A system of physical chemistry - Index of

38

A SYSTEM OF PHYSICAL CHEMISTRY

matter which can emit or absorb such vibrations. Let us suppose that

the material **system** consists **of** a great number **of** similar vibrators

(emitting and absorbing the wave-length A.), each acting independently,

then if we represent by unity the number **of** such resonators which

possess no energy, the term «~'/*'^ gives the number **of** resonators

possessing c units each, etc. If out **of** N such resonators under consideration

M have zero energy, the number **of** resonators, each **of**

which has energy c, is Mi?"'/*'^, the number having energy 2c is M^"'^''*'^,

and so on. Hence, for the total—

N = M + M^-'/*T -v Md--^/*T + M^-^^'/^f + etc.

= M(i -1- ^-*/*'f -f f-2«/*T -h etc.)

=

M

(l _ ^-e/AT)-

And if 2 U is the total energy **of** the N resonators—

5U = M X o + £ X M^~^/*T + 2€ X M^-2«'*T +^ etc.

(i - g-^/*T)2-

Substituting the value for N already given, we obtain—

If we now substitute hv for c, we obtain^—

5U =

And for the energy **of** one such resonator we obtain the fnean value—

Ay

U = ghvlkr _

The same expression may be obtained in a different manner {cf.

Appendix II.).

So much for the energy **of** a single vibrating resonator in radiation

based on the

equilibrium with its surroundings, the expression being

hypothesis that energy is made up **of** units, the magnitude **of** a unit

being directly proportional to the vibration frequency **of** the resonator.

We have now to see the connection between this term U and the radiation

density ?/„, that is, the quantity **of** monochromatic radiation (fre-

quency v) energy per c.c. **of** radiated space. Although «„ is usually

referred to as the radiation density, i.e. energy per unit volume, the term

u^ itself has not got the dimensions **of** energy/volume. The correct

expression for radiation density is u^/iv, where dv represents a narrow

strip **of** the spectrum virtually monochromatic. In using the symbol

My for radiation density the quantity dv is implied. Physically a single

wave-length has no meaning ; we always work with a very narrow strip

**of** spectrum containing the wave-length or frequency denoted by A or v.