DOC.
26
THE PROBLEM OF SPECIFIC HEATS
409
so
that their
displacements
have
opposite
signs
at all
times)
than
when
they move
in
the
same
direction,
since elastic forces act between
the
two
in
the
first,
but
not
in
the
second
case.
Hence,
it must
be
assumed that the
body
behaves
as a
mixture
of
oscillators
of
different
frequencies. Now,
Nernst and Lindemann found that
one
takes
sufficiently
good
account
of the
existing
experimental
evidence
if
one assumes
that the
substance
behaves
as a
mixture
of
oscillators,
with
half of them
having
the
frequency v,
and the
other half the
frequency
v/2.
To
this
assumption
there
corresponds
the
formula
zBv
(I3V~
(4a)
c
=~RI
T
+
____ 2
(
~v
2
l~cT
-
1,
-
i)
However,
in
accordance
with what I have said
before,
I do not believe
that
we are
dealing
here
with
a
theoretical
formula.
The
only way
to
obtain
an
exact
formula
from
(4)
would
be
to
sum over
infinitely many
values
of
v.
But with this
formula Nernst and
Lindemann made
a very
valuable advance in
that
they
obtained
a
better
agreement
with
experience
without
having
to
introduce
a
new
constant
characterizing
the
particular
substance.10
Naturally,
equation
(4)
or
(4a)
also makes it
possible
to represent
the
specific
heat
of
compounds
in
the
solid state. All
one
has to do
is
to
set
up
an expression
of
the form
(4a)
for
each
kind
of
atom,
and add
up
these
expressions.
Compounds
usually display
infrared
proper frequencies
that
show
up
as
optical absorption
bands
in
the infrared
region
and
as
corresponding
regions
of
metallic reflection. As
Drude
has
shown,
these
infrared
proper frequencies correspond
to oscillations
of
charged
ponderable
atoms.
These
are, therefore,
oscillations
of the
same
structures and
under the influence of the
same
forces
as
those
we
have
just
studied. The
only
difference
is that,
in contrast to
the
forces
mediating
thermal
interactions,
the
forces
that
set
the
atoms in
motion
when
the
body
is
irradiated
show
some degree
of orderliness
in
space,
so
that the
oscillation
phases
of
identicallly
charged adjacent
atoms
are
not
independent
of
each
other.
Hence, it
cannot be
stated
without
reservation that the
optical
proper frequencies are
identical
with
the thermal
frequencies; but,
in
any
case, they are
not
likely
to deviate too much
from
the latter.
This
consequence
of
the
theory
also
proves
to be correct.
According
to Nernst,
the
molecular heats of
KCl and NaCl
can
be
satisfactorily explained
based
on
the
assumption
that in
each of these
substances
the metal
atom
and the
halogen
atom have
the
same
proper
frequency.
The
comparison
of the
proper
frequency,
as
calculated
from
the
[18]
[19]
10 An
exact
investigation
of the
specific
heat of
solid
binary
compounds
consisting
of
a
very heavy
and of
a light
atom
might
well be
instructive,
because
the
light
atoms
probably
perform
oscillations
approximating
the monochromatic
oscillations assumed
by
the
theory.