DOC.
2
LAW OF PHOTOCHEMICAL
EQUIVALENCE
91
(1)
Z
=
A pn1.
According
to
what has been
said,
the
proportionality
factor
A
can
depend only
on
the
gas temperature T. According
to
the
foregoing,
the
equation
also holds in the
case
where the radiation
density
p
(at frequency
v0)
is different from the
density
that
corresponds
to
the
temperature
T of the
gas.
As
regards
the recombination
process, we
assume
that it is
a common
second–
order reaction in the
sense
of
the
mass
action
law,
that
is to
say,
that the number of
the molecules
of
the first kind that
are
formed
per
unit volume and time
is
proportional
to the
product
of
the
concentrations
n2/V
and
n3/V,
with the
proportional-
ity
coefficient
depending only
on
the
gas temperature,
but
not
on
the
density
of
the
radiation that
is
present (assumption
III).
Thus,
the number Z' of
the
molecules of the
first kind
formed
per
unit time is
(2)
Z'
=
A'
•
V
•
-
.
V V
The
system
that
we are considering, consisting
of radiation and
gas
mixture,
is
always
in
thermodynamic equilibrium
if
the
number Z of
the
decomposition processes
is
equal to
the number Z' of the combination
processes;
because in that
case
not
only
the
quantity
of each kind of
gas
but also the
quantity
of
the
radiation that
is
present
remains
unchanged.4
This condition reads
«2
«3
(3)
V V
= =
A
nx
T]1
A
'
P,
where
A
and A'
depend only on
the
temperature
of
the
gas
mixture. A
peculiar
consequence
of this
argument
is
that
a
thermodynamic equilibrium
should be
possible
at
a
given gas temperature
and
an arbitrarily given
radiation
density
(i.e.,
also
radiation
temperature).
But there
is
no
violation of the second law
here,
which
is
connected with the
fact that
a specific
chemical
process
is
necessarily
linked
to
a
transfer of heat from the
radiation to the
gas;
one
cannot construct
a perpetuum
mobile of the second kind with the
help
of the
system
considered
by
us.
4While
reading
the
proofs
it
occurs
to
me
that this
conclusion,
which is essential for
what
follows,
holds
only
under the
assumption that,
at
a
given gas temperature, e
is
independent
of
p.
[5]
[6]