DOC.
21
MOLECULAR MOTION IN
SOLIDS
375
If
we
make
use
of d
=
(v/N)1/3
and denote
by
W
the heat
content
of
one
gram-atom
at
the
temperature
T,
we
obtain the
expression
9
_1/3w.mdWdTVN,
-a
-
vv
13
dT
dx
and,
hence,
for the
coefficient
of thermal
conductivity
k
k
=
a
--vv-m-™
-
.
13
dT
If
W
is
measured
in
calories, one
obtains k
in
the
customary
units
(cal/cm
•
sec
•
deg).
If the
substance
obeys
the
Dulong-Petit
law in
the
temperature range
considered, then,
because
dW 3R
3
•
8.3
•
107
.
-
~
o,
dT heat
equivalent
4.2
•
107
we
can, perhaps,
set
k
=
a
.4N-2/3vv-1/3
We
first
apply
this
formula
to
KCl, which, according
to Nernst,
behaves with
regard to
its
specific
heat
like
a
substance
composed
only
of identical
atoms.
Taking
for
v
the
[25]
value 3.5
• 1012,
obtained
by
Nernst from the
specific
heat
curve,
we get
[26]
k
=
a-4-(6.3
•
lO0)"®3^
•
1012-(Z!d)1/3
=
a-0.0007
[27]
whereas
experiment
at
ordinary
temperature10 yields
about
k
=
0.016.
Thus,
the thermal
conductivity
is
much
greater
than
was
to
be
expected
from
our
argument.
But
this
is
not
all.
According
to
our
formula,11
within
the
validity
range
of
the
Dulong-Petit
law
k
should
be
independent
of the
temperature. According
to
Eucken's
results, however,
the
actual
behavior
of
crystalline
nonconductors
is
entirely
different;
k
varies
approximately
as
1/T.
From
this
we
must conclude
that
mechanics
is
[29]
not
capable
of
explaining
the thermal
conductivity
of
nonconductors.12
It
should be
added that the
assumption
of
a
quantized
distribution
of
energy
also does not contribute
anything
to
the
explanation
of Eucken's
results.
[30]
10 Cf. A. Eucken, Ann.
d.
Phys.
34
(1911):
217. [28]
11
Or
according
to
a quite
obvious
argument
by analogy.
12
It
must
be noted that
this also makes
the
arguments
in
§§1
and 2
questionable.