The Kinetic Theory of Gases

According to the kinetic theory, molecules in a gas fly about in all directions, frequently colliding with each other and with their containing walls. Conceptually simple though it may be, this picture is not something suggested directly by any of our experience with matter in bulk. However, it does account at once for the tendency of a gas to expand without limit. Daniel Bernoulli, a Swiss mathematician, worked out the consequences of the kinetic theory in 1738. His work apparently had no impact whatever on the course of science, being noticed only after James Joule in England, and two German physicists, August Kronig and Rudolph Clausius, had developed the same theory independently in the 1840's and 1850s. In the intervening century Charles and Gay-Lussac had clarified the macroscopic laws of gas behavior, the gas thermometer had been perfected, chemical evidence for the existence of atoms and molecules had become overwhelmingly convincing, the steam engine was utilizing heat energy for mechanical work, thermo-dynamics was well launched as a quantitative theory, caloric had been abandoned, and the general law of energy conservation had been formulated. By the time these strides in the science of temperature and heal had caught up with the forward leap of Bernoulli, he was long dead and this part of his work forgotten. Yet, when the time was ripe the same ideas were regenerated by several scientists in different places at nearly the same time in a more typical pattern of scientific development.

It might seem surprising that any mathematical derivation based on the kinetic theory could be simple. At the submicroscopic level, a gas appears to be an incalculable chaos of flying molecules, no two moving in exactly the same way, and none moving far between vigorous collisions with its neighbors. Yet from this chaos flows a beautifully simple derivation of the ideal-gas law which illuminates the content of the kinetic theory and, even more important, which establishes the connection between temperature and molecular energy.

Force and pressure

A liquid presses on the sides and on the bottom of the container in which it rests. It exerts a force both sideways and downwards'. The sides of a cardboard carton of milk will often curve outwards, and this is caused by the sideways force exerted by the milk. Wooden barrels and water tanks are usually strengthened with metal bands: they are reinforced to resist the sideways force exerted by the liquid in these containers.

A liquid also exerts a force upwards on any object which is placed in it. If you push a rubber ball or a plastic boat under the surface of the water in a container, you will feel the upward force against the bottom of these objects. A liquid exerts a force in every direction.

When a liquid presses against the container in which it rests, we say that it exerts a force. Force, however, is not the same as pressure.

A block of metal of mass 10 kg resting on a flat surface such as a table exerts a downward force of about 93 Newton. The downward force exerted by an object is the same as its weight and we measure weight in force units called Newton. But the object does not exert a pressure of 98 N. The pressure which is exerted depends on the area of contact between the object and the table. Pressure is measured by the force divided by the area of the surface on which it acts. Let us suppose that the area of one of the surfaces of an oblong block of steel weighing 200 N is 200 cm (0 • 02 m). If the object is placed on a table-top so that this surface is in contact with the Surface of the table, the pressure between the object and the table will be 200 N/200 cm², which is 10,000 N/m². If the other surface of the object measures 100 cm² (0-01 m²), and if this makes contact with the table-top, the pressure between the object and the table will be 200 N/100 cm², which equals 20,000 N/m. The force exerted by the object is the same in each case, but the pressure varies. Less pressure is exerted when the area of contact is large, and more pressure is exerted when the area of contact is small.