show that the gaseous pressure inside the cup is rapidly increasing. Now let the bell jar be lifted so that the hydrogen is removed from the outside. Water will at once begin to rise in the tube, showing that the pressure within the porous cup is now rapidly decreasing. The explanation is as follows: We have learned that the molecules of hydrogen have about four times the velocity of the molecules of air. Therefore, if there are as many hydrogen molecules per cubic centimeter outside the cup as there are air molecules per cubic centimeter inside, the hydrogen molecules will strike the outside of the wall four times as frequently as the air molecules will strike the inside. Therefore, in a given time the number of hydrogen molecules which pass into the interior of the cup through the little holes in the porous material is four times as great as the number of air particles which pass out; hence the pressure within increases. is removed, the hydrogen which has passed inside begins to pass out faster than the outside air passes in, and hence the inside pressure is diminished. FIG. 52. Diffusion of hydrogen through a porous cup When the bell jar MOLECULAR MOTIONS IN LIQUIDS 69. Molecular motions in liquids and evaporation. Evidence that the molecules of liquids as well as those of gases are in a state of perpetual motion is found, first, in the familiar facts of evaporation. We know that the molecules of a liquid in an open vessel are continually passing off into the space above, since it is only a matter of time until the liquid completely disappears and the vessel becomes dry. Now it is hard to imagine a way in which the molecules of a liquid thus pass out of the liquid into the space above, unless these molecules, while in the liquid condition, are in motion. As soon, however, as such a motion is assumed, the facts of evaporation become perfectly intelligible. For it is to be expected that in the jostlings and collisions of rapidly moving liquid molecules an occasional molecule will acquire a velocity much greater than the average. This molecule may then, because of the unusual speed of its motion, break away from the attraction of its neighbors and fly off into the space above. This is, indeed, the mechanism by which we now believe that the process of evaporation goes on from the surface of any liquid. 70. Molecular motions and the diffusion of liquids. One of the most convincing arguments for the motions of molecules in gases was found in the fact of diffusion. But precisely the same sort of phenomena are observable in liquids. FIG. 53. Diffusion of liquids Let a few lumps of blue litmus be pulverized and dissolved in water. Let a tall glass cylinder be half filled with this water and let a few drops of ammonia be added. Let the remainder of the litmus solution be turned red by the addition of one or two cubic centimeters of nitric acid. Then let this acidulated water, slightly cooled, be introduced into the bottom of the jar through a thistle tube (Fig. 53). In the course of a few hours, even though the jar is kept perfectly quiet, the red color will be found to have spread considerably toward the top, showing that the acid molecules have gradually found their way up. Certainly, then, the molecules of a liquid must be endowed with the power of independent motion. Indeed, every one of the arguments for molecular motions in gases applies with equal force to liquids. Even the Brownian movements can be seen in liquids, though they are here so small that highpower microscopes must be used to make them visible. If a small amount of insoluble carmine is ground into a few drops of water, these movements may be seen with a microscope magnifying four hundred or more diameters. MOLECULAR MOTIONS IN SOLIDS 71. Molecular motions and the diffusion of solids. It has recently been demonstrated that if a layer of lead is placed upon a layer of gold, molecules of gold may in time be detected throughout the whole mass of the lead. This diffusion of solids into one another at ordinary temperatures has been shown only for these two metals, but at higher temperatures (for example, 500° C.) all the metals show this same characteristic to a surprising degree. We know that molecules break away from the surface of certain solids; for example, gum camphor and naphthalene, as their odor may be detected at a considerable distance. The evidence for the existence of molecular motions in solids is, then, no less strong than in the case of liquids. 72. The three states of matter. Although it has been shown that, in accordance with current belief, the molecules of all substances are in very rapid motion, yet differences exist in the kind of motion which the molecules in the three states possess. Thus, in the solid state it is probable that the molecules oscillate with great rapidity about certain fixed points, always being held by the attractions of their neighbors — that is, by the cohesive forces (see § 113) — in very nearly the same positions with reference to other molecules in the body. In rare instances, however, as the facts of diffusion show, a molecule breaks away from its constraints. In liquids, on the other hand, although the molecules are, in general, as close together as in solids, they slip about with perfect ease over one another and thus have no fixed positions. This assumption is justified by the fact that liquids adjust themselves readily to the shape of the containing vessel. In gases the molecules are comparatively far apart, as is evident from the fact that a cubic centimeter of water occupies about 1600 cubic centimeters when it is transformed into steam; and, furthermore, they exert almost no cohesive force upon one another, as is shown by the indefinite expansibility of gases. SUMMARY. The theory of the molecular constitution of matter is now universally accepted. Evidence of molecular motion (the kinetic theory of matter) is found in diffusion, in indefinite expansibility of gases, in Brownian movements, and in the evaporation of liquids and solids. Boyle's law is explained by the assumption that at a given temperature the pressure is determined by the number of molecular blows per second on unit area. The rate of diffusion of a light gas is greater than that of a heavy one because of the greater velocity of its less massive molecules. QUESTIONS AND PROBLEMS * 1. Account for the fact that if ammonia water is spilled in a room, the odor of the ammonia gas may be quickly detected in all parts of the room. 2. Why does not the tendency to unlimited expansion cause the atmosphere to leave the earth? 3. Why does a confined body of gas exert pressure inversely proportional to its volume? 4. A lump of copper sulphate placed at the bottom of a graduate filled with water will dissolve and very slowly pass upward, although a copper-sulphate molecule is many times heavier than a water molecule. Explain. 5. What is the density of the air within an automobile tire that is inflated to a gauge pressure of 30 lb. per square inch? (Take 1 atmosphere = 15 lb. per square inch.) 6. A liter of air at a pressure of 76 cm. is compressed so as to occupy 400 cc. What is the pressure against the walls of the containing vessel? 7. Salt is heavier than water. Why does not all the salt in a mixture of salt and water settle to the bottom? * Supplementary questions and problems for Chapter IV are given in the Appendix. CHAPTER V. FORCE AND MOTION DEFINITION AND MEASUREMENT OF FORCE 73. Distinction between a gram of mass and a gram of force. If a gram of mass is held in the outstretched hand, a downward pull upon the hand is felt. If the mass is 50,000 grams instead of 1, this pull is so great that the hand cannot be held in place. The cause of this pull we assume to be an attractive force which the earth exerts on the matter held in the hand, and we define the gram of force as the amount of the earth's pull at its surface upon 1 gram of mass. Unfortunately, in ordinary conversation we often fail altogether to distinguish between the idea of mass and that of force, and we use the same word "gram" to mean sometimes a certain amount of matter and at other times the pull of the earth upon this amount of matter. That the two ideas are wholly distinct, however, is evident from the consideration that the amount of matter in a body is always the same, wherever the body is in the universe, whereas the pull of the earth upon that amount of matter decreases as we recede from the earth's surface. It will help to avoid confusion if we reserve the simple term "gram" to denote exclusively an amount of matter (that is, a mass) and use the full expression 'gram of force" wherever we have in mind the pull of the earth upon this mass. 74. Method of measuring forces. When we wish to compare accurately the pulls exerted by the earth upon different masses, we find the muscular sense a very untrustworthy guide. An accurate method, however, of comparing these pulls is that furnished by the stretch produced in a spiral |