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.