236 DOC. 20 THEORETICAL ATOMISM
the individual
systems
have different
L
values before the
contact,
then
an equalization
of their
L
values
and, thereby,
a
transfer of
energy
from the
system
with the
higher
L
value
to
the
system
with the lower
L
value
must
take
place upon
the
contact. Thus,
by
virtue
of
this
property,
the
value L
can
immediately be
viewed
as a
measure
of the
system's temperature;
in fact,
we
shall
soon see
that,
up
to
a
numerical
factor,
L
equals
the so-called absolute
temperature.
In what follows, we will
pay
special attention
to
the kinetic theory of gases. In
the solid and
liquid
states,
neighboring
molecules of the substance
must exert
a
considerable force
on
each
other,
since
experience
shows that such bodies offer
significant
resistance
to
a
change
of their volume.
However,
in the
gaseous or vapor
state,
even
neighboring
molecules
must be
thought
of
as
being considerably
far
removed from each
other;
regarding
this
state it
therefore
seems
natural
to
assume
that,
in
general,
the molecules
fly
around
freely,
and that
they
exert
forces
on one
another
only
when
two
of them
come
especially
close
to
each another
(collision).
These
freely moving
molecules will
also
collide with the
wall
of the
vessel
in
which
the
gas
is
contained,
exerting thereby a pressure
p
on
the
wall,
which
can
be
easily
calculated
by means
of mechanics alone if the volume
V
of the
vessel,
the
intensity
L
of the molecular
agitation,
and the number
n
of
gas
molecules
present
in the vessel
are
known. We obtain
2 L
p
=
-n
-.
3
V
This result contains
two
assertions confirmed
by experiment, namely
1.
At
a
constant
temperature (const.
L)
the
gas pressure
is
inversely proportional
to
the volume.
2.
The
gas pressure depends only
on
the
number,
but
not
on
the
nature,
of the
molecules that constitute
the
gas.
The second
proposition
can
be tested
experimentally
insofar
as
the ratio of the
numbers
n
of the molecules
present
in
the
two
different
gases can
be
compared by
chemical methods.
Finally, our result also throws light upon the connection that obtains between the
quantity
L
and the temperature.
In
the theory of heat, the absolute temperature T
is
defined most simply
by
the stipulation that
T is
proportional
to
the pressure of
a gas
whose volume
is
kept
constant.
Our
equation
shows that this
definition
is
also valid
for
the
quantity L;
hence the latter
is, up
to
a
constant,
equal
to
the absolute
temperature.
This
constant is
related
to
the absolute size of the
molecule,
as we
will
now
show.
We
apply
our
equation
to
as
many grams
of
a
chemically simple gas
as
the
molecular
weight
indicates
(e.g.,
to two
grams
of
gaseous hydrogen);
this
quantity
of
substance
is
called
a
gram-molecule.
The number N of molecules in
a
gram-molecule
The Equation
of State of
Ideal Gases.
The Molecu-
ar-theoretical
Meaning of
the Absolute
Temperature.