122

DOC.

5

SUPPLEMENT TO DOC. 2

thermodynamic equilibrium,

in which the radiation

is

black-body

radiation of the

same temperature

as

the

temperature

of

the

gas

mixture. In the

same

way,

at

a

given

temperature

there exist

infinitely many

constitutions of the radiation for which

"extraordinary" thermodynamic equilibrium

must

hold if

n2n3\n1

has

the

appropriate

value. But

in

the

presently

considered

case,

Z

=

Z'

is

no

longer

a

sufficient

condition

for the

thermodynamic equilibrium.

Because for the latter

to

be

present,

it

must

also

be demanded

that,

for

every

effective

elementary region

of

radiation

frequency,

the

radiation

energy

absorbed

per

unit time be

equal

to

the radiation

energy newly

created

per

unit time.

[6]

It

is

easy

to

show

that

cases

of

"extraordinary" thermodynamic equilibrium

must

exist. For

if

we

denote

by

*?10

^20'

V309

P^2)...

the molecular

concentrations and the radiation densities in

a case

of

"ordinary"

thermodynamic equilibrium,

where

both the

gas

mixture and the

acting

radiation

of

the individual

elementary ranges possess

the

temperature

T,

then

Vio

'

V20' V30'

X

^Po".

*Po2).••

are

values for the molecular concentrations and

radiation densities for which

"extraordinary" thermodynamic equilibrium

obtains for

arbitrary

values

of

x

if

only

the

gas

mixture

possesses

the

temperature T.

For it follows from

(1a)

and

(2)

that the

condition Z

=

Z' remains

satisfied; furthermore,

the radiation

energy produced per

unit time

for,

say,

the first

range

remains

unchanged

because

n2

and

n3

have

remained

unchanged,

and neither

are

there

changes

in the

energy

absorbed unit time

from the radiation

of

the first

elementary range,

because the

product

n1.p(1)

has

remained

unchanged.

These

states

of

extraordinary thermodynamic equilibrium,

associated with the

temperature

T of

the

mixture,

are

distinguished by

the fact that the densities

p(1), p(2),

etc.

of

the

elementary ranges vary

as

the

corresponding

densities

p0(1),

p0(2)

etc.

that

these

ranges possess

at

the mixture

temperature

T at

"ordinary" thermodynamic

equilibrium.

If this

necessary

condition for

extraordinary thermodynamic equilibrium

(5)

etc.

P0(1) P0(2)

is

satisfied,

then

one

can

reformulate

(1a)

in the

following way: