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KINETIC THEORY OF GASES
61. Molecular constitution of matter. In order to account for some of the simplest facts in nature for example, the fact that two substances often apparently occupy the same space at the same time, as when two gases are crowded together in the same vessel or when sugar is dissolved in water — it is now universally assumed that all substances are composed of very minute particles called molecules. Spaces are supposed to exist between these molecules, so that when one gas enters a vessel which is already full of another gas the molecules of the one scatter themselves about among the molecules of the other. Since molecules cannot be seen with the most powerful microscopes, it is evident that they must be very minute. The number of them contained in a cubic centimeter of air is 27 billion billion (27 x 1018). It would take as many as a thousand molecules laid side by side to make a speck long enough to be seen with the best microscopes.
62. Evidence for molecular motions in gases. Certain very simple observations lead us to the conclusion that the molecules of gases, even in a still room, must be in continual and quite rapid motion. Thus, if a little chlorine, or ammonia, or any gas of powerful odor is introduced into a room, in a very short time it will have become perceptible in all parts of the room. This shows clearly that enough of the molecules of the gas to affect the olfactory nerves must have found their way across the room.
Again, chemists tell us that if two globes, one containing hydrogen and the other carbon dioxide gas, be connected as in Fig. 53, and the stopcock between them opened, after a few hours chemical analysis will show that each of the globes contains the two gases in exactly the same proportions, a result which is at first sight very surprising, since carbon dioxide gas is about twenty-two times as heavy as hydrogen. This mixing of gases in apparent violation of the laws of weight is called diffusion.
We see, then, that such simple facts as the transference of odors and the diffusion of gases furnish very convincing evidence that the molecules of a gas are not at rest but are continually moving about.
FIG. 53. Illustrat
63. Molecular motions and the indefinite ing the diffusion expansibility of a gas. Perhaps the most striking property which we have found gases to possess is the property of indefinite or unlimited expansibility. The existence of this property was demonstrated by the fact that we were able to attain a high degree of exhaustion by means of an air pump. No matter how much air was removed from the bell jar, the remainder at once expanded and filled the entire vessel. The motions of the molecules furnish a thoroughly satisfactory explanation of the phenomenon.
The fact that, however rapidly the piston of the air pump is drawn up, gas always appears to follow it instantly, leads us to the conclusion that the natural velocity possessed by the molecules of gas must be very great.
64. Molecular motions and gas pressures. How are we to account for the fact that gases exert such pressures as they do against the walls of the vessels which contain them? We have found that in an ordinary room the air presses against the walls with a force of 15 pounds to the square
inch. Within an automobile tire this pressure may amount to as much as 100 pounds, and the steam pressure within the boiler of an engine is often as high as 240 pounds per square inch. Yet in all these cases we may be certain that the molecules of the gas are separated from each other by distances which are large in comparison with the diameters of the molecules; for when we reduce steam to water, it shrinks to 1600 of its original volume, and when we reduce air to the liquid form, it shrinks to about of its ordinary volume.
The explanation is at once apparent when we reflect upon the motions of the molecules. For just as a stream of water particles from a hose exerts a continuous force against a wall on which it strikes, so the blows which the innumerable molecules of a gas strike against the walls of the containing vessel must constitute a continuous force tending to push out these walls. In this way we account for the fact that vessels containing only gas do not collapse under the enormous external pressures to which we know them to be subjected. A soap bubble 6 inches in diameter is, at normal atmospheric pressure, under a total crushing force of one ton.
65. Explanation of Boyle's law. It will be remembered that it was discovered in the last chapter that when the density of a gas is doubled, the temperature remaining constant, the pressure is found to double also; when the density was trebled, the pressure was trebled; etc. This, in fact, was the assertion of Boyle's law. Now this is exactly what would be expected if the pressure which a gas exerts against a given surface is due to blows struck by an enormous number of swiftly moving molecules; for doubling the number of molecules in the given space, that is, doubling the density, would simply double the number of blows struck per second against that surface, and hence would double the pressure. The kinetic theory of gases which is here presented accounts in this simple way for Boyle's law.
66. Brownian movements and molecular motions. It has recently been found possible to demonstrate the existence of molecular motions in gases in a very direct and striking way. It is found that very minute oil drops suspended in perfectly stagnant air, instead of being themselves at rest, are ceaselessly dancing about just as though they were endowed with life. In 1913 it was definitely proved that these motions, which are known as the Brownian movements, are the direct result of the bombardment which the droplets receive from the flying molecules of the gas with which they are surrounded; for at a given instant this bombardment is not the same on all sides, and hence the suspended particle, if it is minute enough, is pushed hither and thither according as the bombardment is more intense first in one direction, then in another. There can be no doubt that what the oil drops are here seen to be doing, the molecules themselves are also doing, only in a much more lively way.
67. Molecular velocities. From the known weight of a cubic centimeter of air under normal conditions, and the known force which it exerts per square centimeter (namely, 1033 grams), it is possible to calculate the velocity which its molecules must possess in order that they may produce by their collisions against the walls this amount of force. The result of the calculation gives to the air molecules under normal conditions a velocity of about 445 meters per second, while it assigns to the hydrogen molecules the enormous speed of 1700 meters (a mile) per second. The speed of a projectile is seldom greater than 800 meters (2500 feet) per second. It is easy to see, then, since the molecules of gases are endowed with such speeds, why air, for example, expands instantly into the space left behind by the rising piston of the air pump, and why any gas always fills completely the vessel which contains it (see mercury-diffusion air pump, opposite page 33).
68. Diffusion of gases through porous walls. Strong evidence for the correctness of the above views is furnished by the following experiment:
Let a porous cup of unglazed earthenware be closed with a rubber stopper through which a glass tube passes, as in Fig. 54. Let the tube be dipped into a dish of colored water, and a jar containing hydrogen placed over the porous cup; or let the jar simply be held in the position shown in the figure, and let illuminating gas be passed into it by means of a rubber tube connected with a gas jet. The rapid passage of bubbles out through the water will 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 inside pressure 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. Hence, 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. Hence, 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. When the bell jar 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. 54. Diffusion of hydrogen through porous cup
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, for it is only a matter of time when 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,