DOC. 26
THE PROBLEM OF SPECIFIC
HEATS
405
the
oscillator
than
it
absorbs,
or
vice
versa.
Equation
(1)
also
remains
valid when
the
energy
variations
in
the
resonator
are
preponderantly
determined
by
the interaction
between the oscillator and the
gas;
it
is certainly
therefore
also valid in
the total
absence
of
an
interaction
with
radiation,
for
example,
when
the
oscillators have
no charge
whatsoever.
The
equation
is
also valid if
the
body interacting
with
the oscillator
is
not
an
ideal
gas
but
any
other
kind
of
body,
as
long
as
the oscillator
vibrates
approximately
monochromatically.
Thus,
if
the function of
v
and T
obtained
in
the
investigations
of
black-body
[6]
radiation
is
substituted for the radiation
density
uv
in
(1),
we
arrive at
the
mean
thermal
energy
of
an approximately
monochromatically
vibrating
structure
as a
function of
v
and
T. Starting
out
from
Planck's
radiation formula
as
the formula confirmed
to
the
highest
degree
of
approximation,
we
obtain from
equation (1)
(3)
r
-
3Av
V
h\
"VT
-
1
where k
=
-
and h
is
the
second constant
of
Planck's
formula
(6.55
•
10-27).
If
we
assume
that
one gram-atom
of
a
solid
element consists
of N
such
approximately
monochromatic
oscillators, we
obtain
its
atomic heat
c by
differentiating
with
respect
to
T and
multiplying by N,
where
we
put h/k
=
ß:
(4)
The
accompanying Fig.
22,
taken
from
a
paper
by Nernst,3
shows
the
extent to which
this
formula
yields
correct values
for the
specific
heats
of
solid
elements
at low
temperatures
in
the
figure.
In the
figure,
the
experimentally
obtained
curves are
drawn
in thick
lines,
and the theoretical
ones
in
thin
lines;
appended
to
the latter
are
the
corre-
sponding
values
of
ßv.
Even
though
systematic
differences
between the observed and the theoretical
values
do
exist,
the
agreement
is
nevertheless
astonishing,
if
one
takes into
account
that each
individual
curve
is completely
determined
by a single
parameter
v, namely,
the
proper
frequency
of the
atom
of the element
in
question.
Thus,
the
retaining
of
equation
(1),
which, according
to
the
foregoing,
did not
seem
completely justified
from
a
purely
theoretical
point
of
view,
has
been
completely
justified by
experiment.
One
thing
needs
3
Zeitschr.
f.
Elektrochemie
17
(1911):
274.
[7]