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14. A ferry barge with vertical sides has a bottom 40 by 15 ft. When several motor cars were on board, it floated 4 in. deeper. How much did the cars weigh?

15. How much force will it take to sink an oak plank in water if it weighs 25 lb. in air and if its specific gravity is 0.8?

16. An alloy of gold and silver is found to have a specific gravity of 16. Find the percentage of weight of silver in the alloy. The specific gravity of pure gold is 19.32, that of pure silver is 10.5.

17. A rectangular block of cast iron, specific gravity 7.6, is 12 in. long, 8 in. thick, and 9 in. high. (a) Find the weight of water it displaces when completely submerged. (b) Find the weight of the iron while under water.

18. A body weighs 18.4 oz. in air, 13.9 oz. when submerged in water, and 14.4 oz. when submerged in a second liquid. Compute (a) the specific gravity of the substance and (b) the specific gravity of the second liquid.

19. How many pounds of wood (specific gravity = 0.6) must be fastened to 5 lb. of copper (specific gravity = 8.9) in order that the combination may barely float in water?

CHAPTER IV

GASES

The weight of air, 35. The pressure produced by the weight of air, 36. Pressure is exerted in all directions, 37. The molecular theory of gases, 38. The barometer, 39. Types of barometers, 40. The pressure of the atmosphere varies with elevation, 41. Pressure gauges, 42. The buoyancy of air, 43. The specific gravity of gases; relative density, 44. The compressibility of gases: Boyle's law, 45. Simple water pumps, 46. Simple air pumps, 47. The siphon, 48.

35. The weight of air. Often one is surprised when he learns for the first time how much weight air really has. A cubic foot of air weighs about 1.3 ounces, a cubic yard about 2.2 pounds. A classroom 30 by 30 by 12 feet high contains about 880 pounds.

It is very easy to show experimentally that air has weight. If a flask or bottle of moderate size is weighed before and after the air has been pumped out of it, the change in weight can be observed on an ordinary balance; or, by the aid of a compression pump (for example, a bicycle pump), air can be compressed into a flask, and the increase in weight of the flask observed.

36. The pressure produced by the weight of air. The earth is surrounded by an immense ocean of air, the total weight of which is so great that the numbers used to express it are too large to have much meaning. The average pressure on the earth's surface produced by the air is the total weight divided by the area of the earth's surface. It is about 14 or 15 pounds per square inch. The total downward force on the floor of a room 15 feet square is several hundred tons. (Must the floor be made stronger on this account?)

The existence of this downward pressure can be shown in a number of different ways. If a rubber membrane is fastened over the open top of a bell jar and the air is partly removed by a filter pump or an ordinary air pump, the membrane is forced downward into the bell jar (Fig. 39). Or, instead of the membrane, the hand can be placed over the open mouth, and the weight of the air felt. Even after feeling it, it is hard to realize that it is the weight of the air above that produces the force. Such experiments as this are often popularly explained as due

to the "suction" of the air pump. A little thought will convince one that there can be no force of suction, that it is the presence of air, not its absence, which produces the force.

To pump

FIG. 39

The actual pressure of the air is seldom constant at any one place for any considerable number of hours. However, the range is only a few per cent-seldom more than 5 per cent. Hence for rough work the pressure of the atmosphere has been used as a unit, or standard, for measuring pressures.

37. Pressure is exerted in all directions. In the experiment of Fig. 39 why is it that the downward pressure is not shown until air is removed from underneath the

hand? It is because air in the bell jar exerts an upward pressure on the hand. When part of the air is removed and the upward pressure is decreased, then the downward pressure becomes greater than the upward, and the difference is observed. In section 36 a question was left unanswered. Must a floor be made stronger on account of the downward pressure of the air? The answer is No, provided that the air in the room below is at ordinary atmospheric pressure. If the room below should contain a

To pump

W

FIG. 40

partial vacuum, then the floor would probably need reënforcing. The upward pressure of air can be shown by a simple, direct experiment. A cylinder, sometimes called a cymometer, or a sevenin-one apparatus, contains a piston as shown in Fig. 40. Attached to this piston is a heavy weight W. When the air inside is partially removed by an air pump, the pressure of the air outside will force the piston up, lifting the heavy weight.

Another familiar experiment is that performed with a tumbler full of water and a card. The card is placed on the tumbler and held there while the tumbler is quickly inverted. The upward pressure of the air will hold the card in place and prevent the water from spilling.

FIG. 41

The Magdeburg hemispheres were invented by Otto von Guericke, about 1654, to show the pressure of air. In Fig. 41 is shown a small modern form for classroom use. The halves of the sphere have their joining edges ground true, so that when covered with vaseline or some other lubricant they form a joint which is nearly air-tight. When the hemispheres are placed together and the air is partly removed, they are held together by a considerable force, usually over a hundred pounds. This force is the same, no matter what the position of the hemispheres may be; hence they can be used to demonstrate that air pressure acts in every direction.

38. The molecular theory of gases. It is now quite well established that ordinary matter is not a uniform continuous mass but is made up of very minute grains called molecules. When the molecules are close together, they exert forces of attraction on each other. In a solid these forces so bind the molecules that they have little freedom of motion, but in a liquid they are not held together in so rigid a way. The forces acting on the molecules are sufficient to keep them from moving apart, so that the volume occupied by the liquid is constant; but the forces are not sufficient to prevent the liquid from changing its shape, or, as is commonly said, from flowing.

In a gas the condition is very different. A gas does not tend to keep a constant volume, but has a tendency to expand. The elastic action of bicycle and automobile tires depends on this fact. Glass bottles tightly sealed may burst when placed in a vacuum. The pressure exerted by steam in boilers or by the ignited gases in gas engines are other examples of this tendency of gases to expand. But why does a gas tend to expand? This is easily explained if we assume that the molecules are relatively far apart and moving continually with high speeds. Under these circumstances the restraining influence of their attraction is too small to overcome the effect of their high speeds, so that they tend to move apart, to fly off in every direction. The molecules in a solid are also supposed to be in rapid motion, but they are so close together that the motion is probably an oscillatory one rather than one which takes the molecule from one part of the body to another, as in the case of a gas. Some idea of the relatively greater distances apart of the molecules of a gas, as compared with those of a solid or liquid, is obtained when we note the difference in the compressibility of gases as compared with liquids or solids. Gases under great pressure are reduced to comparatively small volumes. Under a pressure of 3000 atmospheres the volume of air is reduced to about 1/700 of its original value. Steam when changed back into water occupies only about 1/1600 of its volume. It is believed that the change in volume on compression is due not to changes in the size of the molecules but to changes in the spaces between them.

The kinetic theory of gases gives a simple picture of the way in which a gas exerts pressure when confined in some vessel. Imagine a board struck by a large number of balls, one after another. Practically there would be a constant force acting on the board. A continuous stream of sand blown against a surface exerts just such a pressure. In a gas there are enormous numbers of molecules striking against the walls of the containing vessel, each molecule giving a small impulse. While each of the molecules has a very small mass, yet there are so many of them, and they move with such high speeds, that forces of considerable magnitude are produced. The theory of this phenomenon has been developed to such an extent that it is now possible, if one knows the density of the gas and the pressure exerted by it, to compute the probable average speed of the molecules. This speed at ordinary temperatures is always high; for example, air molecules have an average speed of over 1200 feet per second.

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