92
HEURISTIC VIEW OF
LIGHT
compression
of radiation between
reflecting walls
does not
change
its
entropy.
However,
we
shall
not enter
into
this,
but
will
immediately
investigate
how
the function
cp
can
be
obtained
from
the
black-body
radiation
law.
In
the
case
of
"black-body
radiation,"
p
is
such
a
function
of
v
that the
entropy
is
a
maximum
at
a
given energy,
i.e.,
6
rOO
0
(p(p,v)dv
=
0
,
if
6
rOO
0
pdv
=
0
.
From
this it
follows
that
for
every
choice
of
Sp as
function of
v
rOO
0
Spdv
=
0
,
where
X
is
independent
of
v.
Thus
for
black-body
radiation
dy/dp
is
independent
of
v.
The following equation
applies
when
the
temperature
of
black-body
radiation
of volume
v
=
1
increases
by
dT:
dS
=
V-QQ
g
v=0
0p
Th
dpdv
'
or,
since
d^p/dp
is
independent of
v,
dS
=
dE
Since
dE
equals
the heat
added, and
the
process
is reversible,
we
also
have
dS
=
j
dE
.