68

GENERAL

MOLECULAR THEORY OF HEAT

Doc.

5

ON

THE GENERAL MOLECULAR THEORY

OF

HEAT

by

A.

Einstein

[Annalen

der

Physik 14

(1904):

354-362]

In the

following

I present

a

few

addenda to

an

article I

published

last

year.1

When

I

refer

to

the

"general

molecular

theory

of

heat,"

I

mean

a

theory

that is essentially

based

on

the

assumptions put

forth in

§1

of the article

cited. In order

to

avoid

unnecessary

repetitions,

I

assume

that the reader is

familiar

with that article

and

use

the

same

notations I

have used

there.

First, I derive

an

expression

for

the entropy

of

a

system, which

is

[2] completely analogous to

the

expression found

by

Boltzmann

for ideal

gases

and

[3] assumed

by

Planck

in

his

theory of

radiation.

Then

I

give

a

simple

derivation

of

the

second law.

After that

I examine

the

meaning

of

a

universal

constant,

[4]

which

plays

an

important

role in the

general

molecular

theory

of

heat.

I

conclude with

an

application of

the

theory to black-body

radiation,

which

yields

a

most

interesting

relationship between

the

above-mentioned

universal

[5]

constant,

which is

determined

by

the

magnitudes

of the

elementary quanta of

matter

and

electricity,

and the

order of

magnitude

of

the radiation

wave-

lengths,

without

recourse

to

special

hypotheses.

§1.

On

the

expression

for

entropy

For

a system

that

can

absorb

energy

only

in

the

form

of heat,

or,

in

other

words,

for

a

system

not

affected adiabatically

by

other

systems,

the

following equation

holds

between

the absolute

temperature

T

and

the

energy

E,

according

to

§3

and

§4,

loc.cit.:

[1]

1A.

Einstein,

Ann.

d.

Phys. 11 (1903): 170.