244 DOC. 20 THEORETICAL ATOMISM

[18] principle

the

significance

of which extends

beyond

the

range

of

validity

of

molecular

mechanics.

It follows from what

has

been said

so

far that the kinetic

theory

contains

a

significant

amount

of truth.

However,

we

have known for

a

few

years

that there

are

definite limits

to

the

validity

of molecular

mechanics;

one

must,

in

fact,

say

that

its

general

foundations

are,

strictly

speaking, never

exactly

valid but

are

only

correct to

a

certain

degree

of

approximation.

This will be

briefly explained

in what follows.

The Limit of

Validity

of

Molecular

Me-

chanics.

From the standpoint of the kinetic theory of heat

we

have

to

think of

a

solid,

chemically simple body

as a

system of

an

immensely great number of atoms that can,

indeed, be displaced relative

to

each other but that oppose such

a

displacement with

a

considerable

force,

which increases with

increasing displacement.

Let

us

imagine

that

we constantly keep an eye on one

of these

atoms

so as

to

learn the character of

the motion

it

carries

out.

For the sake of

simplicity,

we

shall

imagine

that all of the

molecules,

excepting

the

one

under

observation,

are

fixed

to

their

equilibrium

positions.

In

that

case

they

will

oppose

a

change

of

position

of the

atom

under

consideration with

a

force that increases with the

increasing displacement

of

the atom

from

its

equilibrium position.

Left

to itself,

the

atom

will oscillate about

its

equilibrium position

in

a

manner

similar

to

a

pendulum.

The mechanical

energy

of

a

body moving

in such

a

way

consists

not

only

of kinetic

energy

but also of

potential

energy,

and

in

an

actual

pendular

motion

(in

which the

period

of

an

oscillation does

not

depend on

the maximum

deflection),

the

mean

potential energy

has the

same

magnitude as

the

mean

kinetic

energy.

But

according

to

the

general

theorems stated

above,

the latter

must

be

equal

to L

or

to

3/2RT/N,

so

that the total mechanical

energy

of the

atom

is

on

average

3RT/N;

hence,

for the

energy

of

one

gram-molecule

a

value

of 3RT

is to

be

expected.

To be

sure,

this

argument

suffers from the

inaccuracy

caused

by

the fact that

we

based

our

argument

on

the

assumption

that the individual

atoms

have

no

influence

on one

another. But

this

assumption

cannot

cause a

substantial distortion

of the

result.

Equating

the above

energy

3RT with the heat

content

of

one

mole,

we

conclude from

our

result that the

specific

heat

per

mole

must

be

3R,

or

equal

to

5.97 when measured

in

gram-calories.

This

is

actually

in

agreement

with the

empirical

law of

Dulong-Petit,

which

is

satisfied to

a

rather

good

degree

of

approximation

at

ordinary temperatures.

However,

contrary

to

the results of molecular

mechanics,

the

specific

heat sinks

to

lower values

at

low

temperatures.

Near absolute

zero

it

even

becomes

vanishingly

small! This result did

not

surprise

theoreticians;

for

they already

knew that the laws

for

the emission

of radiation

by

heated bodies do

not

agree

with molecular

mechanics,

and that

a

close connection

must

exist between the law for the emission