DOC. 20 THEORETICAL ATOMISM 237
is
obviously
the
same
for
all
substances and
is
a
universal
constant
that determines
the absolute size of the molecules. For
one
gram-molecule,
our
equation
reads
2 NL
p
=
.
3
V
On the other
hand, experiment yields
for
a
gram-molecule
the relation
RT
p
V
,
where
R is
an
experimentally
obtained
constant
(8.3
•
107).
A
comparison
of the
two
equations yields
L
=
- -
T.
2
N
This establishes the connection between the
quantities
L
and
T.
Another important result can
be
derived from our equation for the gas pressure.
According
to
the definition of
L,
this
quantity
is
equal
to
the mean kinetic energy of
the
atom,
and hence also
equal
to
the kinetic
energy
of
a
molecule if it consists of
3
only
one
atom. Thus,
the
quantity
NL
or
-
RT
is
equal
to
the total kinetic
energy
of
2
a
mole of
a
monotomic
gas, actually equal
to
the total
energy
of the
gas
insofar
as
the latter
depends
on T,
i.e.,
on
the
intensity
of molecular
agitation. Thus,
the
specific
3
heat
of
a
gas-referred
to
one
gram-molecule-must be
equal
to
-R. This
2
conclusion has been confirmed for all those
gases
whose molecules
must
be
considered monatomic for chemical
reasons.
Thus
far,
our
presentation
did
not
require
our
making any assumptions
about the
nature
of the molecules. The
agreement
of the results
must
therefore be viewed
as an
important
confirmation of the
general
foundations
of the
theory.
However,
what
we
have said
so
far
cannot
provide
full satisfaction for the
following reasons.
We
incorporated
in
the foundations of the
theory
the
assumption
that the
particles (atoms
or
molecules),
the motions of which
are supposed
to constitute
heat,
are
of
very
small,
but
quite
definite,
finite
size; on
the
other
hand,
the results of the
theory
discussed
thus
far,
which
are comparable
with
experiment,
do
not
permit
the
determination of the
true
masses
of
the
atoms
and molecules. This
was
first
accomplished on
the basis of
Clausius's
theory,
which will
now
be
discussed,
with
the
help
of which three
seemingly
quite
disparate phenomena, namely viscosity,
thermal
conduction,
and
diffusion,
were
explained kinetically.
[4]
If
a
gas
(or
otherwise
a
liquid)
is
conducted through
a
tube slowly enough, the
velocity of the flow
is
greatest along the axis of the tube and decreases toward the
wall of
the
tube,
to
vanish altogether right
at
it.
Thus, the internal layers slide relative
to
the outer ones, and experience shows that
a
constant expenditure of work
is
needed
Specific Heat
of Monatomic
Gases.
Viscosity
in
a
Gas.