DOC. 4
KINETIC THEORY LECTURE NOTES
177
This
is
the
constant
of
Maxwell's
law.
If the
law
is
written
in
three
variables,
then the
constant
is
to
be raised
to
the third
power.
Now
we
seek
to calculate
the
mean
square
of the
velocity.
n
systems
constitute
canonical
composite
system.
1
specific gas
molecule in each
system singled out.[62]
In
dnc $
is
between
%
+
d£
We
have
^2
_
El;2
of the selected molecules of
all
systems
=
^2dnt
number of
systems (n)
!dn.
Hence
1
2
xd(e~x2)
=
1
2
xe
+
oo
-
00
oo
*2
dx
00
0
+
qo
z2
We
obtain
2
00
-Q
m
^
Jkonstr^2/m)e
d
*
2
m
©
jkonst
e
52/(2/m»e
^
£
2
_ .
=
0-
+
00
x2dx
xe2~
-
oo
m
2
m
©
+
00
©
m
dx
-
oo
[p. 30]
=
0
m
?
=
V
+
Tl2
+
Ci-
V
w
+
V
me2
_
m-s
•
-c
=
le
2 2
2
30
m
We obtain the
important
theorem that the kinetic
energy
of
a
monatomic
gas
molecule
depends only on
0,
and
is
independent
of the
mass
of the
molecule.
The
mean
kinetic
energy
of
a
monatomic
molecule
depends
only on
the
temperature.[63]