186
DOC.
4
KINETIC THEORY LECTURE NOTES
dpy
dt
dE
99v
for
closed
system
dq~
di
ØE
=- __
äp,
E^-E
5pv
d2E d2E
dqdPv
dpdqV
=
0
Thus,
for
this choice
of
variables
the
canonical
distribution
is
universally
valid
S dW
=
const
e
dp1""dp~dq1'"dq~
Kinetic
energy
essentially positive.
Hence
expression
replaceable
by
Br\, where the
r are
linear
functions
of the
q.
We
have
then
also
dW=ke
S
dp1"dp~dr1""dr~,
where the
constant
can certainly now
depend
on
the
pv.
For
specific
pv we
have
-JE
*/&
dW
=
const
e
0 dr.
/\
1
1
2
6
From
this
we
obtain
mean
value
of JB
rv =
- 2
v
2
a ft
I?
1
=n
2
[p. 38]
Thus,
the
mean
kinetic
energy
is
equal
to:
-
•
number of
degrees
of freedom.
This
2
holds
for
every
configuration
of the
p,
and
thus, generally, as long as
L
is homogeneously
quadratic
in the
q.
diatomic
gas n
=
5
Heat
content
^0
-N
per
gram-molec.