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, " **physical**ly 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 pro**of** **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-