20 DOC.
5
CONTRIBUTIONS TO
QUANTUM
THEORY
Doc.
5
Contributions
to
Quantum
Theory
by
A. Einstein
(Presented
in the session
of
July 24,
1914)
(see
p.
735
above)
[p.
820]
Two considerations
are
presented
here
which-in
some
sense-belong
together,
as
they
show how far the
most
important
newer
results of the
theory
of
heat,
viz.
[1]
Planck's
radiation formula and
Nernst's
theorem,
can
be derived in
a purely
thermodynamical manner, utilizing
basic ideas of
quantum theory
but
not
enlisting
[2]
the
help
of
the
Boltzmann
principle.
Insofar
as
the
following
deductions
correspond
to
reality,
the theorem
by
Nernst
is
valid
for
chemically pure, crystallized
substances,
but
not
for mixed
crystals. Nothing can
be said about
amorphous
substances because of
the
still
extant
vagueness
of
the nature
of the
amorphous
state.
In order
to
justify
the
attempt presented
here
to
grasp
the
Nernst
theorem
theoretically,
I
must
point
to
the fact that
all
efforts
to
theoretically
derive the
Nernst
theorem in
a
thermodynamical
manner,
utilizing
the
experimental
theorem
[3]
that the heat
capacity
vanishes
at
T
=
0,
have failed
completely.
I
am very willing,
[4]
if
colleagues
so
desire,
to
substantiate this claim
against
the individual
attempts
of
proof.
§1. Thermodynamical
Derivation of
Planck's
Radiation Formula. We consider
a
chemically
uniform
gas
whose molecules
carry one
resonator1
each. The
energy
of
these resonators shall
not
assume every arbitrary
value but
only
certain discrete
values
ea
(per
mole). I
take the
liberty
to
consider
two
molecules
chemically
distinct,
[p.
821]
i.e.,
in
principle separable by means
of
semipermeable
walls,
if their
resonator
energies
ea
and
er
are
different.
By doing
so
I
can
view the
gas
that
was
originally
seen
as
uniform
as
also
a
mixture of different
gases
whose constituents
are
characterized
by
distinct values
ea.
By imposing
the condition that this mixture is in
thermodynamical equilibrium
versus
all
changes
in the e-values
of
the
molecules,
I
obtain the statistical law
according
to
which the
resonator
energies
of
the molecules
are
partitioned.
Then,
retroactively treating
the
resonator
energies again
as
"thermal
energy,"
I
get
that
portion
of the
specific
heat of the
gas
which
can
be traced to the
resonators
on
the molecules.
Let
n0,
n1,n2
etc.
be the moles of molecules and
e0, e1,
e2
etc.
be their
1By
"resonator"
we mean
here
quite generally
a
carrier
of
inner molecular
energy,
without
delineating
its
precise
characteristics
here in
advance.