92 DOC.
2
LAW OF PHOTOCHEMICAL
EQUIVALENCE
§2.
Condition
for
the
Thermodynamic Equilibrium
of the
System
Considered
in
§1
If
Ss
is the
entropy
of the radiation contained in the volume
V,
and
Sg
the
entropy
of
the
gas mixture,
then for each of the
equilibrium
states
found in the
previous
paragraph
the condition
must
be fulfilled that the
change
of
the
total
entropy
vanishes
for each
infinitely
small virtual
change
of
the states of the radiation and the
gas.
The
virtual
change
to
be
considered
consists in
the
conversion of
a quantity
of radiation
energy
Ne (in
the
vicinity
of
v0)
into
energy
of
the
gas
mixture,
with
simultaneous
decomposition
of
a
gas
molecule
(gram-mole)
of
the first kind. In such
a
virtual
change
the
temperature
of the mixture would
change
to
a
nonnegligible
extent. To
prevent this,
we imagine
in the
familiar
way
that the
gas
mixture is
in
permanent
thermoconductive connection with
an infinitely large
heat
reservoir
of
the
same
temperature T.
In that
case
the
temperature
of
the
gas
mixture does
not
change
during
the virtual
change;
on
the other
hand,
one
has
to
take into
account
that
during
a
virtual
change
the heat reservoir absorbs the
energy -(8Es
+
8Eg)
in the form of
heat,
if
Es
is the radiation
energy
and
Eg
the
energy
of the
gas.
The condition for the
equilibrium
is
therefore
8E
+
8E
(4)
8Ss
+
-
t
'
=
0.
Now
we
have
to
calculate the individual
terms
of
this
equation. First,
we
have
for
the
virtual
change
under consideration
8Es
=
-Ne,
*ss
=
s
if
Ts
denotes the
temperature
that
corresponds
to
the radiation
density p.
The
variations
relating
to
the
gas we
calculate
according
to the
customary thermodynamic
methods,
whereby
we
treat
the
specific
heats
as
being independent
of the
tempera-
ture-which
is
not essential for what follows. First
one
obtains
Eg=En1{cv1T+b1},
sg
=
lgT.
c,
-
R
lg^!
Here
cv1
is
the heat
capacity per gram-mol.
at
constant
volume,
b1
is the
energy per gram-mol.
of
gas
of kind
1
at
T
=
0
c1
is
an integration
constant
of the
entropy
of
the first kind
of
gas.
These
equations
yield immediately
the
following ones:
[7]