30

THEORY OF THERMAL

EQUILIBRIUM

Doc.

3

KINETIC

THEORY OF THERMAL

EQUILIBRIUM AND

OF THE SECOND

LAW

OF THERMODYNAMICS

by

A.

Einstein

[Annalen

der

Physik

9

(1902):

417-433]

Great

as

the achievements of the kinetic

theory

of heat

have been in

the

domain

of

gas

theory,

the science

of mechanics has

not yet

been

able

to

pro-

duce

an

adequate

foundation

for

the

general

theory

of

heat,

for

one

has not

yet

succeeded in

deriving

the

laws of

thermal

equilibrium

and

the

second

law

of

thermodynamics

using only

the

equations

of

mechanics and

the

probability

calculus,

though

Maxwell's and

Boltzmann's theories

came

close

to

this

goal.

[1] The purpose

of the

following

considerations is

to

close this

gap.

At

the

same

time, they

will yield

an

extension

of

the

second

law

that is of

importance

for

[2]

the

application of

thermodynamics.

They

will also

yield

the mathematical

expression

for

entropy from

the

standpoint of

mechanics.

S1. Mechanical

model

for

a

physical

system

Let

us imagine

an

arbitrary

physical

system

that

can

be represented

by a

mechanical

system

whose

state

is

uniquely

determined

by a

very

large

number

of

[3]

coordinates

P1...Pn

and

the

corresponding

velocities

dh

dPn

TT9

"'TT

'

Let

their

energy E

consist

of

two

additive

terms,

the

potential

energy

V

and

the kinetic

energy

L. The

former

shall

be

a

function of the

coordinates

alone, and

the latter shall

be

a

quadratic

function of

dP*

n IT

~

pu

'