270
DOC. 368
MARCH
1912
radiation
differs
by
a
finite amount from
that of the
system
in
the
equilibrium,
with
whose
fate
I
am
concerned.
I
consider
a
reaction
a
=
c
(1)
that
is
sort
of
a simple
modification
or
conversion
of
a
structure,
as,
for
example,
that
of fumaric
acid
to
the
structure isomeric maleic acid.
The transformation of
optically
isomeric
forms
into
one
another
offers
a
convenient
example
for
the
special
case
where
the
change
of total
energy
in
such
a
conversion
is equal
to
zero.
I
imagine
that the
system
of the
two monochromatic
substances
a
and
c
is
in
isothermal
equilibrium
inside
a
volume
of
finite dimensions. Since
each of the
substances has
only a single,
undamped proper
frequency,
the radiation of
all
wave-
lengths, except
for
the
two
with
proper frequencies
va
and
vc,
travels
through
the
volume
exactly as
if there
were no
absorbing
substance
in
it.
The
black-body
radiation
in the
volume
that
is
required
for
the
thermodynamic equilibrium
of the
system
is brought
about
by
the
enclosing
walls,
which have
the
same
temperature,
and
which
make the
cavity
filled with
the
equilibrium
mixture "black"
in terms
of radiation.
If
we now
put
windows in
the
walls,
we can
send out
radiation of
all
frequencies,
except
for
va
and
vc,
without
influencing
the
system.
But if the
system
in
the
equilibrium
reacts, in that,
for
example,
c
is
progressively
converted
to
a,
then,
according to
what
has
been
said
above,
radiation of
frequency
vc
will be
continually
absorbed and that of
frequency
va
released.
We
assume
that the
absorption
and
release
occur
in
the
outward
direction, through
the
windows in
the
walls
provided
for this
purpose,
and
that
all
of
the
heat transfer between
the
system
and
the environment
is
limited to this
transfer of
radiation. Then
it
is
obvious
that
the
addition
or
removal
of the heat
necessary
for
the
conversion
of the
amount
given by
the
formula, which
is
called the
heat of reaction
and
is
denoted
by Q,
must
be
equal
to
the difference
between
the
amount
of the radiation
that
we
take
up at frequency
va
and
that
we
send off
at
frequency
vc.
Q
= Sc
- Ea
(2)
Because of the
existing
thermodynamic
equilibrium,
the
density
at
which
the radiation
is
absorbed and released
is
the
density
of
the
black-body
radiation
for
the relevant
wavelength
at
the
prevailing temperature.
According
to
thermodynamics,
we
have
dlnK
Q
=
RTr2
(3)
dT
But
according
to
Wien's
law
we
have
for
all
black-body
densities
hv
=
RT2
dlnu
u
=
radiation
density.
dT
Hence
(2)
becomes
Q
=
hvc
-
hva
(4)