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Let us see what some of the properties of steam vapor or any other gas are. |
'The molecules, being separated from one another, will bounce against the walls. |
Imagine a room with a number of tennis balls (a hundred or so) bouncing around |
in perpetual motion. When they bombard the wall, this pushes the wall away. |
--- Trang 39 --- |
` \ế \ |
‡ “ Ả— |
Figure 1-3 |
(Of course we would have to push the wall back.) This means that the gas exerts |
a Jittery force which our coarse senses (not being ourselves magnified a billion |
times) feel only as an ø0erage push. In order to confine a gas we must apply |
a pressure. Figure l-3 shows a siandard vessel for holding gases (used in all |
textbooks), a cylinder with a piston in it. Now, it makes no diference what the |
shapes of water molecules are, so for simplicity we shall draw them as tennis balls |
or little dots. These things are in perpetual motion in all directions. So many of |
them are hitting the top piston all the time that to keep it from being patiently |
knocked out of the tank by this continuous banging, we shall have to hold the |
piston down by a certain force, which we call the pressure (really, the pressure |
times the area is the force). Clearly, the force is proportional to the area, for If |
we increase the area but keep the number of molecules per cubic centimeter the |
same, we increase the number of collisions with the piston in the same proportion |
as the area was increased. |
Now let us put 0wice as many molecules in this tank, so as to double the |
density, and let them have the same speed, ¡.e., the same temperature. Then, to |
a close approximation, the number of collisions will be doubled, and since each |
will be just as “energetic” as before, the pressure is proportional to the density. |
Tf we consider the true nature of the forces between the atoms, we would expect |
a slight decrease in pressure because of the attraction between the atoms, and |
a slipht Increase because of the fnite volume they occupy. Nevertheless, to an |
excellent approximation, if the density is low enough that there are not many |
atoms, £he pressure ¡s proportional to the densit. |
We can also see something else: lÝ we increase the temperature without |
changing the density of the gas, I.e., iŸ we increase the speed of the atoms, what |
1s goïng to happen to the pressure? Well, the atoms hit harder because they are |
--- Trang 40 --- |
moving faster, and in addition they hit more often, so the pressure increases. |
You see how simple the ideas of atomie theory are. |
Let us consider another situation. Suppose that the piston moves inward, so |
that the atoms are slowly compressed into a smaller space. What happens when |
an atom hits the moving piston? Evidently it picks up speed from the collision. |
You can try it by bouncing a ping-pong ball from a forward-moving paddle, for |
example, and you will fnd that ít comes of with more speed than that with |
which ¡9 struck. (Special example: iŸ an atom happens to be standing still and |
the piston hits it, it will certainly move.) So the atoms are “hotter” when they |
come away from the piston than they were before they struck it. Therefore all |
the atoms which are in the vessel wiïll have picked up speed. “This means that |
tuhen tue compress œ gas sÏloulụ, the temperature oƒ the gas ?ncreases. So, under |
SÌlOWw compression, a gas wiÌ] ?merease in temperature, and under sÌOw ezpdnsion |
1t will đecrease in temperature. |
'We now return to our drop of water and look in another direction. Suppose |
that we decrease the temperature of our drop of water. Suppose that the jiggling |
of the molecules of the atoms in the water is steadily decreasing. We know that |
there are forces of attraction between the atoms, so that after a while they will |
not be able to jiggle so well. What will happen at very low temperatures 1s |
indicated in Fig. 1-4: the molecules lock into a new pattern which is ?cc. This |
particular schematic diagram of ice is wrong because it is in two dimensions, but |
1t 1s right qualitatively. The interesting point is that the material has a defnite |
pÌace for cuer œtom, and you can easily appreciate that If somehow or other |
we were to hold all the atoms at one end of the drop in a certain arrangement, |
cach atom in a certain place, then because of the structure of interconnections, |
which is rigid, the other end miles away (at our magnified scale) will have a |
ý Qua gô -—c% ` |
cv @@- |
Figure 1-4 |
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defnite location. So if we hold a needle of ice at one end, the other end resists |
our pushing it aside, unlike the case of water, in which the structure is broken |
down because of the increased jiggling so that the atoms all move around In |
diÑerent ways. The diference between solids and liquids is, then, that in a solid |
the atoms are arranged in some kind of an array, called a crstalline arrau, and |
they do not have a random position at long distances; the position of the atoms |
on one side of the crystal is determined by that of other atoms millions of atoms |
away on the other side of the crystal. Pigure 1-4 is an invented arrangement Íor |
ice, and although it contains many of the correct features oŸ ice, i is not the true |
arrangement. One of the correct features is that there is a part of the symmetry |
that is hexagonal. You can see that iŸ we turn the picture around an axis by 60, |
the picture returns to itself. 5o there is a sựmưmnefrw in the ice which accounts for |
the six-sided appearance of snowflakes. Another thing we can see from Eig. l-4 is |
why ice shrinks when it melts. The particular crystal pattern of ice shown here |
has many “holes” in it, as does the true ice structure. When the organization |
breaks down, these holes can be occupied by molecules. Most simple substances, |
with the exception of water and type metal, ezpand upon melting, because the |
atoms are closely packed in the solid crystal and upon melting need more room |
to jiggle around, but an open structure collapses, as In the case of water. |
Now although ice has a “rigid” crystalline form, its temperature can change—— |
ice has heat. IÝ we wish, we can change the amount of heat. What is the heat in |
the case of ice? "The atoms are not standing still. They are jiggling and vibrating. |
So even thouph there is a defnite order to the crystal—a defnite structure——all of |
the atoms are vibrating “in place” As we increase the temperature, they vibrate |
with greater and greater amplitude, until they shake themselves out of place. We |
call this melting. As we decrease the temperature, the vibration decreases and |
decreases until, at absolute zero, there is a minimum amount of vibration that |
the atoms can have, but noøý zero. This minimum amount of motion that atoms |
can have is not enough to melt a substance, with one exception: helium. Helium |
merely decreases the atomic motions as much as it can, but even at absolute zero |
there is still enough motion to keep it from freezing. Helium, even at absolute |
zero, does not freeze, unless the pressure is made so great as to make the atoms |
squash together. IÝ we increase the pressure, we cøn make it solidIfy. |
1-3 Atomic processes |
So mụuch for the description of solids, liquids, and gases from the atomic point |
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