
further,
we
get
E
E
=
-00
0
CEe
^ME
1
=
E
00
cT-rf
Ce
uEdE
,
o
E
00
(E
-
E)e
2liTw(E)dE
0
-
0
Differentiation
of
this
equation
with
respect to
T
yields