A system of physical chemistry - Index of

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A system of physical chemistry - Index of

MAXWELL'S LAW 9

maintained as long as the temperature is maintained constant. This

average kinetic energy may be written as ^J^mc", where c is the sum

of the squares of the velocities of all the molecules at any given instant

divided by N. This r-?n-s speed is not the same thing as the mean or

average speed, which is simply the sum of all the velocities divided by

N, though the two quantities are not very different numerically. The

above way of expressing Maxwell's law, i.e. the above expression, is of

the general form : y = x'^e'^^ which, it is to be observed, is not identical

with the normal law of errors. The resulting curve is, in fact, not

The alternative mode of expressing Maxwell's law where-

symmetrical.

in the curve is symmetrical, and the distinction between the two modes,

is considered in Appendix I.

Maxwell's law expresses the distribution of velocities as a continuous

function of the number of molecules present. That is, the speed of one

molecule may differ by any amount (down to the infinitesimally small)

from the speed of any other molecule. When we come to consider

the quantum theory we shall find continuous functions replaced by discontinuous

ones, i.e. abrupt changes in finite small steps in place of

gradual change in infinitely small steps. ^

It will be observed that Maxwell's expression involves the squares of

velocities. Since the kinetic energy of a molecule depends upon the

square of its velocity, it should be possible, on similar lines, to express

the distribution of kinetic energy amongst the molecules constituting

a gas system. If we denote by dn the number of molecules which

possess kinetic energy lying between the limits E and E + ^, it can be

shown that at a given temperature—

dn = constant x N x ^"^/At , E"^ .

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