DOC.

9

CRITICAL OPALESCENCE

231

Doc.

9

The

Theory

of the

Opalescence

of

Homogeneous

Fluids and

Liquid

Mixtures

near

the Critical State

by

A.

Einstein.

[Annalen

der

Physik

33

(1910): 1275-1298]

In

an important

theoretical

paper,1

Smoluchowski has shown

that the

opalescence

of

fluids

near

the

critical state

as

well

as

the

opalescence

of

liquid

mixtures

near

the

critical

mixing

ratio and the

critical

temperature

can

be

explained

in

a

simple way

from

the

point

of

view

of the molecular

theory

of heat.

This

explanation

is

based

on

the

following

[2]

general

implication

of Boltzmann's

entropy-probability

principle:

In the

course

of

an

infinitely long

period

of

time, an externally

closed

system passes

through

all

the

states

that

are

compatible

with

the

(constant)

value of

its

energy.

However,

the

statistical

probability

of

a

state

is

noticeably

different from

zero only

when

the

work

that

would

have to be

expended

according

to

thermodynamics

to

produce

the

state in

question

from

the

state

of ideal

thermodynamic equilibrium is

of the

same

order of

magnitude

as

the

kinetic

energy

of

a

monatomic

gas

molecule

at

the

temperature

under consideration.

[3]

If

such

a

small amount

of

work suffices to

bring about,

in volumes

of

fluid

of the

order of

magnitude

of the

cube

of

a wavelength, a

density

that

deviates

markedly

from

the

average density

of

the fluid

or a

mixing

ratio that

deviates

markedly

from

the

average,

then,

obviously,

the

phenomenon

of

opalescence (the

Tyndall

phenomenon)

must

take

place.

Smoluchowski has shown

that

this

condition

is

actually

fulfilled

near

the

critical

[4]

state; however,

he

did not

provide

an

exact calculation

of the

quantity

of

light given

off

laterally

through opalescence.

This

gap

shall

be

filled in

the

following.

§1.

General Remarks

about

the Boltzmann

Principle

[5]

Boltzmann's

principle

can

be

expressed

by

the

equation

(1)

S

= ^lg

W

+

const.,

where

R

is

the

gas

constant,

N

is

the

number

of

molecules in

one gram-molecule,

S

is

the

entropy,

W

is

the

quantity

customarily designated as

the

"probability"

of the

state with which

the

entropy

value S

is

associated.

1

M.

v. Smoluchowski,

Ann.

d.

Phys.

25

(1908):

205-226.

[1]