122
DOC.
5
SUPPLEMENT TO DOC. 2
thermodynamic equilibrium,
in which the radiation
is
black-body
radiation of the
same temperature
as
the
temperature
of
the
gas
mixture. In the
same
way,
at
a
given
temperature
there exist
infinitely many
constitutions of the radiation for which
"extraordinary" thermodynamic equilibrium
must
hold if
n2n3\n1
has
the
appropriate
value. But
in
the
presently
considered
case,
Z
=
Z'
is
no
longer
a
sufficient
condition
for the
thermodynamic equilibrium.
Because for the latter
to
be
present,
it
must
also
be demanded
that,
for
every
effective
elementary region
of
radiation
frequency,
the
radiation
energy
absorbed
per
unit time be
equal
to
the radiation
energy newly
created
per
unit time.
[6]
It
is
easy
to
show
that
cases
of
"extraordinary" thermodynamic equilibrium
must
exist. For
if
we
denote
by
*?10
^20'
V309
P^2)...
the molecular
concentrations and the radiation densities in
a case
of
"ordinary"
thermodynamic equilibrium,
where
both the
gas
mixture and the
acting
radiation
of
the individual
elementary ranges possess
the
temperature
T,
then
Vio
'
V20' V30'
X
^Po".
*Po2).••
are
values for the molecular concentrations and
radiation densities for which
"extraordinary" thermodynamic equilibrium
obtains for
arbitrary
values
of
x
if
only
the
gas
mixture
possesses
the
temperature T.
For it follows from
(1a)
and
(2)
that the
condition Z
=
Z' remains
satisfied; furthermore,
the radiation
energy produced per
unit time
for,
say,
the first
range
remains
unchanged
because
n2
and
n3
have
remained
unchanged,
and neither
are
there
changes
in the
energy
absorbed unit time
from the radiation
of
the first
elementary range,
because the
product
n1.p(1)
has
remained
unchanged.
These
states
of
extraordinary thermodynamic equilibrium,
associated with the
temperature
T of
the
mixture,
are
distinguished by
the fact that the densities
p(1), p(2),
etc.
of
the
elementary ranges vary
as
the
corresponding
densities
p0(1),
p0(2)
etc.
that
these
ranges possess
at
the mixture
temperature
T at
"ordinary" thermodynamic
equilibrium.
If this
necessary
condition for
extraordinary thermodynamic equilibrium
(5)
etc.
P0(1) P0(2)
is
satisfied,
then
one
can
reformulate
(1a)
in the
following way:
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