MOLECULAR FORCES AND MOTIONS
(1) EVIDENCES OF MOLECULAR MOTION IN GASES
=14. Size of Molecules.=--The difference between solids, liquids, and
gases has been explained as due to the different behavior of molecules
in the three states of matter. That is, in solids they cling together,
in liquids they move freely, and in gases they separate. At this time we
are to consider the _evidences_ of molecular motion in gases. It must be
kept in mind that molecules are exceedingly small. It has been said that
if a bottle containing about 1 ccm. of ordinary air has pierced in it a
minute opening so that 100,000,000 molecules (a number nearly equal to
the population of the United States) pass out every second, it would
take, not minutes or hours, but nearly 9000 years for all of the
molecules to escape. The number of molecules in 1 ccm. of air at 0°C.
and 76 cm. pressure has been calculated by Professor Rutherford to be
2.7 × 10¹⁹. It is evident that such minute particles cannot be seen or
handled as _individuals_. We must judge of their size and action by the
results obtained from experiments.
=15. Diffusion of Gases.=--One line of evidence which indicates that a
gas consists of moving particles is the rapidity with which a gas having
a strong odor penetrates to all parts of a room. For example, if
illuminating gas is escaping it soon diffuses and is noticed throughout
the room. In fact, the common experience of the diffusion of gases
having a strong odor is such that we promptly recognize that it is due
to motion of some kind. The gas having the odor consists of little
particles that are continually hitting their neighbors and are being
struck and buffeted in turn until the individual molecules are widely
scattered. When cabbage is boiled in the kitchen soon all in the house
know it. Other illustrations of the _diffusion_ of gases will occur to
anyone from personal experience, such for instance as the pleasing odor
from a field of clover in bloom.
The following experiment illustrates the rapid diffusion of gases.
[Illustration: FIG. 6_a_.--Diffusion of gases.]
[Illustration: FIG. 6_b_.--Effusion of gases.]
Take two tumblers (see Fig. 6_a_), wet the inside of one with a few
drops of strong ammonia water and the other with a little
hydrochloric acid. Cover each with a sheet of clean paper. Nothing
can now be seen in either tumbler. Invert the second one over the
first with the paper between, placing them so that the edges will
match. On removing the paper it is noticed that both tumblers are
quickly filled with a cloud of finely divided particles, the two
substances having united chemically to form a new substance,
ammonium chloride.
On account of their small size, molecules of air readily pass through
porous solids, cloth, unglazed earthenware, etc. The following
experiment shows this fact strikingly. (See Fig. 6_b_.)
A flask containing water is closed by a rubber stopper through
which pass the stem of a glass funnel and a bent glass tube that
has been drawn out to a small opening (_J_). The funnel has
cemented in its top an inverted porous clay jar (_C_), over the top
of the latter is placed a beaker (_B_). A piece of flexible rubber
tubing (_H_) leading from a hydrogen generator is brought up to the
top of the space between the jar and the beaker. When hydrogen gas
is allowed to flow into the space between _C_ and _B_, the level of
the water in _W_ is seen to lower and a stream of water runs out at
_J_ spurting up into the air.
On stopping the flow of hydrogen and removing _B_, the water falls
rapidly in _J_ and bubbles of air are seen to enter the water from
the tube. (The foregoing steps may be repeated as often as
desired).
This experiment illustrates the fact that the molecules of some
gases move faster than those of some other gases. Hydrogen
molecules are found to move about four times as fast as air
molecules. Hence, while both air and hydrogen molecules are at
first going in opposite directions through the walls of _C_, the
hydrogen goes in much faster than the air comes out. In consequence
it accumulates, creates pressure, and drives down the water in _W_
and out at _J_. On removing _B_, the hydrogen within the porous cup
comes out much faster than the air reënters. This lessens the
pressure within, so that air rushes in through _J_. This experiment
demonstrates not only the fact of molecular motion in gases but
also that molecules of hydrogen move much faster than those of air.
(This experiment will work with illuminating gas but not so
strikingly.)
Careful experiments have shown that the speed of ordinary air molecules
is 445 meters or 1460 ft. per second; while hydrogen molecules move at
the rate of 1700 meters or 5575 ft. or more than a mile per second.
=16. Expansion of Gases.=--Gases also possess the property of indefinite
expansion, that is, if a small quantity of gas is placed in a vacuum,
the gas will expand immediately to fill the entire space uniformly. This
is shown by an experiment with the air pump. On raising the piston the
air follows instantly to fill up the space under it. As the air is
removed from the receiver of an air pump the air remaining is uniformly
distributed within.
=17. How Gases Exert Pressure.=--It is further found that air under
ordinary conditions exerts a pressure of about 15 lbs. to the square
inch. In an automobile tire the pressure may be 90 lbs. and in a steam
boiler it may be 200 lbs. or more to the square inch.
How is the pressure produced? The molecules are not packed together
solidly in a gas, for when steam changes to water it shrinks to about
1/1600 of its former volume. Air diminishes to about 1/800 of its volume
on changing to liquid air. The pressure of a gas is not due then to the
gas filling all of the space in which it acts, but is due rather to the
_motion_ of the molecules. The blow of a single molecule is
imperceptible, but when multitudes of molecules strike against a surface
their combined effect is considerable. In fact, this action is known to
produce the pressure that a gas exerts against the walls of a containing
vessel. Naturally if we compress twice as much gas into a given space
there will be twice as many molecules striking in a given time, which
will give twice as much pressure.
If gas is heated, it is found that the heat will cause a swifter motion
of the molecules. This will also make the molecules strike harder and
hence cause the gas to expand or exert more pressure.
=17a. Brownian Movements.=--Direct photographic evidence of the motion
of molecules in gases has been obtained by studying the behavior of
minute drops of oil suspended in stagnant air. Such drops instead of
being at rest are constantly dancing about as if they were continually
receiving blows from many directions. These motions have been called
_Brownian Movements_ (see Fig. 7).
It has been proved that these movements are due to the blows that these
small drops receive from the swiftly moving molecules of the gas about
them. If the drops are made smaller or the gas more dense, the movements
increase in intensity. These effects are especially marked at a pressure
of 0.01 of an atmosphere.
[Illustration: FIG. 7.--Photograph of Brownian movement. This record is
prepared by the aid of Siedentopf's ultra-microscope and a plate moving
uniformly across the field from left to right.]
Important Topics
It is assumed that air and all gases are made up of molecules in rapid
motion; that this motion is dependent upon temperature and pressure.
Evidence of this is shown by (a) diffusion, (b) expansion, (c) pressure.
Brownian Movements.
Questions
1. What is the molecular (kinetic) theory of gases?
2. What three kinds of evidence help to confirm the theory?
3. What have you seen that seems to show that a gas consists of
molecules in motion?
4. How many meters long is a 10-ft. pole?
5. A 50-kg. boy weighs how many pounds?
6. What are three advantages of the metric system?
7. What will 12 qts. of milk cost at 8 cents a liter?
8. A cube 1 meter each way will contain how many cubic centimeters? How
many liters? What will a cubic meter of water weigh?
(2) MOLECULAR MOTION IN LIQUIDS
=18. Diffusion of Liquids.=--From the evidence given in Arts. 14-17, (a)
of diffusion of odors, (b) of the continued _expansion_ of air in the
air pump, and (c) of the pressure exerted by a gas in all directions,
one may realize without difficulty that a _gas consists of small
particles in rapid motion_. Let us now consider some of the evidence of
molecular motion in liquids. If a little vinegar is placed in a pail of
water, all of the water will soon taste sour. A lump of sugar in a cup
of tea will sweeten the entire contents. This action is somewhat similar
to the diffusion of gases but it takes place much more slowly. It is
therefore believed that the motion of liquid molecules is much slower
than that of gas molecules.
Again, if a dish of water is left standing in the open air in fine
weather, within a few days the dish will become dry though no one has
taken anything from it. We say the water has _evaporated_. What was
liquid is now _vapor_. If we were to observe carefully any dish of water
we would find that it continually loses weight on dry days. That is,
there is a constant movement of the molecules of water into the air.
This movement of the molecules is explained as follows. There appear to
be in the dish of water some molecules that by moving back and forth
acquire a greater velocity than their neighbors; when these reach the
surface of the liquid, some vibration or movement sends them flying into
the air above. They are now vapor or gas molecules, flying, striking,
and rebounding like the air molecules. Sometimes on rebounding, the
water molecules get back into the water again. This is especially apt to
happen when the air is damp, _i.e._, when it contains many water
molecules. Sometimes the air over a dish becomes _saturated_, as in the
upper part of a corked bottle containing water. Although molecules are
continually leaving the surface of the water they cannot escape from the
bottle, so in time as many molecules must return to the water from the
space above as leave the water in the same time. When this condition
exists, the air above the water is said to be _saturated_. On very damp
days the air is often saturated. The explanation above shows why wet
clothes dry so slowly on such a day (See Arts. 166-7 on Saturation.)
=19. Cooling Effect of Evaporation.= We have seen that warming a gas
increases its volume. This expansion is due to the increased motion of
the warmed molecules. Now the molecules that escape from a liquid when
it evaporates are naturally the fastest moving ones, _i.e._, the hottest
ones. The molecules remaining are the slower moving ones or colder
molecules. The liquid therefore becomes colder as it evaporates, unless
it is heated. This explains why water evaporating on the surface of our
bodies cools us. In evaporating, the water is continually losing its
warm, fast moving molecules. The _cooling effect_ of evaporation is,
therefore an evidence of molecular motion in liquids.
[Illustration: FIG. 8.--Osmosis Shown by carrot placed in water.]
=20. Osmosis.=--If two liquids are separated by a membrane or porous
partition, they tend to pass through and mix. This action is called
osmose, or _osmosis_.
Such a movement of liquid molecules in osmosis may be illustrated
by filling a beet or carrot that has had its interior cut out to
form a circular opening (see Fig. 8) with a thick syrup. The
opening is then closed at the top with a rubber stopper through
which passes a long glass tube.
If the carrot is immersed in water, as in Fig. 8, a movement of
water through the porous wall to the interior begins at once. Here,
as in the experiment of the hydrogen and air passing through the
porous cup, the lighter fluid moves faster. The water collecting in
the carrot rises in the tube. This action of liquids passing
through porous partitions and mingling is called _osmosis_.
Gases and liquids are alike in that each will _flow_. Each is therefore
called a _fluid_. Sometimes there is much resistance to the flow of a
liquid as in molasses. This resistance is called _viscosity_. Alcohol
and gasoline have little viscosity. They are _limpid_ or _mobile_. Air
also has some viscosity. For instance, a stream of air always drags some
of the surrounding air along with it.
Important Topics
1. Liquids behave as if they were composed of small particles in motion.
2. This is shown by (1) Diffusion, (2) Solution, (3) Evaporation, (4)
Expansion, (5) Osmosis.
Exercises
1. Give an example or illustration of each of the five evidences of
molecular motion in liquids.
2. When is air saturated? What is the explanation?
3. Why does warming a liquid increase its rate of evaporation?
4. Air molecules are in rapid motion in all directions. Do they enter a
liquid with a surface exposed to the air? Give reason.
5. What are some of the inconveniences of living in a saturated
atmosphere?
6. Fish require oxygen. How is it obtained?
(3) MOLECULAR FORCES IN LIQUIDS
=21. Cohesion and Adhesion.=--In liquids "the molecules move about
freely yet tend to cling together." This tendency of molecules to cling
together which is not noticeable in gases is characteristic of =liquids=
and especially of =solids=. It is the cause of the viscosity mentioned
in the previous section and is readily detected in a variety of ways.
For instance, not only do liquid molecules cling together to form drops
and streams, but they cling to the molecules of solids as well, as is
shown by the wet surface of an object that has been dipped in water. The
attraction of like molecules for one another is called _cohesion_, while
the attraction of =unlike molecules= is called _adhesion_, although the
force is the same whether the molecules are alike or unlike. It is the
former that causes drops of water to form and that holds iron, copper,
and other solids so rigidly together. The adhesion of glue to other
objects is well known. Paint also "sticks" well. Sometimes the "joint"
where two boards are glued together is stronger than the board itself.
The force of attraction between molecules has been studied carefully.
The attraction acts only through very short distances. The attraction
even in liquids is considerable and may be measured. The cohesion of
water may be shown by an experiment where the force required to pull a
glass plate from the surface of water is measured.
[Illustration: FIG. 9.--The water is pulled apart.]
Take a beam balance and suspend from one arm a circular glass
plate, Fig. 9. Weigh the plate and its support. Adjust the glass
plate so that it hangs horizontally and just touches the surface of
clean water, the under side being completely wet. Now find what
additional weight is required to raise the glass plate from the
water.
Just as the plate comes from the water its under side is found to be
wet. That is, _the water was pulled apart_, and the plate was not pulled
from the water. The cohesion of the water to itself is not so strong as
its adhesion to the glass.
The cohesion of liquids is further shown by the form a drop of liquid
tends to take when left to itself. This is readily seen in small drops
of liquids. The spherical shape of drops of water or mercury is an
example. A mixture of alcohol and water in proper proportions will just
support olive oil within it. By carefully dropping olive oil from a
pipette into such a mixture, a drop of the oil, an inch or more in
diameter suspended in the liquid, may be formed. It is best to use a
bottle with plane or flat sides, for if a round bottle is used, the
sphere of oil will appear flattened.
[Illustration: FIG. 10 _a_.
FIG. 10 _b_.
FIGS. 10 _a_ AND _b_.--Surface tension of a liquid film.]
=22. Surface Tension.=--The cohesion of liquids is also indicated by the
tendency of films to assume the smallest possible surface. Soap bubble
films show this readily. Fig. 10 _a_ represents a circular wire form
holding a film in which floats a loop of thread. The tension of the
film is shown in Fig. 10 _b_ by the circular form of the loop after the
film within it has been pierced by a hot wire, Fig. 11 shows a
rectangular wire form with a "rider." The tension in the film draws the
rider forward.
[Illustration: FIG. 11.--The rider is drawn forward.]
[Illustration: FIG. 12.--Surface tension causes the pointed shape.]
A soap bubble takes its spherical shape because this form holds the
confined air within the smallest possible surface. A drop of liquid is
spherical for the same reason. Many illustrations of the tension in
films may be given. Users of water colors notice that a dry camel's-hair
brush is bushy. (Fig. 12 _A_). When in water it is still bushy. (Fig. 12
_B_.) But when it is taken from the water and the excess is shaken from
it, it is pointed as in Fig. 12 _C_. It is held to the pointed shape by
the tension of the liquid film about the brush.
[Illustration: FIG. 13.--A needle depresses the surface when floating.]
The surface of water acts as if covered by a film which coheres more
strongly than the water beneath it. This is shown by the fact that a
steel needle or a thin strip of metal may be floated upon the surface of
water. It is supported by the surface film. (See Fig. 13.) If the film
breaks the needle sinks. This film also supports the little water bugs
seen running over the surface of a quiet pond in summer. The surface
film is stronger in some liquids than in others. This may be shown by
taking water, colored so that it can be seen, placing a thin layer of it
on a white surface and dropping alcohol upon it. Wherever the alcohol
drops, the water is seen to pull away from it, leaving a bare space over
which the alcohol has been spread. This indicates that the alcohol has
the weaker film. The _film of greasy benzine is stronger_ than the film
of the pure material. If one wishes to remove a grease spot and places
pure benzine at the center of the spot, the stronger film of the greasy
liquid will pull away from the pure benzine, and spread out, making a
larger spot than before, while if pure benzine is placed _around the
grease spot_, the greasy liquid at the center pulls away from the pure
benzine, drawing more and more to the center, where it may be wiped up
and the grease entirely removed.
[Illustration: FIG. 14.--The molecule at _A_ is held differently from
one within the liquid.]
=23. Explanation of the Surface Film.=--Beneath the surface of a liquid
each molecule is attracted by all the other molecules around it. It is
attracted equally in all directions. Consequently the interior molecules
move very easily over each other in any direction. A molecule at the
surface, as at _A_, Fig. 14, is not attracted _upward_ by other liquid
molecules. Its freedom of motion is thereby hindered with the result
that a molecule at the surface behaves differently from one beneath the
surface. The surface molecules act as if they form an elastic skin or
membrane upon the liquid surface.
[Illustration: FIG. 15.--Capillary attraction in tubes.]
=24. Capillarity.=--A striking action of the surface film of a liquid is
seen in the rise of liquids in tubes of small bore when the liquid
_wets_ them. If the liquid _does not wet_ the tube, as when mercury is
placed in glass, the liquid is depressed. It is found in general that:
_Liquids rise in capillary tubes when they wet them and are depressed in
tubes which they do not wet; the smaller the diameter of the tube the
greater the change of level._ (See Fig. 15.) This action is explained as
follows: The molecules of a liquid have an attraction for each other and
also for the sides of a tube. The former is called "cohesion for
itself," the latter is called "adhesion for the sides of the containing
vessel." If the cohesion for itself is greater than the adhesion for the
side of the containing vessel, the liquid is pulled away from the side
and is depressed. If the adhesion is greater, the liquid is elevated.
This action is called "capillary action" from the Latin word
(_capillus_) signifying hair, since it shows best in fine hairlike
tubes.
There are many common illustrations of capillary action: oil rising in a
wick; water rising in a towel or through clothes; ink in a blotter, etc.
The minute spaces between the fibers composing these objects act as fine
tubes. If cloth is treated with a preparation which prevents water from
adhering to its fibers, the material will not be wet when water is
poured upon it, because the water will not run in between the fibers; a
surface film spreads over the cloth so that no water enters it.
_Cravenette cloth_ has been treated in this way and hence is waterproof.
The action of this film may be shown by the following experiment.
Dip a sieve of fine copper gauze in melted paraffin, thus coating
each wire so that water will not adhere to it. Water may now be
poured into the sieve, if a piece of paper is first laid in it to
break the force of the water. On carefully removing the paper the
surface film of the water will prevent the passage of the water
through the sieve.
=25. Capillary Action in Soils.=--The distribution of moisture in the
soil depends largely upon capillary action. When the soil is compact the
minute spaces between the soil particles act as capillary tubes, thus
aiding the water to rise to the surface. As the water evaporates from
the surface more of it rises by capillary action from the damper soil
below. Keeping the soil loose by cultivation, makes the spaces between
the particles too large for much capillary action, thus the moisture is
largely prevented from rising to the surface.
In the semi-arid regions of the West "_dry farming_" is successfully
practised. This consists in keeping the surface covered with a "dust
mulch" produced by frequent cultivation. In this way the moisture is
kept below the surface, where it can be utilized during the hot dry
summer by the roots of growing plants.
Important Topics
1. Attractive forces between liquid molecules.
2. Cohesion (like molecules); adhesion (unlike molecules).
3. Special effects of this force are classified as (a) capillary action,
and (b) surface tension.
Exercises
1. What evidence of capillary action have you seen outside of the
laboratory?
2. What is the explanation for capillary action?
3. Where are surface films found?
4. What are three common effects of surface films?
5. Explain why cravenette cloth sheds water.
6. If a circular glass disc 10 cm. in diameter requires 50 grams of
force to draw it from the water, what is the cohesion of water per
square centimeter?
7. What is the weight in grams of 1 ccm. of water? of a liter of water?
8. Name five examples of adhesion to be found in your home.
9. Under what conditions will a liquid wet a solid and spread over it?
10. When will it form in drops on the surface?
11. Explain the proper procedure for removing a grease spot with
benzine.
12. What difference is there between a liquid and a fluid?
13. Why cannot a "soap bubble" be blown from pure water?
14. Which are larger, the molecules of steam or those of water? Why?
15. Why is the ground likely to be damp under a stone or board when it
is dry all around?
16. Why does any liquid in falling through the air assume the globule
form?
17. Give three examples of capillary attraction found in the home. Three
out of doors.
18. Why does cultivation of the soil prevent rapid evaporation of water
from the ground?
(4) EVIDENCES OF MOLECULAR FORCES IN LIQUIDS AND SOLIDS
=26. Solutions.=--A crystal of potassium permanganate is placed in a
liter of water. It soon dissolves and on shaking the flask each portion
of the liquid is seen to be colored red. The dissolving of the
permanganate is an illustration of the attraction of the molecules of
water for the molecules of the permanganate. We are familiar with this
action in the seasoning of food with salt and sweetening with sugar.
Water will dissolve many substances, but in varying degrees, _i.e._, of
some it will dissolve much, of others, little, and some not at all.
Further, different liquids have different solvent powers. Alcohol will
dissolve resin and shellac, but it will not dissolve gum arabic, which
is soluble in water. Benzine dissolves grease. Beeswax is not dissolved
by water, alcohol or benzine, but is soluble in turpentine.
It is found that the _temperature_ of the liquid has a marked effect
upon the amount of substance that will dissolve. This is an indication
that the _motions_ of the molecules are effective in solution. It
appears that dissolving a solid is in some respects similar to
evaporation, and just as at higher temperatures more of the liquid
evaporates, because more of the molecules will escape from the liquid
into the air above, so at higher temperatures, more molecules of a solid
will detach themselves through greater vibration and will move into the
liquid.
Further, just as an evaporating liquid may saturate the space above it
so that any escape of molecules is balanced by those returning, so with
a dissolving solid, the liquid may become _saturated_ so that the
solution of more of the solid is balanced by the return of the molecules
from the liquid to the solid condition.
=27. Crystals and Crystallization.=--This return from the liquid to the
solid state, of molecules that are in solution, is especially noticeable
when the solution is cooling or evaporating and hence is losing its
capacity to hold so much of the solid. On returning to the solid, the
molecules attach themselves in a definite manner to the solid portion,
building up regular solid forms. These regular forms are _crystals_. The
action that forms them is called _crystallization_.
Each substance seems to have its own _peculiar form of crystal_ due to
the manner in which the molecules attach themselves to those previously
in place. The largest and most _symmetrical crystals are_ those in which
the molecules are deposited slowly with no disturbance of the liquid.
Beautiful crystals of alum may be obtained by dissolving 25 g. of alum
in 50 ccm. of hot water, hanging two or three threads in the solution
and letting it stand over night. The thread fibers provide a foundation
upon which crystals grow.
When a _solution_ of a solid evaporates, the molecules of the _liquid_
escape as a gas, the molecules of the _solid_ remain accumulating as
crystals. This principle has many uses: (a) sea water is purified by
_evaporating the water and condensing the vapor_, which of course forms
pure water. (b) water is forced down to _salt_ beds where it dissolves
the salt. The brine is then raised and evaporated, leaving the salt in
the evaporating pans.
=28. Absorption of Gases by Solids and Liquids.=--If a piece of
heated charcoal is placed in a test-tube containing ammonia gas,
inverted in mercury, the ammonia is seen to disappear, the mercury
rising to take its place. The ammonia has been absorbed by the
charcoal, the gas molecules clinging closely to the solid. The
charcoal being very porous presents a large surface to the action
of the gas.
This experiment indicates that attraction exists between gas molecules
and other molecules. Many porous substances have this power of absorbing
gases. We have all noticed that butter has its flavor affected by
substances placed near it.
That _liquids absorb gases_ is shown by slowly heating cold water in a
beaker. Small bubbles of air form on the sides and rise before the
boiling point is reached. Ammonia gas is readily absorbed in water, the
bubbles disappearing almost as soon as they escape into the water from
the end of the delivery tube. _Household ammonia_ is simply a solution
of ammonia gas in water. On warming the solution of ammonia the gas
begins to pass off; thus, warming a liquid tends to drive off any gas
dissolved in it.
_Soda water_ is made by forcing carbon dioxide gas into water under
strong pressure. When placed in a vessel open to the air the pressure is
lessened and part of the gas escapes. The dissolved gas gives the
characteristic taste to the beverage.
Important Topics
1. The solution of solids is increased by heating.
2. The solution of gases is decreased by heating.
3. Pressure increases the quantity of gas that can be dissolved in a
liquid.
4. The attraction (cohesion) of molecules of a dissolved solid for each
other is shown by crystallization.
Exercises
1. How do fish obtain oxygen for breathing?
2. Why does warming water enable it to dissolve more of a salt?
3. Why does warming water lessen the amount of a gas that will stay in
solution?
4. Will water absorb gases of strong odor? How do you know?
5. Name three solvents. Give a use for each.
6. What liquids usually contain gases in solution? Name some uses for
these dissolved gases.
7. What is the weight of a cubic meter of water?
8. Name three substances obtained by crystallization.
9. How is maple sugar obtained?
10. Name five crystalline substances.
(5) EVIDENCE OF MOLECULAR FORCES IN SOLIDS
=29. Differences between Solids and Gases.=--In studying gases, it is
seen that they behave as if they were composed of small particles in
rapid motion, continually striking and rebounding, and separating to
fill any space into which they are released. This action indicates that
there is practically no attractive force between such molecules.
Between the molecules of a solid, however, the forces of attraction are
strong, as is shown by the fact that a solid often requires a great
force to pull it apart; some, as steel and iron, show this property in a
superlative degree, a high-grade steel rod 1 cm. in diameter requiring
nearly 9 tons to pull it apart. Tests show that the breaking strengths
of such rods are directly proportional to their areas of cross-section.
That is, twice the area has twice the breaking strength.
[Illustration: FIG. 16.--Elasticity of bending.]
=30. Elasticity.=--Fully as important as a knowledge of the breaking
strengths of solids, is the knowledge of what happens when the forces
used are not great enough to break the rods or wires.
Take a wooden rod (as a meter stick) and clamp one end to the table
top, as in Fig. 16. At the other end hang a weight. Fasten a wire
to this end so that it projects out in front of a scale. Add
successively several equal weights and note the position of the
wire each time. Remove the weights in order, noting the positions
as before. The rod will probably return to the first position.
This simple experiment illustrates a characteristic of solids: that of
changing shape when force is applied and of returning to the original
shape when the force is removed. This property is called _elasticity_.
Tests of elasticity are made by subjecting wire of different materials
but of the same dimensions to the same tension. The one changing least
is said to have the greatest _elastic force_ or elasticity. If greater
forces are applied to the wire and then removed, one will finally be
found that will permanently stretch the wire so that it will not return
exactly to the former length. The wire has now passed its _elastic
limit_ and has been permanently stretched.
Just as there are great differences between the _elastic forces_ of
different substances, so there are great differences in the _limits of
elasticity_. In some substances the limit is reached with slight
distortion, while others are _perfectly elastic_ even when greatly
stretched. India rubber is an example of a body having _perfect_
elasticity through wide limits. Glass has great _elastic force_ but its
_limit_ of _elasticity_ is soon reached. Substances like India rubber
may be said to have great "_stretchability_," but little elastic force.
In physics, elasticity refers to the elastic force rather than to
ability to endure stretching.
=31. Kinds of Elasticity.=--_Elasticity may be shown in four ways_:
_compression_, _bending_ or _flexure_, _extension_ or _stretching_,
_twisting_ or _torsion_. The first is illustrated by squeezing a rubber
eraser, the second by an automobile spring, the third by the stretching
of a rubber band, the fourth by the twisting and untwisting of a string
by which a weight is suspended.
_There are two kinds of elasticity_: (1) elasticity of form or shape;
(2) elasticity of volume. Gases and liquids possess elasticity of
volume, but not of shape, while solids may have both kinds. Gases and
liquids are perfectly elastic because no matter how great pressure may
be applied, as soon as the pressure is removed they regain their former
volume. No solid possesses perfect elasticity, because sooner or later
the limit of elasticity will be reached.
=32. Hooke's Law.=[A]--On examining the successive movements of the end
of the rod in Art. 30, we find that they are approximately equal.
Carefully conducted experiments upon the elasticity of bodies have shown
that the changes in shape are _directly proportional_ to the forces
applied, provided that the limit of elasticity is not reached. This
relation, discovered by Robert Hooke, is sometimes expressed as follows:
"_Within the limits of perfect elasticity, all changes of size or shape
are directly proportional to the forces producing them._"
[A] A law is a statement of a constant mode of behavior. It is
often expressed in mathematical language.
=33. Molecular Forces and Molecular Motions.=--If a solid is compressed,
on releasing the pressure the body regains its former shape if it has
not been compressed too far. This indicates that at a given temperature
the "molecules of a solid tend to remain at a fixed distance from each
other, and resist any attempt to decrease or increase this distance."
This raises the question, Why does not the cohesion pull the molecules
tightly together so that compression would be impossible? The reason is
that heat affects the size of solid bodies. On lowering the temperature,
bodies do contract, for as soon as the temperature is lowered the
vibration of the molecule is lessened. On raising the temperature the
molecules are pushed farther apart.
The size of a body, then, is the result of a balance of opposing forces.
The attractive force between the molecules pulling them together is
_cohesion_, while the force which pushes them apart is due to the
motions of the molecules. Raising the temperature and thus increasing
the motion causes expansion; lowering the temperature decreases the
molecular motion and so causes contraction. If an outside force tries to
pull the body apart or to compress it this change of size is resisted by
either cohesion or molecular motion.
=34. Properties of Matter.=--Many differences in the physical properties
of solids are due to differences between the cohesive force of different
kinds of molecules. In some substances, the attraction is such that they
may be rolled out in very thin sheets. Gold is the best example of this,
sheets being formed 1/300,000 of an inch thick. This property is called
_malleability_. In other substances the cohesion permits it to be drawn
out into fine threads or wire. Glass and quartz are examples of this.
This property is called _ductility_. In some, the cohesion makes the
substance excessively _hard_, so that it is difficult to work or scratch
its surface. The diamond is the hardest substance known. Some substances
are _tough_, others _brittle_. These are tested by the ability to
withstand sudden shocks as the blow of a hammer.
Important Topics
1. Molecular forces in solids; (_a_) adhesion, (_b_) cohesion.
2. Elasticity, Hooke's Law.
3. Contraction on cooling.
4. Malleability, ductility, hardness, brittleness, etc.
Exercises
1. Give an illustration of Hooke's Law from your own experience.
2. What devices make use of it?
3. Do solids evaporate. Give reasons.
4. When iron is welded, is cohesion or adhesion acting?
5. When a tin basin is soldered, is cohesion or adhesion acting?
6. Sometimes a spring is made more elastic by _tempering_ and made soft
by _annealing_. Look up the two terms. How is each accomplished?
7. Review the definitions: solid, liquid, and gas. Why do these
definitions mean more to you now than formerly?
8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what force
will stretch it 0.75 cm? Explain.
9. How long will it take under ordinary conditions for a gas molecule to
cross a room? Give reasons for your answer.
10. What is meant by the elastic limit of a body?
11. Without reaching the elastic limit, if a beam is depressed 4 mm.
under a load of 60 kg., what will be the depression under a load of 400
kg.? Of 600 kg.?
12. Name three substances that possess elasticity of volume.
13. Give three examples of each; elasticity of (1) compression, (2)
stretching, (3) torsion, (4) flexure.
Review Outline: Introduction and Molecules
Physics; definition, topics considered, physical and chemical changes.
Science; hypothesis, theory, law. Knowledge; common, scientific.
Matter; three states, molecular theory. Mass, weight, volume.
Metric system; units, tables, equivalents, advantages.
Evidences of molecular motions; gases (3), liquids (5), solids (3).
Evidences of molecular forces; liquids (3), solids (many) special
properties such as: elasticity, tenacity, ductility, hardness, etc.
Hooke's law; applications.