244 DOC. 20 THEORETICAL ATOMISM
[18] principle
the
significance
of which extends
beyond
the
range
of
validity
of
molecular
mechanics.
It follows from what
has
been said
so
far that the kinetic
theory
contains
a
significant
amount
of truth.
However,
we
have known for
a
few
years
that there
are
definite limits
to
the
validity
of molecular
mechanics;
one
must,
in
fact,
say
that
its
general
foundations
are,
strictly
speaking, never
exactly
valid but
are
only
correct to
a
certain
degree
of
approximation.
This will be
briefly explained
in what follows.
The Limit of
Validity
of
Molecular
Me-
chanics.
From the standpoint of the kinetic theory of heat
we
have
to
think of
a
solid,
chemically simple body
as a
system of
an
immensely great number of atoms that can,
indeed, be displaced relative
to
each other but that oppose such
a
displacement with
a
considerable
force,
which increases with
increasing displacement.
Let
us
imagine
that
we constantly keep an eye on one
of these
atoms
so as
to
learn the character of
the motion
it
carries
out.
For the sake of
simplicity,
we
shall
imagine
that all of the
molecules,
excepting
the
one
under
observation,
are
fixed
to
their
equilibrium
positions.
In
that
case
they
will
oppose
a
change
of
position
of the
atom
under
consideration with
a
force that increases with the
increasing displacement
of
the atom
from
its
equilibrium position.
Left
to itself,
the
atom
will oscillate about
its
equilibrium position
in
a
manner
similar
to
a
pendulum.
The mechanical
energy
of
a
body moving
in such
a
way
consists
not
only
of kinetic
energy
but also of
potential
energy,
and
in
an
actual
pendular
motion
(in
which the
period
of
an
oscillation does
not
depend on
the maximum
deflection),
the
mean
potential energy
has the
same
magnitude as
the
mean
kinetic
energy.
But
according
to
the
general
theorems stated
above,
the latter
must
be
equal
to L
or
to
3/2RT/N,
so
that the total mechanical
energy
of the
atom
is
on
average
3RT/N;
hence,
for the
energy
of
one
gram-molecule
a
value
of 3RT
is to
be
expected.
To be
sure,
this
argument
suffers from the
inaccuracy
caused
by
the fact that
we
based
our
argument
on
the
assumption
that the individual
atoms
have
no
influence
on one
another. But
this
assumption
cannot
cause a
substantial distortion
of the
result.
Equating
the above
energy
3RT with the heat
content
of
one
mole,
we
conclude from
our
result that the
specific
heat
per
mole
must
be
3R,
or
equal
to
5.97 when measured
in
gram-calories.
This
is
actually
in
agreement
with the
empirical
law of
Dulong-Petit,
which
is
satisfied to
a
rather
good
degree
of
approximation
at
ordinary temperatures.
However,
contrary
to
the results of molecular
mechanics,
the
specific
heat sinks
to
lower values
at
low
temperatures.
Near absolute
zero
it
even
becomes
vanishingly
small! This result did
not
surprise
theoreticians;
for
they already
knew that the laws
for
the emission
of radiation
by
heated bodies do
not
agree
with molecular
mechanics,
and that
a
close connection
must
exist between the law for the emission
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