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Let mercury be poured into a bent glass tube until it stands at the same level in the closed arm AC as in the open arm BD (Fig. 35). There is now confined in AC a certain volume of air under the pressure of one atmosphere. Call this pressure P1. Let the length AC be measured and called V1. Then let mercury be poured into the long arm until the level in this arm is as many centimeters above the level in the short arm as there are centimeters in the barometer height. The confined air is now under a pressure of two atmospheres. Call it P. Let the new volume A1C(= V2) be measured. It will be found to be just half its former value.
Hence we learn that doubling the pressure exerted upon a body of gas halves its volume. If we had tripled the pressure, we should have found the volume reduced to one third its initial value, etc. That is, the pressure which a given quantity of gas at constant temperature exerts against the walls of the containing vessel is inversely proportional to the volume occupied. of demonstrating This is algebraically stated thus:
FIG. 35. Method
This is Boyle's law. It may also be stated in slightly different form. Doubling, tripling, or quadrupling the pressure must double, triple, or quadruple the density, since the volume is made only one half, one third, or one fourth as much, while the mass remains unchanged. Hence the pressure which a gas exerts is directly proportional to its density, or, algebraically,
48. Extent and character of the earth's atmosphere. From the facts of compressibility and expansibility of air we may * A laboratory experiment on Boyle's law should follow this discussion. See, for example, Experiment 9 of the authors' Manual.
know that the air, unlike the sea, must become less and less dense as we ascend from the bottom toward the top. Thus, at the top of Mont Blanc, an altitude of about three miles, where the barometer height is but 38 centimeters, or one half of its value at sea level, the density also must, by Boyle's law, be just one half as much as at sea level.
FIG. 36. Extent and character of atmosphere
No one has ever ascended higher than 7 miles, which was approximately the height attained in 1862 by the two daring English aëronauts Glaisher and Coxwell. At this altitude the barometric height is but about 7 inches, and the temperature about 60° F. Both aëronauts lost the use of their limbs, and Mr. Glaisher became unconscious. Mr. Coxwell barely succeeded in grasping with his teeth the rope which opened a valve and caused the balloon to descend. Again, on July 31, 1901, the French aëronaut M. Berson rose without injury to
a height of about 7 miles (35,420 feet), his success being due to the artificial inhalation of oxygen. The American aviator Lieutenant John A. Macready of the United States Army, on September 28, 1921, ascended in an airplane to a height of 34,563 feet. He found the temperature - 58° F.
By sending up self-registering thermometers and barometers in balloons which burst at great altitudes, the instruments being protected by parachutes from the dangers of rapid fall, the atmosphere has been explored to a height of 35,080 meters (21.8 miles), this being the height attained on December 7, 1911, by a little balloon which was sent up at Pavia, Italy. These extreme heights are calculated from the indications of the self-registering barometers.
At a height of 35 miles the density of the atmosphere is estimated to be but 30000 of its value at sea level. By calculating how far below the horizon the sun must be when the last traces of color disappear from the sky, we find that at a height as great as 45 miles there must be air enough to reflect some light. How far beyond this an extremely rarified atmosphere may extend, no one knows. It has been estimated at all the way from 100 to 500 miles. These estimates are based on observations of the height at which meteors first become visible, on the height of the aurora borealis, and on the darkening of the surface of the moon just before it is eclipsed by the shadow of the solid earth.
QUESTIONS AND PROBLEMS
1. The deepest sounding in the ocean is about 6 mi. Find the pressure in tons per square inch at this depth. (Specific gravity of ocean water = 1.026.) Will a pebble thrown overboard reach the bottom? Explain.
2. What sort of a change in volume do the bubbles of air which escape from a diver's suit experience as they ascend to the surface?
3. With the aid of the experiment in which the rubber dam was burst under the exhausted receiver of an air pump explain why high
mountain climbing often causes pain and bleeding in the ears and nose. Why does deep diving produce similar effects?
4. Blow as hard as possible into the tube of the bottle shown in Fig. 37. Then withdraw the mouth and explain all of the effects observed.
5. If a bottle or cylinder is filled with water and inverted in a dish of water, with its mouth beneath the surface (see Fig. 38), the water will not run out. Why?
6. If a bent rubber tube is inserted beneath the cylinder and air blown in at o (Fig. 38), it will rise to the top and displace the water. This is the method regularly used in collecting gases. Explain what forces the gas up into it, and what causes the water to descend in the tube as the gas rises.
7. Why must the bung be removed from a cider barrel in order to secure a proper flow from the faucet?
8. When a bottle full of water is inverted, the water will FIG. 37 gurgle out instead of issuing in a steady stream. Why?
9. If 100 cu. ft. of hydrogen gas at normal pressure are forced into a steel tank having a capacity of 5 cu. ft., what is the gas pressure in pounds per square inch?
10. An automobile tire having a capacity of 1500 cu. in. is inflated to a pressure of 90 pounds per square inch. What is the density of the air within the tire? To what volume would the air
expand if there should be a "blow-out"?
11. Under ordinary conditions a gram of air occupies about 800 cc. Find what volume a gram will occupy at the top of Mont Blanc (altitude 15,781 ft.), where the barometer indicates that the pressure is only about one half what it is at sea level.
12. The mean density of the air at sea level is about .0012. What is its density at the top of Mont Blanc? What fractional part of the earth's atmosphere has one left beneath him when he ascends to the top of this mountain? 13. If Glaisher and Coxwell rose in their balloon until the barometric height was only 18 cm., how many inhalations were they obliged to make in order to obtain the same amount of air which they could obtain at the surface in one inhalation?
14. 1 cc. of air at the earth's surface weighs .00129 g. If this were the density all the way up, to what height would the atmosphere extend?
49. The siphon. Let a rubber or glass tube be filled with water and then placed in the position shown in Fig. 39. Water will be found to flow through the tube from vessel A into vessel B. If then B be raised until the water in it is at a higher level than that in A, the direction of flow will be reversed. This instrument, which is called the siphon, is very useful for removing liquids from vessels which cannot be overturned, or for drawing off the upper layers of a liquid without disturbing the lower layers. Many commercial applications of it are found in various siphon flushing systems.
FIG. 39. The siphon
The explanation of the siphon's action is readily seen from Fig. 39. Since the tube acb is full of water, water must evidently flow through it if the force which pushes it one way is greater than that which pushes it the other way. Now the upward pressure at a is equal to atmospheric pressure minus the downward pressure due to the water column ad, while the upward pressure at b is the atmospheric pressure minus the downward pressure due to the water column be.
Hence the pressure at a exceeds the pressure at b by the pressure due to the water column fb. The siphon will evidently cease to act when the water is at the same level in the two vessels, since then fb = 0 and the forces acting at the two ends of the tube are therefore equal and opposite. It will also cease to act when the bend c is more than 34 feet above the surface of the water in A, since then a vacuum will form at the top, atmospheric pressure being unable to raise water to a height greater than this in either tube.
Would a siphon flow in a vacuum?
FIG. 40. Intermittent siphon