A system of physical chemistry - Index of

A system of physical chemistry - Index of

8 A SYSTEM OF PHYSICAL CHEMISTRY

This is known as the normal law of errors. The curve is shown in

Fig. I. X denotes the error and y the probability of its occurrence.

As X increases numerically, positively, or negatively, decreases jj' rapidly,

and when x becomes large y becomes vanishingly small. It will be

observed that the curve is symmetrical.

Maxwell's Law.— Maxwell has applied the principle of probability

to the problem of the distribution of velocities among the molecules of

a gas, the gas being in a condition of statistical equilibrium at a uniform

temperature throughout. A gas is to be regarded as a molecular

chaos, the speed of any molecule varying from zero to infinity, its instantaneous

value being the result of chance collisions with its neighbours.

Although all values are theoretically possible for the speed of

a molecule, it is found that in a system containing a large number of

molecules, there are very few possessing either very great or very small

speeds.

Negative Errors. Positive Errors.

Fig, I.

The majority of the molecules possess speeds which lie within

relatively restricted limits. A numerical illustration taken from Meyer's

Kinetic Theory of Gases is given in Appendix I.

There are, as a matter of fact, two ways of expressing Maxwell's

law of distribution. One of these ways has already been stated in

Chap. I., Vol. I. This way of expressing the law may be form—

put in the

dn — constant x N x e^^'^'/''^

'

c^ •

dc

where N is the total number of molecules in the system, and dn is the

number whose speeds lie between the limits c and c + dc. It is to

be clearly understood that the speed here referred to is simply a velocity

magnitude, and no restriction has been introduced as to direction of

motion. The term ~c is known as the root-mean-square speed (or

r-m-s speed). At a given temperature the system is characterised by

a certain mean or average kinetic energy of its molecules, which is

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