402
DOC. 26
THE PROBLEM OF SPECIFIC HEATS
Doc.
26
On the Present State
of
the
Problem of
Specific
Heats
by
A.
Einstein
[Eucken,
Arnold,
ed.,
Die Theorie
der
Strahlung
und der
Quanten.
Verhandlungen
auf einer
von
E.
Solvay einberufenen
Zusammenkunft
(30.
Oktober
bis
3.
November
1911),
mit einem
Anhange
über
die
Entwicklung
der
Quantentheorie
vom
Herbst
1911 bis
Sommer 1913.
Halle
a.
S.:
Knapp,
1914. (Abhandlungen
der Deutschen Bunsen Gesellschaft
für
angewandte
physikalische Chemie,
vol.
3,
no.
7), pp.
330-352]
§1.
The Connection between
Specific
Heats
[1]
and
the Radiation
Formula
It
was
in
the domain of
specific
heats that the kinetic
theory
of heat
achieved
one
of
its
earliest and finest
successes
in
that
it
permitted
the
exact calculation
of the
specific
heat
of
a
monatomic
gas
from the
equation
of
state.
It
is
now,
again,
in
the domain of
specific
heats that the
inadequacy
of molecular
mechanics has
come
to
light.
According
to
molecular
mechanics,
the
mean
kinetic
energy
of
an
atom not
bound
3 RT
rigidly
to
other
atoms
is
in
general
if
one
lets R
denote the
gas
constant,
T
the
2-,
N
absolute
temperature,
and
N
the number of
molecules in
a gram-molecule.
From
this
it follows
directly
that the
specific
heat of
an
ideal
monatomic
gas
at constant
volume
is
3
-R,
or
2.97
calories,
per
gram-molecule,
which is in
very
good agreement
with
2
experience.
If the
atom does not
move
freely
but
is
bound
in
an equilibrium
position,
then
it
possesses
not
only
the
mean
kinetic
energy
mentioned
above, but,
in
addition,
also
a
potential
energy; we
must
assume
this to be
the
case
for
solid bodies.
For the
arrangement
of
atoms to
be
stable,
the
potential energy corresponding
to
the
displace-
ment
of
an
atom from its
equilibrium position
must be
positive.
Further,
since
the
mean
distance
from the
equilibrium position
must
increase
with
the thermal
agitation, i.e.,
with
the
temperature,
this
potential energy
must
always
correspond
to
a positive
component
of the
specific
heat.
Thus,
according
to
our
molecular
mechanics,
the atomic heat of
a
solid
body
must
always
be
greater
than
2.97. As
we know,
in
the
case
where the
forces
binding
the
atom to its
equilibrium position
are
proportional
to
the
displacement,
the
theory
yields
the
value
of 2•2.97
=
5.94
for the atomic heat. It
has
been
known for
a
long
time that for
most
of the
solid
elements the
atomic
heats
possess
values
that
do not
deviate
substantially
from
6
at
ordinary temperatures (Dulong-Petit
law).
But
it also has
been
known
for
a long
time
that there
are
elements with
smaller atomic heats.
Thus,
already
in
1875,
H.F.
Weber found
that the
value
of the atomic heat of diamond
at
[2]
-50°C
is roughly
the
value
0.76,
far smaller than that
permitted
by
molecular
mechan–