Physics Part 12

1. Do you think Archimedes' Principle applies to the air? Does Pascal's Law? Why?

2. Find the downward pressure of the mercury in a barometer tube if the cross-section is 1 sq. cm. and the height 75 cm. at the level of the mercury surface in contact with the air. (The density of mercury is 13.6 grams per cc.)

3. What is the weight of the air in a room if it is 10 8 4 meters?

4. What weight of air is in a room 10 15 10 ft.?

5. When smoke rises in a straight line from chimneys, is it an indication of a high or low barometric pressure? Why?

6. Why does a tumbler filled with water and inverted in a dish with its rim under water remain full?

7. If the barometer tube is inclined the mercury remains at the same horizontal level. How can this be explained?

8. When the mercurial barometer stands at 76 cm., how high would a water barometer stand? Explain.

9. Explain why it is possible for one to suck soda water through a tube?

10. Fill a tumbler with water. Place a sheet of paper over the top and invert. The paper clings to the tumbler and prevents the water from escaping. Explain. (See Fig. 35.)

11. Why must a kerosene oil can have two openings in order to allow the oil to flow freely?

12. Explain the action of the modern drinking fountain (Fig. 36).

(2) COMPRESSIBILITY AND EXPANSIBILITY OF THE AIR

=57. Effect of Pressure on Liquids and Gases.=--Both cla.s.ses of fluids, liquids and gases, have many characteristics in common. Both are composed of molecules that move freely; hence both _flow_. At any point within a fluid the _pressure is the same in all directions_. Archimedes'

Principle applies, therefore, to both liquids and gases.

We now come to an important _difference_ between liquids and gases.

_Liquids_ are _practically incompressible_. "So much so, that if water is subjected to a pressure of 3000 kg. per sq. cm., its volume is reduced only about one-tenth." Gases show a very different behavior from liquids on being subjected to pressure. They may readily be compressed to a small fraction of their volume as is noticed on inflating a pneumatic tire. A gas has also the _ability to spring back_ to a larger volume as soon as the pressure is released, as when a cork is driven from a pop gun. Not only is compressed air able to expand, but air under ordinary conditions will expand if it is released in a s.p.a.ce where the pressure is less.

Hollow bodies, animals and plants, are not crushed by atmospheric pressure, because the air and gases contained within exert as much force outward as the air exerts inward.

=58. Boyle's Law.=--The relation between the volume and pressure of a gas was first investigated by Robert Boyle in the seventeenth century.

The experiment by which he first discovered the law or the relation between the volume and the pressure of a gas is briefly described as follows:

[Ill.u.s.tration: FIG. 37 _a_.

FIG. 37 _b_.

FIGS. 37 _a_ AND 37 _b_.--Boyle's law apparatus.]

A gla.s.s tube is bent in the form of the capital letter J, the short arm being closed. A little mercury is poured in to cover the bend.

(See Fig. 37 _a_.) Since the mercury is at the _same level in both arms_, the pressure in (_A_) is the same as in (_B_). Mercury is now poured into (_A_) until it stands in the long tube at a height above that in (B) which is equal to the height of the mercury column of the barometer. (See Fig. 37 _b_.) The air in (_BC_) is now under a pressure of two atmospheres (one atmosphere is due to the mercury column). On measurement the air in (_BC_) will be found to have just one-half of its original volume.

Thus doubling the pressure to which a gas is subjected reduces its volume to one-half. Tripling the pressure, reduces the volume to one-third and so on.

Careful experiments reveal the following law: _The volume of a given ma.s.s of gas at constant temperature is inversely proportional to the pressure to which it is subjected_.

This law is often expressed mathematically. _P/P' = V'/V_, or _PV = P'V'_. Since doubling the pressure reduces the volume one-half, it doubles the density. Tripling the pressure triples the density. We therefore have _P/P' = D/D'_ or the density of a gas directly proportional to its pressure.

[Ill.u.s.tration: FIG. 38.--Height and density of the air.]

=59. Height of the Atmosphere.=--From its properties of _compression_ and _expansion_, the air varies in density and pressure as one ascends in it. At a height of 3 miles the pressure is reduced to about one-half.

This is an indication that one-half of the air is below this level.

Balloonists have gone to a height of 7 miles, Glaser and c.o.xwell in England in 1862 and Berson in France in 1901. The atmosphere has been explored to a height of 30,500 meters (18.95 miles) by sending up self-registering barometers in small balloons which burst at great alt.i.tudes. A parachute protects the instruments from breakage from too rapid fall. This height of 30,500 meters was reached by a balloon sent up by William R. Blair, at Huron, South Dakota, September 1, 1910.

At a height of 35 miles, the density is estimated at 1/30,000 of its value at sea-level. (See Fig. 38.) It is believed that some rarefied air exists for a considerable distance above this point, some estimates placing the extent at 100 miles, and others from 200 to 500 miles.

Evidences of some air at such heights are shown by: (a) the height at which meteors first appear, (b) the height of the Aurora Borealis, and (c), the distance that the sun is below the horizon when the last traces of color disappear from the sky in the evening.

Although the exact limits of the atmosphere are unknown, the weight of a column of air 1 sq. cm. in cross-section, and extending _upward as high as the atmosphere_, may be accurately computed. For this column of air exactly balances the column of mercury in the tube of the barometer.

Below sea-level, the air increases rapidly in density and it is estimated that at a depth of 35 miles, the density of the air would be a thousand times that at the earth's surface, or more than that of water.

Important Topics

1. Evidence of compressibility of gases and incompressibility of liquids.

2. Boyle's Law. Proof, applications.

3. Extent of the atmosphere--three evidences.

Exercises

1. Mention three ill.u.s.trations of the compressibility and expansibility of air that you know from your own experience.

2. Increasing the pressure increases the amount of a gas that will be absorbed by a liquid? Explain this. Have you ever observed this fact?

Where?

3. If a toy balloon containing 2000 ccm. of gas at the earth's surface where the barometer reading is 76 cm., rises to an elevation where the barometer reads 54 cm., the balloon will tend to expand to what volume?

Explain. Will it attain this volume?

4. If a gas is compressed, it changes in temperature. How do you explain this?

5. What change in temperature will occur when compressed air is allowed to expand? Explain.

6. Air blowing up a mountain side has its pressure lessened as it approaches the top. How will this affect the temperature? Why? What may result from this change in temperature? Explain.

7. To what pressure must 500 ccm. of air be subjected to compress it to 300 ccm. the barometer reading at first being 75 cm. Explain.

[Ill.u.s.tration: FIG. 39.--The air pump.]

(3) PNEUMATIC APPLIANCES