138
DOC.
11
ARGUMENTS FOR MOLECULAR AGITATION
varied
arbitrarily, independently
of the
temperature.
The
dependence
of the
energy
on
the
frequency
at
constant
temperature
would
depend considerably
on
the existence
of
a
zero-point energy. Unfortunately,
we
have
no
experience
with
structures
of
this
kind. But
we are
familiar with
structures-namely,
rotating gas
molecules-whose
thermal motions exhibit
a far-reaching similarity1
to
those
of monochromatic
structures,
and for which the
mean frequency
varies with
temperature.
Thus,
the
justification
for
assuming
a
zero-point energy should,
first of
all,
be checked in the
case
of
these
structures.
In
what follows
we
will first
investigate
to
what extent
conclusions about the theoretical
behavior
of
such
structures
can
be drawn from
Planck's formula.
The
Specific
Heat of
Hydrogen
at Low
Temperatures
The
question
at issue
is how
the rotational
energy
of
a
diatomic molecule
depends
on
the
temperature. By analogy
with the
theory
of the
specific
heat of
solids,
we
are
justified
in
assuming
that the
mean
kinetic
energy
of rotation does
not
depend
on
whether the
molecule does
or
does
not
possess an
electric
moment
in the direction
[4]
of
its
symmetry
axis. If
the
molecule does
possess
such
a
moment,
it must
not
disturb
the
thermodynamic equilibrium
between
gas
molecules and radiation. From this
we
can
conclude that
the kinetic
energy
of rotation which the molecule
acquires
under
the influence of radiation alone
must
be the
same
as
that which it
acquires through
collisions with other molecules.
Thus,
the
question
is,
for what
mean
value of
rotational
energy
will
an
unreactive,
rigid dipole
be in
equilibrium
with radiation
of
[5] a
specific temperature.
Whatever the laws of radiation
might
be,
one
will still have
to
keep
the
assumption
that
a rotating dipole
radiates
twice
as
much
energy per
unit
time
as a
one-dimensional
resonator,
for which the
amplitude
of
the electric and
mechanical
moment
equals
the electric and mechanical
moment
of the
dipole.
An
analogous assumption
shall hold for the
mean
value
of
the absorbed
energy. If,
for
the sake
of
simplicity,
we
also
assume
that,
approximately,
all
dipoles
of
our gas
rotate
with the
same speed
at
a
given temperature,
we
will be led
to
the conclusion
that
at
equilibrium
the kinetic
energy
of
a
dipole
must
be twice
as
great
as
that
of
a
one-dimensional
resonator
of
the
same
frequency.
Based
on
the
assumptions
that
we
have
made,
we can
use
expressions
(1)
and
(2)
to
calculate
directly
the kinetic
energy
of
a
gas
molecule
rotating
with two
degrees
of
freedom,
where at each
temperature
E and
v are
related
by
the
equation
[3] 1The
first to draw attention to this
was Nernst,
cf.
Zeitschr.
f.
Elektroch.
17
(1911):
270,
825.