DOC.
26
THE PROBLEM OF SPECIFIC HEATS
423
all
molecules,
then the relation between the rotational
energy
E,
the
frequency,
and the
temperature
will not differ
substantially
from the
corresponding
relation for the linear
oscillator.
We
will have
approximately
h\
tr
=
Av
e™
-
1
If
we
denote
by
I the
moment
of inertia
with
respect
to
an
axis
through
the
center
of
gravity
of the molecule and
perpendicular
to
the
line
connecting
its
atoms,
then
we
must
assume,
in
accordance
with
mechanics,
E
=
i/(2*v)2.
These
two
equations
contain the relation between E
and T
we
have
been
looking
for;
all
that remains
is
to
eliminate
v.20
Nernst and Lindemann
have
already pointed
[47]
out21
that
it
would
be of
exceedingly
great
interest to
investigate
the
infrared
absorption
of
diatomic
gases
whose
molecules,
probably
as
in
HCl, possess
an
electric
moment.
In
such
cases one
could
use
Kirchhoff's law to find from
absorption
coefficients
the
emission
coefficients
for the different
frequencies,
and from these the number of
molecules
momentarily present
with
a
particular angular
velocity-the statistical law
of rotational
motion.
Of
course,
a
part
of
absorption phenomena
would have to
be ascribed
to
the
relative oscillation
of the
two molecules
[atoms].
Let
us now
turn to
Sommerfeld's
hypothesis
concerning elementary
collisions.
One of the
areas
left
unaffected
by
molecular
mechanics
is
the kinetic
theory
of
monatomic
gases,
since in this
case
the mechanism of
collisions
is
immaterial.
But
we
can
learn
something
about the latter
from
the radiation
formula, using a
procedure
that
is completely
analogous
to
that
adopted
for the
oscillator; unfortunately,
for the
time
being
we
must
do without
an
exact
theory
in this
case as
well.
As in
§1,
assume
that thermal radiation
and
a
monatomic
gas are
in
thermal
equilibrium
in
some
enclosure. In
this
case, however,
the
possibility
of thermal
interaction
between
gas
and
radiation shall
be
brought
about
by endowing
individual
gas
molecules with
an
electric
charge.
If
these molecules collide with
other molecules
or
with
the
wall,
they will
emit and absorb radiation. Let
us assume
that these
collisions
are so
infrequent
that
each collision
can
be considered
by itself,
as an
isolated
event.
The
radiation emitted
in
a
collision
is
easy
to
determine
with
the
aid
of
Maxwell's
theory,
if
the
velocity
of the
emitting
atom
is
given as
a
function of
time.
20
Instead of the second of these
relations,
Nernst
assumed
the relation
ßv
=
a\Jr But
this
relation
could
only
be
satisfied if
the
specific
heat
were
independent
of the
temperature.
21
Zeitschr.
f.
Elektroch.
17
(1911):
826.
[48]