DOC. 22 SOLVAY DISCUSSION REMARKS 269

results

of

thermodynamics.

It is well known that

many consequences

drawn

from the

theorem had been confirmed

by experience.

On the other

hand,

it has

already

been

emphasized

that

our

physical

sensibilities

struggle against admitting

the existence of

the adiabatics

(ruled out

by

the

theorem)

of

type

BC in the above

figure.

But there is

a

theoretical

argument

that must

instill

some misgivings regarding

Nernst's

theorem, probably

the

same

argument

that induced Planck

to

restrict the

theorem

to

chemically homogeneous

bodies. To

wit,

there

are

terms in the

expression

for the

entropy

of certain

systems

that

depend only on

the

way

in which

things

are

arranged

and

not

on

the

temperature,

and it

is

uncommonly

difficult to

imagine

that

these

terms

would

drop

out

as we

approach

absolute

zero.

An

example:

a

gram-molecule

of

a

substance in dilute state is dissolved in the

partial

volume

v

of

a

solvent of total volume

v0.

The

entropy

of the

system

shows

a

dependence

on

the size

of

the

partial

volume

v

that

is

given

by

the

equation

S

= S0

+

R

log

v.

As

we

all

know,

the law

of

osmotic

pressure

follows from the

term R

log

v;

the

existence

of

this

term

is

connected with the

degree

of

order

of the

system,

which

consists in the fact that all of

the

dissolved molecules

are present

in the

part v

instead

of

being randomly

distributed

over

the entire volume

v0.

This

term

has

nothing

to

do

with

energetic

factors

(temperature, specific

heats,

molecular

forces,

etc.),

but

concerns

exclusively

the order

properties

with

respect to

the

geometric arrangement.

It is therefore

difficult

to

imagine

how this

term

could lose its

meaning

at

low

temperatures,

and this

difficulty by

no means

disappears

if

one

subjects

Van't Hoff's

and Planck's

thermodynamic

theories

of

dilute solutions

to

a

careful revision. It is

difficult

to find

a

reason

why

these theories should fail

at

low

temperatures.

In

any case,

it

is

practically hopeless

to

investigate

osmotic

pressures

at

temperatures

so

low that

we are sure

to find ourselves in

a thermally

abnormal

region,

where the dissolved substance

possesses

a

smaller value of the

mean

kinetic

energy

of

translatory

motion of the

molecules than that

prescribed by

statistical

mechanics.

However,

there is

a

second domain of

phenomena

in which

entropy

differences

also

play

a

role,

and in which this difference

rests

only

on a

change

of

order with

respect

to

the

geometric

arrangement, namely,

the domain

of

paramagnetic

phenomena.

Here the orientation of the molecule

plays

the

same

role

as

the

position

of its

center

of

mass

in osmotic

phenomena.

The

Curie-Langevin

law

expresses

the

resistance

put up by

thermal

agitation against

an

alignment

of the molecules in

just

the

same way

as

the law

of

osmotic

pressure

is determined

by

the resistance

put up

by

thermal

agitation against

a

restriction

of

the

space

available

to

the molecule

during

its diffusional

wandering.

It

is

therefore

of

the

utmost

importance

to learn

whether,

in

principle,

the

Curie-Langevin

law loses its

validity

at

low

temperatures.

To be

more precise,

the

question

arises: Is the

Curie-Langevin

law

connected to those