DOC.

2

LAW OF PHOTOCHEMICAL

EQUIVALENCE

89

Doc.

2

Thermodynamic

Proof of the Law of Photochemical

Equivalence

by

A.

Einstein

[Annalen

der

Physik

37 (1912):

832-838]

In what

follows,

the Wien radiation law and the law of

photochemical equivalence

will be derived

simultaneously

in

an

essentially thermodynamic way. By

the

photochemical equivalence

law

I

understand the

proposition

that the

decomposition

of

a gram-equivalent by

a

photochemical process requires

the absorbed radiation

energy Nhv,

if N

denotes the number of molecules in

a

gram-molecule,

h

the familiar

constant

in Planck's radiation

formula,

and

v

the

frequency

of the

acting

radiation.1

The law

appears essentially

to

be

a

consequence

of the

assumption

that the number

of molecules

decomposed per

unit time is

proportional

to

the

density

of

the

acting

radiation;

however,

it

should be

emphasized

that the

thermodynamic relationships

and

the radiation law do

not

permit

the

replacement

of this

assumption

by any

other

arbitrary

assumption, as

will

be shown in brief

at

the end of this

paper.

Furthermore,

the

following

shows

clearly

that the

equivalence

law

and

the

assumptions leading

to

it

are

valid

only

as

long

as

the

acting

radiation

is

within the

region

of

validity

of the Wien law.

But

now

for such radiation the

validity

of the law

can hardly

be doubted

any longer.

§1.

On the

Thermodynamic Equilibrium

between Radiation

and

a

Partially

Dissociated Gas

from

the

Standpoint

of

the Mass Action Law

Suppose

that

a

mixture of three

chemically

different

gases

with molecular

weights

m1,

m2, m3

is

present

in

a

volume

V.

Let

n1

be the number of moles

of

the first

gas,

n2

of the

second,

n3

of the

third.2

Suppose

that

a

reaction

is

possible

between these three

kinds of

molecules

in

which

a

molecule of the first kind

decomposes

into

a

molecule

of the second

kind and

a

molecule of the third kind. In

a

state

of

thermodynamic

equilibrium,

the reactions

1Cf.

A.

Einstein,

Ann. d.

Phys.

17

(1905): 132.

2Naturally,

one

of

the

gases

with the indices

2 and

3

can

consist

of

electrons.

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