178
DOC. 4 KINETIC THEORY
LECTURE NOTES
We
will show
that
we
have
thereby
proved
Avogadro's
law
for monatomic
gases, i.e.,
that
at
a given
pressure
&
a given
temperature
a
unit
volume
always
contains the
same
number of molecules
independently
of the
nature
of the
gas.
If
we
have
an
ideal
gas
of
arbitrary volume,
then the
virial
theorem
implies
that
L
=
IpV
2
If
V
= 1,
we
have
j
ryttlC2
3
L
=
Z
=
-p
2
2
If,
in
accordance
with
analysis given
above,
we
set
Hf-
=
-0
,
we
thus
obtain
Z
=
-,
where 0
depends on
the
temperature alone,
which
proves
Avogadro's
law for
0
monatomic
gases.
[p. 31]
Beyond
this, we
investigate
to what extent
the
equation
of
state
for
ideal
gases
can
be deduced
from
the
investigations
carried
out thus far.
We derived
from
the
virial
theorem
L
=
-pV
2
If
one
gram-molecule
is present,
then
V
is
the molecular
volume.
We
have
then,
in
addition,
L
=
N-
=
N-1&
2 2
Hence,
by substituting
into
the
above
formula,
Pv
=
m
Thus,
pV
depends
linearly
on
the
temperature
function 0 that
we
introduced,
and
depends only on
it.
We
have thus shown
that
according
to
the
kinetics
of monatomic
gases,
pV is
a
function of
temperature
alone.
One
can
also
deduce
from kinetics alone
that
this
function must
be
equal
to