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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.
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 a few drops of ammonia 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 be introduced into the bottom of the jar through a thistle tube (Fig. 55). In a few minutes the line of separation between the acidulated water and the blue solution will be fairly sharp; but 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.
FIG. 55. Diffusion of liquids
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 apparent.
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 temperature has been shown only for these two metals, but at higher temperatures (for example, 500° C.) all of the metals show the same characteristics to quite a surprising degree.
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 § 112), 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, while 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 necessitated 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.
QUESTIONS AND PROBLEMS
1. If a vessel with a small leak is filled with hydrogen at a pressure of 2 atmospheres, the pressure falls to 1 atmosphere about four times as fast as when the same experiment is tried with air. Can you see a reason for this?
2. What is the density of the air within an automobile tire that is inflated to a pressure of 80 lb. per square inch? (1 atmosphere = 14.7 lb. per sq. in.)
3. 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?
4. If an open vessel contains 250 g. of air when the barometric height is 750 mm., what weight will the same vessel contain at the same temperature when the barometric height is 740 mm.?
5. Find the pressure to which the diver was subjected who descended to a depth of 304 ft. Find the density of the air in his suit, the density at the surface being .00128 g. per cubic centimeter and the temperature being assumed to remain constant. Take the pressure at the surface as 30 in.
6. A bubble of air which escaped from this diver's suit would increase to how many times its volume on reaching the surface?
7. Salt is heavier than water. Why does not all the salt in a mixture of salt and water settle to the bottom?
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 g. 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 one gram of mass.
Unfortunately, in ordinary conversation we often fail altogether to distinguish between the idea of mass and the idea of force, and 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, however, wholly distinct is evident from the consideration that the amount of matter in a body is always the same, no matter where the body is in the universe, while 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 such sensations as those described in the
preceding paragraph very untrustworthy guides. An accurate method, however, of comparing these pulls is that furnished by the stretch produced in a spiral spring. Thus, the pull of the earth upon a gram of mass at its surface will stretch a given spring a given distance, ab (Fig. 56); the pull of the earth upon 2 grams of mass is found to stretch the spring a larger distance, ac; upon 3 grams, a still larger distance, ad; etc. In order to graduate a spring balance (Fig. 57) so that it will thenceforth measure the values of any pulls exerted upon it, no matter how these pulls may arise, we have only to place a fixed surface behind the pointer and make lines upon it corresponding to the points to which it is stretched by the pull of the earth upon different masses. Thus, if a man stretch the spring so that the pointer is opposite the mark corresponding to the pull of the earth
FIG. 56. Method of measuring forces
upon 2 grams of mass, we say that he exerts 2 grams of force; if he stretch it the distance corresponding to the pull of the earth upon 3 grams of mass, he exerts 3 grams of force; etc. The spring balance thus becomes an instrument for measuring forces.
FIG. 57. The
75. The gram of force varies slightly in different localities. With the spring balance it is easy to verify the statement made above, that the force of the earth's pull decreases as we recede spring balance from the earth's surface; for upon a high mountain the stretch produced by a given mass is indeed found to be slightly less than at sea level. Furthermore, if the balance is simply carried from point to point over the earth's surface, the stretch is still found to vary slightly. For example, at Chicago it is about one part in 1000 less than it