222
THEORY
OF
SPECIFIC
HEAT
If
the infrared
proper
oscillation
frequencies
v
of
a
solid
are
known,
then
according
to
the aforesaid its specific heat
as
well
as
its
dependence
on
[26]
the
temperature would be completely
determined
by
equation (8a). Pronounced
deviations
from
the relation
c
=
5.94
n
would
have to be expected
at
normal
temperatures
if the substance in
question
showed
an
optical infrared
proper
frequency
for
which
A
48
u;
at
sufficiently
low
temperatures
the specific
heats
of
all solid bodies
should
decrease significantly with
decreasing
[27]
temperature.
Further, the
Dulong-Petit
law
as
well
as
the
more
general law
c
=
5.94
n
must
hold for all bodies
at
sufficiently
high temperatures
unless
new
degrees
of
freedom
of
motion
(electron-ions)
become apparent
at
the
[28]
latter.
Both above-mentioned
difficulties
are
resolved
by
the
new
interpretation
and I
believe it
likely
that the latter will
prove
its validity
in principle.
Of course,
an
exact
agreement
with the facts is
out
of the
question.
During
[29]
heating, solids
experience
changes
in
molecular
arrangement
(e.g.,
changes
in
volume)
that
are
associated
with
changes
in
energy
content;
all solids that
conduct
electricity contain
freely
moving
elementary
masses
that
make
a
contribution
to
the
specific heat;
the
random
heat oscillations
have possibly
a
somewhat
different
frequency
than the
proper
oscillations
of
the
elementary
structures
during
optical
processes.
Finally,
the
assumption
that the
pertinent
elementary structures
have
an
oscillation
frequency
that is
independent
of the
energy
(temperature)
is
undoubtedly
inadmissible.
Nevertheless, it is
interesting
to
compare
our
conclusions with obser-
vation. Since
we
are
concerned
with
rough
approximations only,
we
assume,
in
accordance
with
F.
Neumann-Kopp's
rule, that
every
element
contributes
equally
to
the
molecular specific heat of all its solid
compounds
even
if its
specific heat is
abnormally
small.
The
numerical
data presented in
the
[30] following
table
are
taken
from
Roskoe's textbook
of
chemistry.
We
note
that
all elements with
abnormally low
atomic
heat
have
low
atomic
weights;
according
to
our
interpretation,
this is
to be expected,
since, ceteris
paribus,
low
atomic
weights
correspond
to high
oscillation frequencies.
The
last
column
of the table lists the values
of
A
in
microns
that
are
obtained
from
these
numbers,
if
one
assumes
that
they
are
valid
at
T
=
300,
with the
help of
the
curve
showing
the relation
between
x
and
c.
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Extracted Text (may have errors)


222
THEORY
OF
SPECIFIC
HEAT
If
the infrared
proper
oscillation
frequencies
v
of
a
solid
are
known,
then
according
to
the aforesaid its specific heat
as
well
as
its
dependence
on
[26]
the
temperature would be completely
determined
by
equation (8a). Pronounced
deviations
from
the relation
c
=
5.94
n
would
have to be expected
at
normal
temperatures
if the substance in
question
showed
an
optical infrared
proper
frequency
for
which
A
48
u;
at
sufficiently
low
temperatures
the specific
heats
of
all solid bodies
should
decrease significantly with
decreasing
[27]
temperature.
Further, the
Dulong-Petit
law
as
well
as
the
more
general law
c
=
5.94
n
must
hold for all bodies
at
sufficiently
high temperatures
unless
new
degrees
of
freedom
of
motion
(electron-ions)
become apparent
at
the
[28]
latter.
Both above-mentioned
difficulties
are
resolved
by
the
new
interpretation
and I
believe it
likely
that the latter will
prove
its validity
in principle.
Of course,
an
exact
agreement
with the facts is
out
of the
question.
During
[29]
heating, solids
experience
changes
in
molecular
arrangement
(e.g.,
changes
in
volume)
that
are
associated
with
changes
in
energy
content;
all solids that
conduct
electricity contain
freely
moving
elementary
masses
that
make
a
contribution
to
the
specific heat;
the
random
heat oscillations
have possibly
a
somewhat
different
frequency
than the
proper
oscillations
of
the
elementary
structures
during
optical
processes.
Finally,
the
assumption
that the
pertinent
elementary structures
have
an
oscillation
frequency
that is
independent
of the
energy
(temperature)
is
undoubtedly
inadmissible.
Nevertheless, it is
interesting
to
compare
our
conclusions with obser-
vation. Since
we
are
concerned
with
rough
approximations only,
we
assume,
in
accordance
with
F.
Neumann-Kopp's
rule, that
every
element
contributes
equally
to
the
molecular specific heat of all its solid
compounds
even
if its
specific heat is
abnormally
small.
The
numerical
data presented in
the
[30] following
table
are
taken
from
Roskoe's textbook
of
chemistry.
We
note
that
all elements with
abnormally low
atomic
heat
have
low
atomic
weights;
according
to
our
interpretation,
this is
to be expected,
since, ceteris
paribus,
low
atomic
weights
correspond
to high
oscillation frequencies.
The
last
column
of the table lists the values
of
A
in
microns
that
are
obtained
from
these
numbers,
if
one
assumes
that
they
are
valid
at
T
=
300,
with the
help of
the
curve
showing
the relation
between
x
and
c.

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