DOC.
60
389
following.
Let
the cavity
contain
a
very
large
number
(N)
of
resonators
of
frequency
v0. How
does
the
entropy
of this
system
of
resonators depend
on
the latter's
energy?
To
solve this
problem,
Mr.
Planck
uses
the
general
relation
between
entropy
and
the probability
of
the
state
as
inferred
by
Boltzmann from
his
investigations
on
the
theory of
gases.
We
have,
in
general,
entropy
=
k.log
W,
where
k
denotes
a
universal
constant
and
W
the
probability
of
the
state
under consideration. This probability is
measured
by
the "number of
complexions,"
a
number
that indicates in
how
many
different
ways
the
state
in
question
can
be
realized.
In
the
case
of the above
problem,
the
state of the
resonator
system
is
defined
by
its total
energy,
so
that the
problem
to be
solved
reads:
In
how
many
different
ways can
the
given
total
energy
be
distributed
among
N
resonators? In order
to
determine this,
Mr.
Planck
divides the total
energy
into
equal
small parts
of
a
certain
magnitude
e.
A
complexion
is determined
by
stating
how
many
such
e's
belong
to each
reso-
nator.
The number
of
such
complexions,
which yield
the total
energy,
is
determined
and set equal to
W.
From
the
Wien
displacement law,
which
can
be
derived
thermodynamically,
Mr.
Planck then concludes further that
one
has to set
e
=
hv,
where
h
denotes
a
number
that is
independent
of
v.
This
way
he
arrives
at
his
radiation
formula
^
_
8TThi/3 1
P
- c3
*
]lv '
-
1
which
fully
agrees
with
experience
thus far.
It
might
seem
that
according
to
this derivation the Planck radiation
[23]
formula has
to
be viewed
as
a
consequence
of the
current electromagnetic
theory
of radiation.
However,
this is
not
the
case,
especially
for the
following
reason.
The number
of
complexions
just
discussed could
be viewed
as
an
expression
of the multiplicity
of
probabilities
of distribution
of the
total
energy
among
N
resonators
only
in
case
every imaginable
distribution
of
energy
would
appear,
at
least
to
some
approximation,
among
the
complexions