DOCUMENT 18 JULY 1914 39

Besten

Gruss Ihr

W.

Nernst

N. B.

Auf

die Konfusion,

die dem

Obigen

entsprechend

bei Stern

bezüglich

sei-

nem

L0

u.

Ä0

-Modell

herrscht,

lohnt sich wohl

nicht

weiter

einzugehen.[8]

ALS. [18 440].

On the

verso,

Einstein has

written down

the

first

two

terms

of

the

high-temperature

(or low-frequency) expansion

of

the

expression

for

U

given

in this document.

[1]In

the

equations

below,

X

is

the heat of

evaporation,

which

for low

temperatures can

be

written

as

in the second

equation.

A version

of

this

expression

without

the terms

involving

U

was

derived

in

Nernst

1914;

see

Nernst

1918,

pp.

135-138, for

a

derivation

of

a

formula

very

similar to the

one

given

here.

[2]In

the

equation below,

M

is the molar

weight

and

log

denotes

the

common logarithm.

Sackur

1912

gives a

value

of

-1.18 for the

first

term

on

the

right-hand

side

if

the

pressure

is

expressed

in

atmospheres.

Nernst

1918, p. 152, gives

-1.6.

[3]See Stern, O.

1913. The

expression

for

U,

which

was

first derived

by

Einstein

(see

Einstein

1907a

[Vol.

2,

Doc.

38]),

is valid for

a

system

of

monochromatic harmonic oscillators

following

Planck’s law.

[4]In

fact,

as

Nernst

points

out

himself

in

Nernst

1918,

pp.

139-142, Stern’s

result

is in

complete

agreement

with the

expression

for

lnp

given

here.

Nernst

overlooks the fact

that,

in

the

notation

employed

here,

Stern’s C differs

from

that used here

precisely

by

the

amount

31nßv.

[5]Stern

arrived

at

his

result for

the

vapor pressure

in two different

ways:

from

thermodynamics

together

with Sackur’s and Tetrode’s

expression

for the

entropy

constant,

and from kinetic

theory.

The

model

used in the latter

approach was

that of

a system

of

particles moving

in

a space,

in which

a num-

ber

of

points

P

attract the

particles

with

a

force

proportional

to the distance but with

a

finite

range.

Thus,

each

point

P

is surrounded

by a sphere

in which

particles

vibrate

harmonically.

It

is

supposed

that

each

sphere

contains,

on average, one particle.

[6]In

the

thermodynamical part

of

his

paper,

Stern

assumed

the

existence

of

a

zero-point

energy

of

hv/2

per

degree

of

freedom.

[7]A

slight

variation in the

last

couplet

of

the first

prank

in Wilhelm Busch’s Max

und

Moritz.

At

this

point

in the

original

text,

Nernst

indicates

a phrase

that he has

appended

at the foot

of

the

page:

“Nämlich das

Diagramm

In the

diagram, A might

be

the

affinity

and

q

the reaction heat. One

of

the formulations

of

the heat

theorem

is that in the

limit of

low

temperatures

these

quantities

approach

each other in such

a way

that

dA/dT

=

dq/dT

=

0

(see,

e.g.,

Nernst

1918,

cha.p 1).

[8]In

Stern’s

paper,

L0

represents

the heat

of

evaporation

at absolute

zero,

and

X()

the

potential en-

ergy.

In accordance with the

hypothesis

of

zero-point energy,

the two

quantities

are

connected

through

L0

+

(3/2)Nhv

= X0

.

18. To

Max

Planck

Dahlem. 7. VII. 14

Lieber Herr

Kollege!

Auf

dem

Heimwege

ist mir

eine kleine Grille

zu unserer Besprechung aufge-

taucht,

die ich Ihnen

mitteilen

muss.

Setzen Sie den

Fall,

das

Institut käme

zu–