As a preliminary to examining further into the nature of atomic or molecular motion and the differences of character of this motion, let us try to picture the state of things which would exist in a mass of solid matter in which all the atoms are imagined to be at rest relatively to one another. The fact that a solid body in its natural state is capable both of compression and of dilata tion indicates that its atoms must not be supposed to be fixed rigidly in position relative to one another ; the further fact that a motion of either compression or of dilatation is opposed by forces which are brought into play in the interior of the solid suggests that the position of rest is one in which the atoms may be regarded as being in stable equilibrium under their mutual forces. Such a mass of imaginary matter as we are now con sidering may be compared to a collection of heavy particles held in position relatively to one another by a system of light spiral springs, one spring being supposed to connect each pair of adjacent particles. Let two such masses of matter be suspended by strings from the same point, and then let one mass be drawn aside, pendu lum-wise, and allowed to impinge on the other. After impact the two masses will rebound, and the process may be repeated any number of times, but ultimately the two masses will be found again hanging in contact side by side. At the first impact each layer of surface atoms which takes the shock of the impact will be thrust back upon the layer behind it ; this latter layer will in this way be set into motion and so influence the layer still further be hind ; and so on indefinitely. The impact will accordingly result in all the atoms in the mass being set into motion, and by the time that the masses have ceased impinging on one another the atoms of which they are composed will be performing oscillations about their positions of equilibrium. The kinetic energy with which the moving mass originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual atoms of which the bodies are composed.
Common experience, however, shows that when two bodies impinge, the kinetic energy which appears to be lost from the mass-motion of the bodies is in reality transformed into heat energy. Thus the atomic theory of matter, as we have now pictured it, leads us to identify heat-energy in a solid with the energy of motion of the atoms of the body relatively to one another. A body in which all the atoms were at rest relatively to one another would be a body devoid of heat. This conception of the nature of heat leads at once to an absolute zero of tempera ture—a temperature of no heat-motion—which is identical, as will be seen later, with that reached in other ways, namely, about —273° C.
The point of view which has now been gained enables us to interpret most of the thermal properties of solids in terms of atomic theory. Suppose, for instance, that two bodies, both devoid of heat, are placed in contact with one another, and that the surface of the one is then rubbed over that of the other. The atoms of the two surface-layers will exert forces upon one another, so that, when the rubbing takes place, each layer will set the atoms of the other into motion, and the energy put into the act of rubbing will be used in establishing this heat-motion.
In this we see the explanation of the phenomenon of the genera tion of heat by friction. At first the heat-motion will be confined to atoms near the rubbing sur faces of the two bodies, but, as already explained, these will in time set the interior atoms into motion, so that ultimately the heat-motion will become spread throughout the whole mass. Here we have an instance of the conduction of heat ; it does not, however, explain the whole phenomenon of conduction of heat, for other processes also help in the process, especially in substances which are conductors of electricity. When the atoms of a solid are oscillating about their equilibrium positions there is no reason why their mean distance apart should be the same as when they are at rest. This leads to an interpretation of the fact that a change of dimensions usually attends a change in the temperature of a substance. Suppose, for instance, that two atoms, when at rest in equilibrium are at a distance a apart. It is very possible that the repulsive force they exert when at a distance a—e may be greater than the attract ive force they exert when at a distance a—e. If so, their mean distance apart, averaged through a sufficiently long interval of their motion, will be greater than a. A body made up of atoms
of this kind will expand on heating.
As the temperature of a body increases, the average energy of its atoms will increase, so that the range of their excursions from their positions of equilibrium will also increase. At a certain temperature a stage will be reached in which it becomes a fre quent occurrence for an atom to wander so far from its position of equilibrium that it does not return but falls into a new posi tion of equilibrium and oscillates about this. When the body is in this state, the relative positions of the atoms are not per manently fixed, so that the body is no longer of unalterable shape; is has assumed a plastic or molten condition. The electric forces between the wandering atoms now causes them to combine into permanent molecules. The substance attains to a perfectly liquid state as soon as the energy of motion of the molecules is so great that there is constant rearrangement of position among them.
A molecule moving from its original position in a liquid mass will usually fall into a new position in which it will be acted on by forces from a new set of neighbouring molecules. But if a wandering molecule which was originally close to the surface happens to start off in the right direction it may escape from the liquid mass altogether and describe a free path in space until it is checked by meeting a second wandering molecule or other obstacle. The liquid is continually losing mass by the loss of individual molecules in this way, and this explains the process of evaporation. Moreover, the molecules which escape are, on the whole, those with the greatest energy. The average energy of the molecules which remain in the liquid is accordingly lowered by the process. In this we see the explanation of the fall of tempera ture which accompanies evaporation. When a liquid undergoing evaporation is contained in a closed vessel a molecule which has left the liquid will, after a certain number of collisions with other free molecules and with the sides of the vessel, fall back again into the liquid. Thus the process of evaporation is necessarily accompanied by a process of recondensation. When a stage is reached such that the number of molecules lost to the liquid by evaporation is exactly equal to that regained by condensation, we have a liquid in equilibrium with its own vapour. If the whole liquid becomes vaporized before this stage is attained, a state will exist in which the vessel is occupied solely by free molecules, describing paths which are disturbed only by encounters with other free molecules or the sides of the vessel. The whole mass is now in the gaseous state.
At normal temperature and pressure the density of a substance in the gaseous state is of the order of one-thousandth of the density of the same substance in the solid or liquid state. It follows that the average distance apart of the molecules in the gaseous state is roughly ten times as great as in the solid or liquid state, and hence that in the gaseous state the molecules are at distances apart which are large compared with their linear dimensions. (If the molecules of air at normal temperature and pressure were arranged in cubical order, the edge of each cube would be about 3.3 X I cms. ; the average diameter of a mole cule in air is 3.7X cms.) Further important evidence as to the nature of the gaseous state of matter is provided by the experi ments of Joule and Kelvin. These experiments showed that when a gas is allowed to stream out into a vacuum, its change of tem perature is in general very slight. In terms of the molecular theory this indicates that the total energy of the gas is very approximately equal to the sum of the separate energies of its different molecules : the potential energy arising from inter molecular forces between pairs of molecules may be treated as negligible when the matter is in the gaseous state. These two simplifying facts bring the properties of the gaseous state of matter within the range of mathematical treatment. The kinetic theory of gases attempts to account, in terms of the molecular structure of matter, for all the non-chemical and non-electrical properties of gases. The remainder of this article is mainly de voted to a brief statement of the methods and results of the kinetic theory. No attempt will be made to follow the historic order of development, but the main outlines of the present theory will be set out in their most logical form and order.