DOC.

39

225

Doc. 39

ON

THE

LIMIT

OF

VALIDITY

OF THE

LAW

OF THERMODYNAMIC EQUILIBRIUM AND

ON

THE

POSSIBILITY

OF

A

NEW

DETERMINATION OF THE ELEMENTARY

QUANTA

by

A.

Einstein

[Annalen

der

Physik

22 (1907):

569-572]

[1]

Let the state of

a

physical

system

be

determined

in

the

thermodynamic

sense by

parameters

A,

u,

etc.

(e.g.,

readings

of

a

thermometer,

length

or

volume

of

a

body,

amount

of

a

substance

of

a

certain kind in

one

phase).

If,

as we

assume,

the

system

is

not

interacting with

other

systems,

then, accord-

ing to

the

laws of

thermodynamics,

equilibrium

will

occur

at

particular values

A0,

u0, etc.

of the

parameters,

for

which

the

system's entropy S

is

a

maximum. However, according to

the molecular

theory

of

heat, this is

not

exactly

but

only approximately correct; according to

this theory,

the

value of

the

parameter

A

is

not constant

even

at

temperature equilibrium,

but

shows

irregular

fluctuations,

though

it is

very

rarely

much

different

from

A0.

At

first

glance

the theoretical examination of the statistical

law

that

governs

these fluctuations

would

seem

to require

that

certain

stipulations

regarding

the molecular

model must

be applied.

However,

this is

not

the

case.

[2]

Rather,

essentially it is sufficient

to

apply

the

well-known Boltzmann

rela-

tion

connecting

the

entropy

S

with the statistical

probability of

a

state.

As

we

know,

this relation is

S

=

R/N

lg

W ,

where

R

is

the constant of

the

gas

equation

and

N

is the

number

of

molecules

in

one

gram-equivalent.

We

consider

a

state

of the

system

in

which

the

parameter

X

has

a

value

A0+e

differing

very

little

from

X0.

To

bring

the

parameter

X

from

the

value

X0

to

the value

X

along

a

reversible

path at constant

energy E, one

will

have to

supply

some

work

A

to

the

system

and to withdraw

the

corre-

sponding amount

of

heat.

According

to

thermodynamic

relations,

we

have

A=fdE-fTdS,