Page:Elementary Text-book of Physics (Anthony, 1897).djvu/246

333 that any one will miss the target entirely; the vast majority of the shots will meet the target, and their distances from the centre will lie around a certain average distance. Similarly, it is extremely improbable that any molecule of a gas will have a velocity far exceeding the average; the great majority of them will have velocities which lie around a certain mean velocity. The law of distribution of velocities among molecules of liquids and solids is not known, but it probably possesses the essential characteristics of the law for gases.

When a gas is heated, all but a very small part of the heat which enters it is uoed in increasing the kinetic energy of the molecules; this is not true for solids and liquids, because, when they are heated, work is done against their molecular forces which does not appear as kinetic energy. The kinetic energy of the molecule is the sum of the kinetic energy due to the motion of its centre of mass or to its translation, and of the kinetic energy due to its motion relative to its centre of mass. This latter energy may be thought of as due either to rotation about the centre of mass or to the vibrations of the atoms constituting the molecule. We will subsequently prove that the temperature of a gas is proportional to the kinetic energy of its molecules. It is therefore natural to assume that the measure of temperature is some part of the kinetic energy of the molecule. The most consistent explanation of all the effects of heat can be reached by supposing that the energy of atomic vibration or of molecular rotation is directly proportional to the temperature measured on the absolute scale (§ 212). The total kinetic energy of the molecules of a body measures the heat in the body.

222. Kinetic Theory of Gases.—The foundation of the theory of matter now under discussion is the kinetic theory of gases. In this theory a perfect gas consists of an assemblage of free, perfectly elastic molecules in constant motion. Each molecule moves in a straight line with a constant velocity, until it encounters some other molecule, or the side of the vessel. The impacts of the molecules