A system of physical chemistry - Index of

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A system of physical chemistry - Index of

DEFINITION OF STATISTICAL MECHANICS 3

method of treatment with that of generalised dynamics, and points

out that the disadvantage of the latter compared with the former lies

in the fact that, "the results are expressed in terms of dynamical

quantities, such as energy, momentum, or velocity, and so require

further knowledge before we can translate them in terms of the phy.^ical

quantities we wish to measure, such as intensity of a current tempera-

ture, and so on ; a knowledge which in all cases we do not possess.

The second law of thermodynamics, on the other hand, being based on

experience, does not involve any quantity which cannot be measured in

the laboratory."

It is evident that generalised dynamics and thermodynamics have

the great merit in common that they are essentially generalisations, and

their application does not require any specialised information such as

that involved in the molecular kinetic theory. What has been said

therefore in Volume II. in regard to the advantage which this quality

confers in the case of thermodynamics applies to much the same ex-

tent to generalised dynamics. The same disadvantage manifests itself

of course, viz. that we do not get any clearer picture of the phenomenon

in question in terms of the molecules taking part therein.

It is very necessary, however, to attempt to deal with processes

which are essentially molecular in terms of the molecules themselves.

The difficulty lies in the fact that when a system consists of a very large

number of individuals {e.g. the molecules in a gas), it is quite impossible

to follow out the extremely complicated path pursued by each single in-

dividual. In order to advance beyond the mode of treatment employed

in the elementary kinetic theory of Volume I.— in which we got round

the difficulty here presented by making the certainly untrue assumption

that all molecules were identical in all respects— it is necessary to proceed

in quite a different manner by introducing a new idea into mechanics

which will enable us to deal with physical and chemical problems in a

more exact and logical way. This new idea— the introduction of which

into mechanics we owe principally to Maxwell and to Boltzmann— is

embodied in the theory of Probability. When we bring probability considerations

into mechanics we arrive at a mode of treatment known as

statistical mechanics.^ By treating molecular processes from the standpoint

of statistical mechanics we are able to take account of the fact

that all the molecules are not really identical but differ from one another

in general in respect of velocity, direction, and energy content. The

results obtained are indeed average results— as they must be if they are

to be amenable to experimental test— but such results represent the

combined effect of all the molecules present, due allowance being made

for the lack of equality in the actual contribution made by each individual

molecule to the total observed effect. This must not be taken

as meaning that we have to calculate the particular position, velocity,

and energy of each individual molecule at various intervals of time.

' For an account of this method of treatment, the reader is referred to the forth-

coming; work on General Dynamics and Statistical Mechanics, by J. Rice, M.A.,

which is specially adapted to the needs of physicists and chemists.

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