A system of physical chemistry - Index of

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A system of physical chemistry - Index of

170

A SYSTEM OF PHYSICAL CHEMISTRY

is possible with this assumption so to chose the co-ordinates that the

total internal energy, kinetic and potential,

involves only squares of the

co-ordinates and velocities, so that we can write the total internal energy

e as—

e = aj^f' -f . . . -I- a^q^ + b^q^ -F . . . b^q^

where . . .

. . .

a^ an., b-^ bn are constants.

In this manner and under the conditions laid down we can, as it

were, partition the energy among the various degrees of freedom, a.^q{^

being, for example, the kinetic energy " belonging to " the first degree of

freedom, and b^q^ the potential energy belonging to the same degree of

freedom, and so on. There is in addition, of course, the kinetic energy

of translation of the molecule as a whole, viz. \mx^ -f \my^ -i- \mz~y

which we will write as.K (kappa) involving three more degrees of freedom,

with the energy as before partitioned between the three degrees.

We can now state some* results of the application of statistical

mechanics to a system of such molecules. It must be understood,

however, that these results rest on the validity of the classical dynamics.

Of late these results have been impugned by Planck and others,

and the foundations of dynamics are undergoing a revision. It will,

however, enable the reader to grasp the modifications proposed if he

masters the following few statements and accepts their truth at all

events provisionally.

As the molecule moves about and its parts oscillate with regard to

each other, its energy changes, not only in toto but also in its several

terms. It can be shown, however, that the mean energy, kinetic or

potential, belonging to any co-ordinate, averaged over a considerable

period of the molecule's history, is the same for all the degrees of freedom

and is equal to ^kT. That is—

\mx^ = \nijp- = \mz^ — a^q-^ = ciij-i = . • . =

b^q-^ = b.iq

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