in alcohol, and to a depth of 18 cm. in brine. What is the density of the alcohol and of the brine?

8. A gla.s.s stopper weighs in the air 25 g., in water 15 g., in oil 18 g.

Find the density and volume of the stopper. Find the density of the oil.

9. What would a cubic foot of wood weigh if the specific gravity were 0.5.?

10. The specific gravity of aluminum is 2.7. Find the weight of a cubic foot of it.

11. A block of wood weighs 40 g. A piece of lead appears to weigh 70 g.

in water. Both together appear to weigh 60 g. in water. Find the density of the wood.

12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt water. Find the density of the salt water.

13. Will iron sink in mercury? Why?

14. A submarine boat weighing 200 tons must have what volume in order to float?

15. Find the weight of 2 cu. ft. of copper from its density.

16. What is the weight in water of a ma.s.s whose specific gravity is 3.3 and whose weight is 50 kg.?

17. A block of granite weighs 1656 lbs.; its volume is 10 cu. ft., what is its density?

18. If the specific gravity of hard coal is 1.75 how would you determine how many tons of coal a bin would hold?

19. A hollow copper ball weighs 2 kg. What must be its volume to enable it to just float in water?

20. A ma.s.s having a volume of 100 ccm. and a specific gravity of 2.67 is fastened to 200 ccm. of wood, specific gravity 0.55. What will the combination weigh in water?

21. A block weighing 4 oz. in air is tied to a sinker which appears to weigh 14 oz. in water. Both together appear to weigh 6 oz. in water.

What is the specific gravity of the block?

CHAPTER IV

MECHANICS OF GASES

(1) WEIGHT AND PRESSURE OF THE AIR

=51. Weight of Air.=--It is said that savages are unaware of the presence of _air_. They feel the _wind_ and hear and see it moving the leaves and branches of the trees, but of air itself they have little conception.

To ordinary observers, it seems to have no weight, and to offer little resistance to bodies pa.s.sing through it. That it has weight may be readily shown as follows: (See Fig. 29.) If a hollow metal sphere, or a gla.s.s flask, provided with tube and stopc.o.c.k, be weighed when the stopc.o.c.k is open, and then after the air has been exhausted from it by an air pump, a definite loss of weight is noticeable.

[Ill.u.s.tration: FIG. 29.--Proof that air has weight.]

If the volume of the sphere is known and it is well exhausted of air, a fair approximation of the weight of air may be obtained. Under "_standard conditions_," which means _at the freezing temperature_ and a barometric pressure of 76 cm., a liter of air weighs 1.293 g. while 12 cu. ft. of air weigh approximately 1 lb.

=52. Pressure of Air.=--Since air has weight it may be supposed to exert pressure like a liquid. That it does so may be shown in a variety of ways.

If a plunger fitting tightly in a gla.s.s cylinder be drawn upward, while the lower end of the tube is under water, the water will rise in the tube (Fig. 30). The common explanation of this is that the water rises because of "suction." The philosophers of the ancient Greeks explained it by saying that "nature abhors a vacuum," and therefore the water rises. Neither explanation is correct. It was found in 1640 that water would not rise in a pump more than 32 ft. despite the fact that a vacuum was maintained above the water. Galileo was applied to for an explanation. He said, "evidently nature's horror of a vacuum does not extend above 32 ft." Galileo began tests upon "the power of a vacuum"

but dying left his pupil Torricelli to continue the experiment.

Torricelli reasoned that if water would rise 32 ft., then mercury, which is 13.6 times as dense as water, would rise about 1/13 as much. To test this, he performed the following famous experiment.

[Ill.u.s.tration: FIG. 30.--Air pressure forces the liquid up the tube.]

=53. Torricelli's Experiment (1643).=--Take a gla.s.s tube about 3 ft.

long, sealed at one end, and fill it with mercury. Close the end with the finger and invert, placing the end closed by the finger under mercury in a dish (Fig. 31). Remove the finger and the mercury sinks until the top of the mercury is about 30 in. above the level of the mercury in the dish. Torricelli concluded that the rise of liquids in exhausted tubes is due to the pressure of the atmosphere acting on the surface of the mercury in the dish.

To test this, place the tube with its mercury upon the plate of an air pump and place a tubulated bell jar over the apparatus so that the tube projects through a tightly fitting stopper. (See Fig. 32.) If the air pressure is the cause of the rise of mercury in the tube, on removing the air from the bell jar the mercury should fall in the tube. This is seen to happen as soon as the pump is started. It is difficult to remove all the air from the receiver so the mercury rarely falls to the same level in the tube as in the dish. A small tube containing mercury is often attached to air pumps to indicate the degree of exhaustion. Such tubes are called _manometers_.

[Ill.u.s.tration: FIG. 31.--Torricelli's experiment.]

[Ill.u.s.tration: FIG. 32.--The mercury drops as the air is removed.]

=54. The Amount of Atmospheric Pressure.=--Torricelli's experiment enables us to compute readily the pressure of the atmosphere, since it is the atmospheric pressure that balances the column of mercury in the tube. By Pascal's Law, the pressure of the atmosphere on the surface of the mercury in the dish is transmitted as an exactly equal pressure on the mercury column in the tube at the same level as the mercury outside.

This pressure, due to the air, must balance the weight of the column of mercury in the tube. It therefore equals the weight of the column of mercury of unit cross-section. The average height of the column of mercury at sea-level is 76 cm. Since the weight of 1 cc. of mercury is 13.6 grams, the pressure inside the tube at the level of the surface of the mercury in the dish is equal to 1 76 13.6 or 1033.6 g. per square centimeter. Therefore the _atmospheric pressure_ on the surface of the mercury in the dish is 1033.6 g. per square centimeter, approximately _1 kg. per square centimeter or 15 lbs. per square inch_.

=55. Pascal's Experiment.=--Pascal tested in another way the action of atmospheric pressure upon the column of mercury by requesting his brother-in-law, Perrier, who lived near a mountain, to try the experiment on its top. Perrier found that on ascending 1000 meters the mercury fell 8 cm. in the tube. Travelers, surveyors, and aviators frequently determine the alt.i.tude above sea-level by reading the barometer, an ascent of 11 meters giving a fall of about 1 mm. in the mercury column, or 0.1 in. for every 90 ft. of ascent.

[Ill.u.s.tration: FIG. 33.--A standard barometer.]

_56. The Barometer._--The modern barometer (Fig. 33), consists of a Torricellian tube properly mounted. Reading a barometer consists in accurately reading the height of the mercury column. This height varies from 75 to 76.5 cm. or 29 to 30 in. in localities not far from the sea-level. The atmospheric pressure varies because of disturbances in the atmosphere. It is found that these disturbances of the atmosphere pa.s.s across the country from west to east in a somewhat regular manner, hence a series of readings of the barometer may give reliable information of the movement of these disturbances and so a.s.sist in forecasting the weather. The weather Bureau has observations taken at the same moment at various stations over the country. These observations form the basis for the daily forecast of the weather.

[Ill.u.s.tration: FIG. 34.--An aneroid barometer]

Another form of barometer in common use is the _Aneroid Barometer_ (Fig. 34). Its essential parts are a cylindrical air-tight box with an elastic corrugated cover. Inside the box is a partial vacuum.

This makes the cover very sensitive to slight changes of pressure.

The motion of the top of the box is conveyed by a series of levers to an indicating hand which moves over a dial. This barometer can be made so sensitive as to indicate the change of air pressure from a table top to the floor. It is much used by travelers, explorers, surveying parties and aviators, since the mercurial barometer is inconvenient to carry.

Important Topics

1. _Weight_ and _Pressure_ of air in English and metric units. How shown. Evidences.

2. Work of Galileo, Torricelli, and Perrier.

3. Barometer: construction, action, mercurial, aneroid.

[Ill.u.s.tration: FIG. 35.--Air pressure keeps the water In the tumbler.]

[Ill.u.s.tration: FIG. 36.--Cross-section of a modern drinking fountain.]

Exercises