402

DOC. 26

THE PROBLEM OF SPECIFIC HEATS

Doc.

26

On the Present State

of

the

Problem of

Specific

Heats

by

A.

Einstein

[Eucken,

Arnold,

ed.,

Die Theorie

der

Strahlung

und der

Quanten.

Verhandlungen

auf einer

von

E.

Solvay einberufenen

Zusammenkunft

(30.

Oktober

bis

3.

November

1911),

mit einem

Anhange

über

die

Entwicklung

der

Quantentheorie

vom

Herbst

1911 bis

Sommer 1913.

Halle

a.

S.:

Knapp,

1914. (Abhandlungen

der Deutschen Bunsen Gesellschaft

für

angewandte

physikalische Chemie,

vol.

3,

no.

7), pp.

330-352]

§1.

The Connection between

Specific

Heats

[1]

and

the Radiation

Formula

It

was

in

the domain of

specific

heats that the kinetic

theory

of heat

achieved

one

of

its

earliest and finest

successes

in

that

it

permitted

the

exact calculation

of the

specific

heat

of

a

monatomic

gas

from the

equation

of

state.

It

is

now,

again,

in

the domain of

specific

heats that the

inadequacy

of molecular

mechanics has

come

to

light.

According

to

molecular

mechanics,

the

mean

kinetic

energy

of

an

atom not

bound

3 RT

rigidly

to

other

atoms

is

in

general

if

one

lets R

denote the

gas

constant,

T

the

2-,

N

absolute

temperature,

and

N

the number of

molecules in

a gram-molecule.

From

this

it follows

directly

that the

specific

heat of

an

ideal

monatomic

gas

at constant

volume

is

3

-R,

or

2.97

calories,

per

gram-molecule,

which is in

very

good agreement

with

2

experience.

If the

atom does not

move

freely

but

is

bound

in

an equilibrium

position,

then

it

possesses

not

only

the

mean

kinetic

energy

mentioned

above, but,

in

addition,

also

a

potential

energy; we

must

assume

this to be

the

case

for

solid bodies.

For the

arrangement

of

atoms to

be

stable,

the

potential energy corresponding

to

the

displace-

ment

of

an

atom from its

equilibrium position

must be

positive.

Further,

since

the

mean

distance

from the

equilibrium position

must

increase

with

the thermal

agitation, i.e.,

with

the

temperature,

this

potential energy

must

always

correspond

to

a positive

component

of the

specific

heat.

Thus,

according

to

our

molecular

mechanics,

the atomic heat of

a

solid

body

must

always

be

greater

than

2.97. As

we know,

in

the

case

where the

forces

binding

the

atom to its

equilibrium position

are

proportional

to

the

displacement,

the

theory

yields

the

value

of 2•2.97

=

5.94

for the atomic heat. It

has

been

known for

a

long

time that for

most

of the

solid

elements the

atomic

heats

possess

values

that

do not

deviate

substantially

from

6

at

ordinary temperatures (Dulong-Petit

law).

But

it also has

been

known

for

a long

time

that there

are

elements with

smaller atomic heats.

Thus,

already

in

1875,

H.F.

Weber found

that the

value

of the atomic heat of diamond

at

[2]

-50°C

is roughly

the

value

0.76,

far smaller than that

permitted

by

molecular

mechan–