142
DOC.
137 NOVEMBER
1915
137. From Max Planck
Grunewald,
7 November
1915
Dear
Colleague,
I
have
now performed
the
comparison
of
my
formulas
to
those of
Tetrode and
proceeded
in
the
following
manner.[1]
If formulas
(17)
and
(16)
in Tetrode’s
paper
are
subtracted
from each
other,
the
entropy originating from
the rotations
of
the diatomic molecules
results:[2]
S(17)
-
S(16)
=
kN{ln(kT)
+
ln(2nJ)
-
2ln h
+
ln(47r)
+
1}
The
same
quantity
results from
the
theory
developed by
me
based
on
the
formula
for
the
thermodynamic
function I
recently
set down in
writing:[3]
fp 00
V
=
--
=
AbUn^(2n
+
l).
e-(»2
*+»+èV,
2
o
where
F
is
the
free
energy,
o
=
h2/8ir2JkT,
when
you
assume
T
there
very large. [4]
Then the
sum
may
be
written
as an
integral, namely:
F
=
-TNk
In
f°°
dn-2
(n+\)
e“[(n+^2+i]°
Jo 2
=
-TNk
In
=
TNk
+ In
aj
.
If
you
consider
now
that
S
=
-°L
&T'
then, through
substitution
of
the
value for
a,
we
get:
8tPJkTe
S
=
Nk
In
h2
This
is
precisely
Tetrode’s
value.[5]
I
now applied
the
theory
for
an
arbitrary
(also
“incoherent,”
or
however
else
you
want to
express
it)
degree
of freedom
as
well.[6]
It
all works
very
well
and
reliably,[7]
[Some
of
the
sidetracks
were
horrendous,
though.
But
you
probably
understand
that.]
so
that
even
the
specific
heat
of
polyatomic (rigid)
molecules
as
well
as
the
energy
of spatial
oscillators
are
easily
calculated.
I
shall tell
you
about that in
person.
With
cordial
greetings, yours,
Planck.