146
DOC.
4
KINETIC THEORY LECTURE NOTES
m?
l
3
r"
=
rnc j i\
rrT
or
=

=
[5]
3 RT
2
N 2N
'
^
M
Thus,
according
to
the
equation
of
state,
the
mean
kinetic
energy
of
a
monatomic
gas
depends on
the
temperature
but not
on
the constitution
(mass)
of the
molecule and not
on
the
density
of the
molecules.
We
shall
see
later that
it
is
also
possible
to
prove
this
law
on
the
basis
of
purely
moleculartheoretical considerations without
resorting
to
the
equation
of
state,
that
is to
say,
the
equation
of
state
can
be deduced
entirely
by means
of the molecular
theory.[6]
From the
constant
of
the
equation
of
state
We
can use (1)
to calculate
the
mean
velocities
of the
gas molecules,[7]
& this calculation
obviously applies
in
the
case
of
polyatomic
molecules
as
well.
Here
L
denotes then the
kin.
energy
of translational
motion.
L


ol/applied
to
a
unit volume

=
p
=
nH^
=
c1
2
V 2
2
2
j
3p
,
T
3
T7
mc1 3 8.3
•
107
300
[p.
2]
CL
or
also L
=
pV
=
n =
JP_
2
2 2 2
~RT
=Mc

3RT
[8]
2 2
27W
18.109
1.8.1010
1.3.105
cm.
For
For
T
=
273, one
obtains
in this
way
about
1840 m/sec
for
hydrogen,
etc.
Our
analysis
leads
further
to
Avogadro's
rule.
The
rule
that
at
the
same
temperature
and
pressure
a given space always
contains the
same
number of
molecules
can
be
presented
as a
consequence
of the
theory
only
after
it has
been
proved
by
purely
moleculartheoretical considerations that the
mean
kinetic
energy
of the translational
motion of
a
molecule
depends
only
on
the
temperature.[9]