408
DOC.
26
THE PROBLEM OF SPECIFIC HEATS
analysis.
Lindemann8 chose
the
melting
temperature
Ts
as
the third
defining
quantity
and
so
obtained the formula
T
(6)
v
=
2.12
1012
2
Mv3
in which
the numerical factor
is
determined
empirically, and in which
Ts
denotes
the
melting
temperature,
v
the atomic volume, and
M
the (gram) atomic weight.
Thus far, this
formula
has shown an unexpectedly close
agreement
with
the
facts.
The
following table has
been taken
from the previously cited
paper
by
Nernst:
v
.
10-12 v
.
10-12
Element from specific from
heat
Lindemann's
formula
Pb
....
1.44 1.4
Ag
....
3.3 3.3
Zn
....
3.6 3.3
Cu
....
4.93
5.1
Al ....
5.96 5.8
I ....
1.5 1.4
Now we ask again: Why does
the observed temperature dependence of
specific
heat
deviate from
the theoretically determined dependence?
In my opinion,
the
cause
for
this
deviation must be sought
in
the
fact
that the thermal
oscillations
of the
atoms deviate
markedly from
monochromatic
oscillations, and
therefore
do
not
actually have a definite
frequency but rather
a
range
of
frequencies.9 Above we
mentioned the
calculation
of
v
from elastic forces; in this calculation we
introduced the
simplifying
assumption that
the
atoms
surrounding the
oscillating
atom under consideration are kept
fixed
in
place.
In actual fact, however, they do oscillate
as
well, and continually influence the motions
of the atom considered.
I will
not seek
to go into a
more detailed
examination
of
the
actual atomic motion,
but
will
only use an intuitive special case to
demonstrate that
a
definite
frequency
is
out of the
question.
If
we
picture
two
adjacent
atoms oscillating
along
the
line
connecting
them, while all
other
atoms stay fixed,
then
it
is
obvious
that
these
atoms must have a
greater
frequency when they oscillate in
opposite
directions (i.e.,
8
Physik.
Zeitschr.
11
(1910):
609.
9
On
this question
there
is
no consensus whatsoever. Thus Nernst, who rescued all
the
results
pertaining
to this
question from their theoretical
limbo, does
not share
my
opinion
(cf.,
e.g.,
Sitzungsberichte
d. Berl.
Akad. (1911),
part
XXII).
[15]
[17]
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