DOC.
26
THE PROBLEM OF SPECIFIC HEATS
403
ics.
This
one
result
already
shows
that molecular
mechanics
cannot
yield
correct
specific
heats
for solid
bodies-at
least not at low
temperatures. Further,
the
laws
of
dispersion
led to
the
conclusion
that instead of
consisting
of
only one
material
point,
the
atom
may
possess electrically
charged
material
points (polarization electrons)
that
move
indepen-
dently
of the
atom
as a
whole and
which-statistical
mechanics
notwithstanding-make
no
contribution
to
the
specific
heat.
[3]
We
were
not in
the
position
to
relate these
inconsistencies
of the
theory
to
other
physical
properties
of
matter
until
a
few
years ago,
when Planck's
investigations
on
thermal radiation
quite unexpectedly
shed
new light on
this area.1
Though
we
have not
yet come
to
the
point
where
we
need
to
supplant
classical mechanics with
a
mechanics
that
would
be
able to
yield
correct
results for
fast
thermal
oscillations
as
well,
still
we
have
found the
law from which
the
deviations from
the
Dulong-Petit
law
follow,
and
we
learned that these
deviations
are
related
by
law to
other
physical
properties
of the
substances.
In
what
follows,
I
shall outline the
train of
reasoning
in
Planck's
investiga-
tions in
a manner
that
will
bring
out
clearly
the connection
with
our
problem.
It
is
possible
to arrive at
a
theory
of the law of
cavity
radiation
at
thermal
equilibrium
(the
law
of
black-body
radiation)
by doing
a
theoretical
analysis
to
determine
the
density
and
composition
at
which
the radiation
is
in statistical
equilibrium
with
an
ideal
gas, given
the
presence
of
structures
that
make
an
energy
exchange
between the radiation and the
gas possible.
One
such structure
is
a
material
point
bound
to
a
point
in
space by
forces
proportional
to its
displacement
from this
point (oscillator); we
shall
assume
that the
material
point
of
the
oscillator is
provided
with
an
electric
charge.
Let thermal
radiation,
an
ideal
gas,
and
oscillators
of the
kind
indicated
be
enclosed
in
a
volume bounded
by
perfectly reflecting
walls.
By
virtue of their electric
charges,
the
oscillators must
emit
radiation and
continually
receive
new
momentum from
the radiation
field.
On the other
hand,
the material
point
of
the individual
oscillator
collides with
gas
molecules
and in this
way exchanges energy
with
the
gas.
The
oscillators
thus
bring
about
an
energy
exchange
between the
gas
and
the
radiation,
and the
energy
distribution of the
system
in
the
state
of
statistical
equilibrium is
completely
determined
by
the total
energy,
if
we assume
that
oscillators
of
all
frequencies are present.
In
an
investigation
based
on
Maxwell's
electrodynamics
and
on
the
mechanical
equations
for the motion of the material
point
of the
oscillator,
Planck has
now
shown
that-assuming
that
only
oscillator
and
radiation
are
present,
but
not
the gas-the
following
relation
exists
between the
mean
kinetic
energy
Ev
of
an
oscillator
of
frequency
v,
and
the radiation
density
uv2
1
M.
Planck,
Vorl.
über
d.
Theorie
der
Wärmestrahlung, pp.
104-166.
2
We
assume
here
an
oscillator with
three
degrees
of
freedom.
[4]