A system of physical chemistry - Index of

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A system of physical chemistry - Index of

i6o A SYSTEM OF PHYSICAL CHEMIS2RY

ture pressure and density. Here, among other things, answers have

been found to such questions as refer to distribution of the positions

and velocities of the molecules, the mean number of molecular colli-

sions per second, the mean free path, the connection between these

quantities and the pressure, temperature, viscosity, rate of diffusion,

etc., of the gas. We proceed to quote some known results concerning

the distribution of the molecules in position and in velocity.

As regards the positions of the molecules, we conceive the enclosure

to be subdivided into a great number, say n, " physically small " volumes

or cells. This means that each cell is supposed too small to be dealt

with separately by our experimental apparatus and yet large enough

to contain an enormous number of molecules. As it is known that the

number of molecules in one cubic mm. of a gas at N.T.P. is about

we have

3 X lo^'', this condition is easily complied with. Suppose

altogether N molecules in the enclosure, then the average number of

molecules per cell is N/« which is assumed to be a large number.

Suppose we express the actual number of molecules in any cell as

N/« . (i +8) where 8 is the fractional variation of this molecular density

from the mean molecular density N/«, and may be positive or negative.

It can be proved that there is an enormous probability against the

possibility of 8 acquiring values of an order of magnitude greater than

the order of i/N. As N is enormous, this practically means that there

is an enormous probability in favour of uniform distribution of the

molecules in position.

It should be noted as a feature of this statisti-

cal proposition that the proof of it does not prove the impossibility of

the number of molecules in any cell deviating seriously from the mean

number ; it proves that such a state is extremely improbable, and that

the dynamical conditions which would produce it occur so infrequently

and exist for so brief a time that actual demonstration of its existence

would elude our experimental arrangements.

When we come to deal with the distribution of the molecules in

terms of velocity, we do not find this uniformity of distribution. Taking

the question of speed alone, apart from questions of direction, there

is certainly a theoretical upper limit to the possible speed attainable

by any one molecule ;

it is in fact the speed which that molecule would

have if it possessed the entire energy of the gas, the other molecules

being absolutely at rest. Such a speed is, however, far beyond any

in the

practical limit ; although there is no dynamical impossibility

state of affairs pictured, there is an enormous it.

probability against

The application of statistical methods to this problem leads to the

view that certain speeds are more privileged than others. Thus there

is one speed such that there are at a given instant more molecules

possessing velocities within, say, one foot per second of this speed, than

there are molecules possessing speeds within one foot per second of

any other speed ; and if we choose speeds smaller and smaller or larger

and larger than this " "

maximum probability speed, these speeds are

less and less privileged, until, when we arrive at zero speed or at speeds

very great compared with the maximum probability speed, the proba-

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