A system of physical chemistry - Index of


A system of physical chemistry - Index of



mixed- up-ness" to the concept of entropy for ; maximum mixed-upness

means on the mechanical view maximum stabihty or equihbrium,

and hence when equihbrium exists the entropy is a maximum. The

same idea is involved in the term "run-down-ness "

employed by

Tolman as a descriptive mechanical term for entropy. The latter term

appeals to the mind as being particularly applicable to a chemical reaction

which proceeds in order to attain an equilibrium state at which

the system will, chemically speaking, have


completely run down ".

The Principle of Equipartition of Kinetic Energy.

This principle, which has been deduced on the basis of statistical

mechanics by Maxwtll and by Boltzmann {cf. Jeans, Dynamical Theory

of Gases), has already been employed in Chap. I. of Vol. I. in dealing

with Perrin's method of determinmg the Avogadro Constant from

measurements made upon emulsions. The principle states that in a

system consisting of a large number of particles {e.g. molecules) the

kinetic energy is on the average equally distributed amongst the various

degrees of freedom possessed by these particles. The first point with

which we have to deal is the term degree offreedom.

A degree of freedom is represented by a co-ordinate. We may

take the term as meaning an independent mode in which a body may

be displaced or a possible mode or direction of motion. We shall con-

sider briefly the problem of the number of degrees of freedom possessed

by bodies in the gaseous and solid* states of matter respectively.

First of all a word about energy in general. We are familiar with the

two kinds of energy which material systems may possess, namely, kinetic

and potential. These " kinds " of energy are not to be confused with

the "types" of energy of which we are about to speak. A "type"

may consist of kinetic and potential energy together, or simply kinetic

alone. A gas molecule can possess theoretically three types of energy,

each of which is a function of the temperature :

(i) Energy of Translation

; (2) Energy of Vibration., and (3) Energy of Rotatiofi.

1. Energy of Tratislation.—This type of energy is possessed in virtue

of the free translational motion of the molecules along free paths

throughout the whole of the system. The energy in this case is entirely

kinetic. It has been represented diagrammatically in Chap. I. of Vol. I.

in connection with Perrin's work on Brownian movement. Every gas

molecule possesses translational motion and consequtntly translational

energy. Since the direction of any movement of this kind can be represented

by the three space co-ordinates, we conclude that translational

energy corresponds to three degrees of freedom. The energy of translation

is the same for any moving molecule at a given temperature.

Further, such a molecule possesses just three degrees of freedom in re-

spect of translation whether the molecule be monatomic or polyatomic ;

the constitution of a molecule does not enter into the question of its

translational energy.

2, Energy of Vibration.—This type of energy exists in virtue of the

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