Feynman_Lectures_on_Physics_Volume_1_Chapter_01.pdf

Atoms in Motion

1-1 Introduction

This two-year course in physics is presented from the point of view that you,

the reader, are going to be a physicist. This is not necessarily the case of course,

but that is what every professor in every subject assumes! If you are going to

be a physicist, you will have a lot to study: two hundred years of the most rapidly

developing field of knowledge that there is. So much knowledge, in fact, that

you might think that you cannot learn all of it in four years, and truly you cannot;

you will have to go to graduate school too!

Surprisingly enough, in spite of the tremendous amount of work that has been

done for all this time it is possible to condense the enormous mass of results to

a large extent—that is, to find laws which summarize all our knowledge. Even

so, the laws are so hard to grasp that it is unfair to you to start exploring this

tremendous subject without some kind of map or outline of the relationship of

one part of the subject of science to another. Following these preliminary remarks,

the first three chapters will therefore outline the relation of physics to the rest

of the sciences, the relations of the sciences to each other, and the meaning of

science, to help us develop a "feel" for the subject.

You might ask why we cannot teach physics by just giving the basic laws on

page one and then showing how they work in all possible circumstances, as we do

in Euclidean geometry, where we state the axioms and then make all sorts of de-

ductions. (So, not satisfied to learn physics in four years, you want to learn it in

four minutes?) We cannot do it in this way for two reasons. First, we do not yet

know all the basic laws: there is an expanding frontier of ignorance. Second, the

correct statement of the laws of physics involves some very unfamiliar ideas

which require advanced mathematics for their description. Therefore, one needs

a considerable amount of preparatory training even to learn what the words

mean. No, it is not possible to do it that way. We can only do it piece by piece.

Each piece, or part, of the whole of nature is always merely an approximation

to the complete truth, or the complete truth so far as we know it. In fact, every-

thing we know is only some kind of approximation, because we know that we do

not know all the laws as yet. Therefore, things must be learned only to be unlearned

again or, more likely, to be corrected.

The principle of science, the definition, almost, is the following: The test of

all knowledge is experiment. Experiment is the sole judge of scientific "truth."

But what is the source of knowledge? Where do the laws that are to be tested

come from? Experiment, itself, helps to produce these laws, in the sense that it

gives us hints. But also needed is imagination to create from these hints the great

generalizations—to guess at the wonderful, simple, but very strange patterns be-

neath them all, and then to experiment to check again whether we have made the

right guess. This imagining process is so difficult that there is a division of labor

in physics: there are theoretical physicists who imagine, deduce, and guess at new

laws, but do not experiment; and then there are experimental physicists who ex-

periment, imagine, deduce, and guess.

We said that the laws of nature are approximate: that we first find the "wrong"

ones, and then we find the "right" ones. Now, how can an experiment be "wrong" ?

First, in a trivial way: if something is wrong with the apparatus that you did not

notice. But these things are easily fixed, and checked back and forth. So without

snatching at such minor things, how can the results of an experiment be wrong?

Only by being inaccurate. For example, the mass of an object never seems to

1-1

1-1 Introduction

1-2 Matter is made of atoms

1-3 Atomic processes

1-4 Chemical reactions

change; a spinning top has the same weight as a still one. So a "law" was in-

vented: mass is constant, independent of speed. That "law" is now found to be

incorrect. Mass is found to increase with velocity, but appreciable increases require

velocities near that of light. A true law is: if an object moves with a speed of

less than one hundred miles a second the mass is constant to within one part in

a million. In some such approximate form this is a correct law. So in practice

one might think that the new law makes no significant difference. Well, yes and

no. For ordinary speeds we can certainly forget it and use the simple constant-

mass law as a good approximation. But for high speeds we are wrong, and the

higher the speed, the more wrong we are.

Finally, and most interesting, philosophically we are completely wrong with

the approximate law. Our entire picture of the world has to be altered even though

the mass changes only by a little bit. This is a very peculiar thing about the

philosophy, or the ideas, behind the laws. Even a very small effect sometimes

requires profound changes in our ideas.

Now, what should we teach first? Should we teach the correct but unfamiliar

law with its strange and difficult conceptual ideas, for example the theory of

relativity, four-dimensional space-time, and so on? Or should we first teach the

simple "constant-mass" law, which is only approximate, but does not involve such

difficult ideas? The first is more exciting, more wonderful, and more fun, but the

second is easier to get at first, and is a first step to a real understanding of the

second idea. This point arises again and again in teaching physics. At different

times we shall have to resolve it in different ways, but at each stage it is worth

learning what is now known, how accurate it is, how it fits into everything else,

and how it may be changed when we learn more.

Let us now proceed with our outline, or general map, of our understanding

of science today (in particular, physics, but also of other sciences on the periphery),

so that when we later concentrate on some particular point we will have some idea

of the background, why that particular point is interesting, and how it fits into

the big structure. So, what is our over-all picture of the world?

1-2 Matter is made of atoms

If , in some cataclysm, all of scientific knowledge were to be destroyed, and only

one sentence passed on to the next generations of creatures, what statement would

contain the most information in the fewest words? I believe it is the atomic

hypothesis (or the atomic fact, or whatever you wish to call it) that all things are

made of atoms—little particles that move around in perpetual motion, attracting

each other when they are a little distance apart, but repelling upon being squeezed

into one another. In that one sentence, you will see, there is an enormous amount

of information about the world, if just a little imagination and thinking are applied.

To illustrate the power of the atomic idea, suppose that we have a drop of

water a quarter of an inch on the side. If we look at it very closely we see nothing

but water—smooth, continuous water. Even if we magnify it with the best optical

microscope available—roughly two thousand times—then the water drop will be

roughly forty feet across, about as big as a large room, and if we looked rather

closely, we would still see relatively smooth water—but here and there small

football-shaped things swimming back and forth. Very interesting. These are

paramecia. You may stop at this point and get so curious about the paramecia

with their wiggling cilia and twisting bodies that you go no further, except per-

haps to magnify the paramecia still more and see inside. This, of course, is a subject

for biology, but for the present we pass on and look still more closely at the water

material itself, magnifying it two thousand times again. Now the drop of water

extends about fifteen miles across, and if we look very closely at it we see a kind

of teeming, something which no longer has a smooth appearance—it looks some-

thing like a crowd at a football game as seen from a very great distance. In order

to see what this teeming is about, we will magnify it another two hundred and

fifty times and we will see something similar to what is shown in Fig. 1-1. This

is a picture of water magnified a billion times, but idealized in several ways.

1-2

WATER MAGNIFIED ONE BILLION TIMES

Figure 1-1

In the first place, the particles are drawn in a simple manner with sharp edges,

which is inaccurate. Secondly, for simplicity, they are sketched almost schemati-

cally in a two-dimensional arrangement, but of course they are moving around in

three dimensions. Notice that there are two kinds of "blobs" or circles to represent

the atoms of oxygen (black) and hydrogen (white), and that each oxygen has two

hydrogens tied to it. (Each little group of an oxygen with its two hydrogens is

called a molecule.) The picture is idealized further in that the real particles in

nature are continually jiggling and bouncing, turning and twisting around one

another. You will have to imagine this as a dynamic rather than a static picture.

Another thing that cannot be illustrated in a drawing is the fact that the particles

are "stuck together"—that they attract each other, this one pulled by that one,

etc. The whole group is "glued together," so to speak. On the other hand, the

particles do not squeeze through each other. If you try to squeeze two of them too

close together, they repel.

The atoms are 1 or 2 X 10 -8 cm in radius. Now 10 -8 cm is called an

angstrom (just as another name), so we say they are 1 or 2 angstroms (Å) in radius.

Another way to remember their size is this: if an apple is magnified to the size

of the earth, then the atoms in the apple are approximately the size of the original

apple.

Now imagine this great drop of water with all of these jiggling particles stuck

together and tagging along with each other. The water keeps its volume; it does

not fall apart, because of the attraction of the molecules for each other. If the

drop is on a slope, where it can move from one place to another, the water will

flow, but it does not just disappear—things do not just fly apart—because of

the molecular attraction. Now the jiggling motion is what we represent as heat:

when we increase the temperature, we increase the motion. If we heat the water,

the jiggling increases and the volume between the atoms increases, and if the

heating continues there comes a time when the pull between the molecules is not

enough to hold them together and they do fly apart and become separated from

one another. Of course, this is how we manufacture steam out of water—by

increasing the temperature; the particles fly apart because of the increased motion.

In Fig. 1-2 we have a picture of steam. This picture of steam fails in one

respect: at ordinary atmospheric pressure there might be only a few molecules in

a whole room, and there certainly would not be as many as three in this figure.

Most squares this size would contain none—but we accidentally have two and a

half or three in the picture (just so it would not be completely blank). Now in

the case of steam we see the characteristic molecules more clearly than in the case

of water. For simplicity, the molecules are drawn so that there is a 120° angle

between them. In actual fact the angle is 105°3', and the distance between the

center of a hydrogen and the center of the oxygen is 0.957 Å, so we know this

molecule very well.

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.

(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) feels only as an average push. In order to confine a gas we must apply a

pressure. Figure 1-3 shows a standard vessel for holding gases (used in all

textbooks), a cylinder with a piston in it. Now, it makes no difference 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.

Figure 1-2

Figure 1-3

1-3

Now let us put twice as many molecules in this tank, so as to double the den-

sity, and let them have the same speed, i.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. If 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 slight

increase because of the finite volume they occupy. Nevertheless, to an excellent

approximation, if the density is low enough that there are not many atoms, the

pressure is proportional to the density.

We can also see something else: If we increase the temperature without

changing the density of the gas, i.e., if we increase the speed of the atoms, what

is going to happen to the pressure? Well, the atoms hit harder because they are

moving faster, and in addition they hit more often, so the pressure increases.

You see how simple the ideas of atomic 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 find that it comes off with more speed than that with which

it struck. (Special example: if 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 will have picked up speed. This means that when we compress

a gas slowly, the temperature of the gas increases. So, under slow compression,

a gas will increase in temperature, and under slow expansion it will decrease 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 is in-

dicated in Fig. 1-4: the molecules lock into a new pattern which is ice. This

particular schematic diagram of ice is wrong because it is in two dimensions, but

it is right qualitatively. The interesting point is that the material has a definite

place for every atom, 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, each

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 definite 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 different ways. The differ-

ence between solids and liquids is, then, that in a solid the atoms are arranged in

some kind of an array, called a crystalline array, 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. Figure 1-4 is an invented arrangement for ice, and although it con-

tains many of the correct features of ice, it 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 if we turn the picture around an axis by 120°, the picture returns to itself.

So there is a symmetry in the ice which accounts for the six-sided appearance of

snowflakes. Another thing we can see from Fig. 1-4 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, expand 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. If we wish, we can change the amount of heat. What is the heat in

1-4

Figure 1-4

the case of ice? The atoms are not standing still. They are jiggling and vibrating.

So even though there is a definite order to the crystal—a definite 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 not 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. If we increase the pressure, we can make it solidify.

1-3 Atomic processes

So much for the description of solids, liquids, and gases from the atomic

point of view. However, the atomic hypothesis also describes processes, and so we

shall now look at a number of processes from an atomic standpoint. The first

process that we shall look at is associated with the surface of the water. What

happens at the surface of the water? We shall now make the picture more com-

plicated—and more realistic—by imagining that the surface is in air. Figure 1-5

shows the surface of water in air. We see the water molecules as before, forming

a body of liquid water, but now we also see the surface of the water. Above the

surface we find a number of things: First of all there are water molecules, as in steam.

This is water vapor, which is always found above liquid water. (There is an

equilibrium between the steam vapor and the water which will be described later.)

In addition we find some other molecules—here two oxygen atoms stuck together

by themselves, forming an oxygen molecule, there two nitrogen atoms also stuck

together to make a nitrogen molecule. Air consists almost entirely of nitrogen,

oxygen, some water vapor, and lesser amounts of carbon dioxide, argon, and

other things. So above the water surface is the air, a gas, containing some water

vapor. Now what is happening in this picture? The molecules in the water are

always jiggling around. From time to time, one on the surface happens to be hit

a little harder than usual, and gets knocked away. It is hard to see that happening

in the picture because it is a still picture. But we can imagine that one molecule

near the surface has just been hit and is flying out, or perhaps another one has

been hit and is flying out. Thus, molecule by molecule, the water disappears—

it evaporates. But if we close the vessel above, after a while we shall find a large

number of molecules of water amongst the air molecules. From time to time, one

of these vapor molecules comes flying down to the water and gets stuck again.

So we see that what looks like a dead, uninteresting thing—a glass of water with

a cover, that has been sitting there for perhaps twenty years—really contains a

dynamic and interesting phenomenon which is going on all the time. To our eyes,

our crude eyes, nothing is changing, but if we could see it a billion times magni-

fied, we would see that from its own point of view it is always changing: molecules

are leaving the surface, molecules are coming back.

Why do we see no change? Because just as many molecules are leaving as

are coming back! In the long run "nothing happens." If we then take the top of

the vessel off and blow the moist air away, replacing it with dry air, then the

number of molecules leaving is just the same as it was before, because this depends

on the jiggling of the water, but the number coming back is greatly reduced be-

cause there are so many fewer water molecules above the water. Therefore there

are more going out than coming in, and the water evaporates. Hence, if you wish

to evaporate water turn on the fan!

Here is something else: Which molecules leave? When a molecule leaves it

is due to an accidental, extra accumulation of a little bit more than ordinary

energy, which it needs if it is to break away from the attractions of its neighbors.

Therefore, since those that leave have more energy than the average, the ones that

are left have less average motion than they had before. So the liquid gradually

1-5

Figure 1-5

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