242

DOC.

4

KINETIC THEORY

LECTURE NOTES

AD.

[3 003].

This document

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in

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x

21.5

cm,

of

white

squared

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and

is

written

in ink.

The

first

entries

are

found

on

the inside

cover

of the

notebook, to

which

no page

number has been

assigned. Starting

from the

first

page,

the material

presented

here

as [pp. 1-51] is sequential. Page

numbers

assigned

to

the

manuscript appear

in

the

outside

margin

of the

transcription

in

square

brackets. Blank

pages

are

not

numbered.

[P.

51]

is

followed

by twenty-seven

blank

pages,

the

remnants

of

a

torn-out sheet,

another blank

page

with text

upside-down

on

its

verso (omitted

here),

the

remnants

of

six torn-out

sheets,

four

loose sheets

(omitted

as well),

and another loose sheet of

plain

white

paper, presented

here

at

the end of the notebook

as

[pp. 53-54].

After

this there

is

a

final

page,

the

recto

of which

has

an upside-down

text

presented

as

[p.

52].

The

verso, containing

a

fragment

of unrelated

calculations

in

pencil,

is

omitted.

All

other omitted material contains calculations

that

seem

to

be

related

to

the

quantization

of the motion of

a

rigid

rotator.

The notebook also contains

a

photocopy

of another loose sheet of

plain

white

paper presented

here

at

the end of the

note-

book

as [p.

55].

On the back

cover

of the notebook

the

following

formula

is

written

in

pencil:

[1]Dated

on

the

assumption

that Einstein

prepared

these notes

for his

course

in the

summer

semester 1910 at

the

University

of

Zurich, 19

April

to

5

August 1910

(see

Zürich

Verzeichnis

1910a,

title

page).

[2]These

notes,

written

on

the

back of the

flyleaf

adjacent

to

[p.

1],

contain

the

two

deriva-

tions

of

the ideal

gas law

that

are

hinted at in

the

first sentence

of [p.

1].

The law

is derived

directly

from the kinetic

theory

and with

the

help

of the

virial theorem, respectively.

Here and

in

the

following,

L

denotes the

mean

kinetic

energy

of

the

gas

and

X

the

x-component

of

the

force acting

on

the

molecules. For

a

more

detailed discussion

of the

two derivations

see

Boltzmann

1896,

§2,

and

Boltzmann

1898,

§§49,

50;

for

a

historical discussion

see

Brush

1976,

§11.4.

The

notes presented

below

as

[p.

52] seem

to

be

an

extension of the derivation

via the

virial theorem, taking

into

account

intermolecular forces and

finite

molecular dimensions.

[3]Dalton's

law states

that

the total

pressure

exerted

by a

mixture

of

gases

is

equal to

the

sum

of the

partial

pressures

of

its constituents.

For

a

contemporary

discussion of this

law in

the

framework of kinetic

theory,

see, e.g.,

Meyer, O.

E.

1899,

part

1,

§17.

[4]In

Eichelberg's notes

the

equation pV

=

(2/3)L

is characterized

by

the

term "Theorie,"

the

ideal

gas equation pV

=

RT

by

the

term

"Erfahrung"; a

similar characterization

is

made

in

Einstein

1915a,

pp.

255-256.

[5]Here

and

in

the

following

material,

the

mass

of

a

molecule

is

denoted

by

m

and the

mass

of

a

mole

by

M.

N

is

the number

of molecules

per mole,

and

n

the number

density.

The

mass

density is

denoted

by p.

[6]See

[p.

31].

[7]The word "mittleren"

is

interlineated

in

the

original.

Calculating

the

mean

thermal veloc-

ity

of

a

molecule

directly

from the

mean

kinetic

energy

of

a

gas is

a

simplification

made

in

the

first

part

of these

notes

when

compared

to

Boltzmann

1896. A

more

sophisticated

calculation

from the Maxwellian

velocity

distribution will be

given on

[p. 32].

[8]While

the factor

3/2

should

be

3,

both

in

the formula and in the numerical

example,

the

value of

1840 m/sec

for the

mean

velocity

of

hydrogen

is

correct.

[9]The

words "der fortschreitenden

B[ewegung]"

are

interlineated in

the

original.

The theo-

rem

that the kinetic

energy

of

a

molecule

depends only

on

temperature

is derived

on [p.

30].

[10]cxv

is expressed

in

calories.

[11]See

Kundt and

Warburg 1876

for

a very

accurate

experimental

determination of the ratio

of the

specific

heats of

mercury vapor.

These authors found

a

value of

1.666

with

an

uncertainty

of

roughly

0.1%.

This

experimental

verification

was widely seen as an

important

success

for

kinetic

theory; see,

e.g.,

Meyer, O.

E.

1899,

part

1,

§54,

and Einstein 1914

(Doc. 26), p.

330.

[12]Einstein's

treatment

below follows

Boltzmann

1896,

§11;

see,

however, note

7.

In the

following

formulas

c

or

c

denotes the

mean

thermal

velocity

of

the

molecules

as

calculated

above,

i.e., c

=

Jc2;

K

denotes

a

solid

angle.

[13]In

the

following

equation sin3g

should

be cos3g.

The

final

result

for F

is

correct.

4F2

F-

-~/5q

A.

RT