A system of physical chemistry - Index of


A system of physical chemistry - Index of


Introductory— Definitions— Probability — Statistical mechanics— Entropy and thermodynamic

probability — Principle of equipartition of kinetic energy among

degrees of freedom— Application of the equipartition principle to specific heats

and radiation phenomena — Necessity of modifying the principle of equipartition.

Definition of Statistical Mechanics.

In what we may call classical mechanics, developed in the first instance

by Newton, we become acquainted with the concepts of mass, length,

and time as the fundamental physical quantities, and from these we

pass on to derived concepts, such as velocity, acceleration, force, and

energy, by means of which we arrive at certain principles and laws

which govern physical phenomena. We say that we have " explained "

a physical or chemical phenomenon, when we can restate it in terms of

mechanics ; that is, when we can show that the phenomenon in question

is to be anticipated on the basis of a number of mechanical principles

logically applied. In Volume I. we have seen how the application of

mechanics to the small discrete particles, which we recognise as mole-

cules and atoms, leads to a reasonable explanation of many physicochemical

phenomena. We have restricted ourselves, however, hitherto

by certain simplifying assumptions, i.e. we have dealt with systems of

molecules as though all the molecules possessed exactly the same value

for their velocity and therefore for their kinetic energy, throughout the

given mass of material, an elementary gas, for example. It is known,

however, that such an assumption is by no means true. We have

already indicated this in Chap. I., Vol. I., when referring to the distribution

of velocities among a large number of gas molecules in terms,

of Maxwell's distribution law. It is true that all our experimental

measurements deal with average effects, and henc(j by regarding every

molecule as in an average state and applying the principles of mechanics^

we are able to arrive at a number of very important and useful conclusions

in terms of the elementary kinetic theory, for which we find

experimental evidence.

This mode of treatment, however, has its limitations. Certain problems

present themselves which we are quite unable to solve on the

basis of the elementary kinetic theory.

We have already met a number

of these in Volume II., and have shown how they may be dealt with

from the standpoint of thermodynamics. By way of illustration we

may cite : the relation between the lowering of vapour pressure, lower-

ing of freezing point, and rise of boiling point of a liquid as a result of



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