9. Water is drawn from a hydrant at the rate of 1 gal. in 5 sec. How much power is required at the pumping-station to maintain a pressure of 50 lb./sq. in. at the station?

10. If the efficiency of a water motor is 50 per cent, how much water per minute must be supplied to it at a pressure of 30 lb./sq. in. in order that it may develop one quarter of a horse power?

State in which case energy is the more expensive: at 10 per kilowatthour or at 10 & per hundred cubic feet of water at a pressure of 40 lb./sq. in. 12. A water turbine has an efficiency of 80 per cent and develops 100 H. P. How many cubic feet of water must be supplied per hour from a reservoir 100 ft. higher than the turbine ?

13. How many cubic feet of water must be supplied per hour to the turbine of Problem 12 if the supply has a pressure of 60 lb./sq. in. ?

CHAPTER XIV

THE MOLECULAR AND ATOMIC THEORY. SPECIAL
PROPERTIES OF SOLIDS AND LIQUIDS

DUE TO MOLECULAR ACTION

The molecular and atomic theory of matter, 158. Evaporation, 159. Molecular forces, 160. Surface tension, 161. Measurement of surface tension, 162. Cause of surface tension, 163. Capillarity, 164. Capillary action in the soil, 165. Effects of surface tension on floating bodies, 166. Diffusion of liquids, 167. Diffusion of solids, 168. Diffusion of gases, 169. Diffusion through porous walls, 170. Osmosis; osmotic pressure, 171.

158. The molecular and atomic theory of matter. It was stated in Chapter IV that ordinary bodies are built of molecules. The molecule in turn is built of atoms, the water molecule being a cluster of two hydrogen atoms and one oxygen atom. There are about eighty-seven kinds of atoms which have different chemical properties. Different kinds of molecules are built of different combinations of these atoms. A substance that contains only atoms with the same chemical properties is called an element, while one built of molecules that contain atoms with different chemical properties is called a compound. Gold, silver, iron, oxygen, and hydrogen are elements; wood, water, common salt, and acids are compounds. In general the structures of molecules are so firm and compact that ordinary mechanical treatment of matter does not break them up.

Long ago the chemist was able to measure the relative masses of atoms and molecules. To say that the atomic mass of the nitrogen atom is 14 and that of the oxygen atom is 16 means only that their masses are proportional to these numbers. In recent years tremendous strides have been made in discovering the properties and structure of molecules and atoms. Unexpected and practically conclusive evidence of the correctness of the molecular theory has been furnished by work in the discharge of electricity through rarefied gases and by the study of the properties of radioactive substances and their radiations. Methods have been devised for determining the absolute mass of atoms and molecules. But, more important yet, a body smaller than an atom has been discoveredthe electron. As a result the theory of the molecule has been extended, and now attempts are being made to explain the structure of the atom. It seems probable that the atom consists of a nucleus with electrons as satellites revolving around it. This nucleus is very small, -small compared even with an atom. Evidence seems to indicate that it is about one millionth of the size of an atom. The atoms of different elements differ from one another in the size of the nucleus and the number of satellites (electrons). An atom of greater atomic mass has a nucleus of greater mass and a larger number of satellites. A great deal has been found out about the electron, and it plays so conspicuous a part that the "electron theory" of some of the phenomena of heat, electricity, magnetism, and light has become a very prominent part of the study of those topics.

It was formerly thought that all atoms which had the same chemical properties had the same mass. Now it is thought that chemical properties depend on the number and arrangement of the satellites around the nucleus, and not on the mass. It has, in fact, been discovered that in some cases atoms of different atomic mass have the same chemical properties. For example, ten or a dozen different atoms have the chemical properties of lead. Those atoms which have different atomic masses but the same chemical properties are called isotopes. Common lead is a mixture of several kinds of atoms, all having the same chemical properties but different atomic masses. Chlorine is a mixture of two isotopes of atomic masses 35 and 37. Evidence is rapidly accumulating which shows that this is true of many of the so-called elements.

Considerable progress is being made in the study of the structure of the nucleus of the atoms. Present information leads to the view that the nuclei of atoms are built of three different kinds of units: the nucleus of the hydrogen atom, the nucleus of the helium atom, and the electron.

Recent investigations, too abstruse for explanation here, indicate that the following are close to the correct values:

Mass of a hydrogen atom is 1.66 × 10-24 grams.

The number of molecules per cubic centimeter in a gas at atmospheric pressure and 0°C. is 2.70 x 1019.

A method for finding the mass of a hydrogen atom is indicated in Chapter XXXI. The approximate mass of any atom may be found by multiplying its atomic mass by the value given above for the mass of a hydrogen atom. The numbers given above are far beyond the range of our comprehension. For example, the number of molecules in 500 cubic centimeters (about 1 pint) of air at ordinary pressure is 500 × 2.7 × 1019, or 1.4 × 1022. Suppose that a flask of 500 cubic centimeters could have the air entirely removed from it and then be sealed up. Suppose, further, that a minute hole could now be made in the flask, and that the air should flow in at the rate of 10,000,000, or 107, molecules per second. How long would it take to fill the flask to ordinary atmospheric pressure? The student can verify the following:

Since in one year there are approximately 32 × 106 seconds, the number of molecules flowing into the flask in one year would be 32 × 106 × 107, or 3.2 × 1014. Hence the number of years required to fill the flask would be

But this is equal to forty million years!

159. Evaporation. The evaporation of water is a molecular process. In the interior of water the molecules are in a constant state of motion, some of them breaking through the surface and forming water vapor in the space above. If the molecules in the liquid were at rest and not in a continual state of motion, there would be no reason for supposing that they would leave the liquid. All liquids evaporate, some of them very rapidly (for example, alcohol and gasoline); others, such as heavy oils and mercury, evaporate slowly.

Some solids will evaporate at noticeable rates; for example, gum camphor and iodine. The evaporation of solids is often called sublimation. The so-called permanent metals, such as iron, copper, and tin, do not evaporate while in the solid form, but will evaporate when heated into liquids.

After one learns that substances are made of molecules and that these molecules are probably not in contact, it is natural to wonder why all substances do not fall to pieces, or evaporate at very high rates. The molecules must exert attractions on each other.

160. Molecular forces. Molecules are so extremely small that the attraction between them produces no appreciable effect unless they are relatively close together. In order to obtain an attraction which can be detected it is necessary to bring a large number of molecules close together. If two very clean and smooth pieces of lead are pressed tightly together, they will stick. Two pieces of iron may be brought into such close contact by welding that they practically become one piece. Two pieces of lead or iron simply brought together do not show this attraction, for they touch at only a few points. Usually there are dust particles, and even when these are removed there may be left a thin air film. Two pieces of clean plate glass when laid one on the top of the other will have a comparatively thick film of air between them. This is the reason the top one slides so easily over the other. When one strikes th wo together, with the surfaces parallel, there is not the metalle sound that should be obtained from glass striking glass, but a distinctly muffled sound due to the air film. This film can be partly removed by pressing the glass plates together and, at the same time, sliding one around on the other. When this film becomes very thin, the plates will cling together. When the experiment is tried in a vacuum, where complications due to atmospheric pressure are to a large extent removed, the attractive force between the plates is shown more conclusively.

That molecular forces are often very great can be shown when the contact between surfaces is sufficiently intimate, as in welding or soldering. It is found that a considerable amount of work must be done to make water evaporate; that is, to tear the molecules apart. (In the chapters on heat it will be shown that energy must be added to water when it evaporates.)

Sometimes a distinction is made between the case where the attraction is between molecules which are alike and the case where it is between different kinds of molecules. The force between like molecules is called