Download An Introduction To Energy

An Introduction To Energy
Lecture Notes
[slide 1]
In today’s class, we are going to be discussing, a very interesting question in the study of
Physics, and a question that helps illustrate the limits to our understanding, of the way
things work in this, vast, magnificent, Universe that we find ourselves in today. The
question is, [slide 2] of What is Energy?
There is a fact, or, if you prefer, a law, governing all natural phenomena known to date.
There is no known exception to this law—it is exact, so far as we know. This law, [click]
is the Conservation of Energy. It states, that there is a certain quantity, which we call
energy, that does not change, through all of the many complex and countless changes
that Nature may undergo. This idea, is a very abstract idea, because it is in fact a
mathematical principle. It is not a description of a mechanism, or anything concrete; it is
just, a strange fact, that we can calculate some number, and when we finish watching
Nature go through all her tricks, and calculate the number again, it is always the same.
Since this is such an abstract concept, we find it helpful, to illustrate the meaning by
means, of an analogy. This is a story, that was used as a teaching aid, by the legendary
physicist Richard Feynman, at the California Institute of Technology, and I like it quite
well.
So consider that we know a young boy—and his name is Dennis [slide 3]—who has a
set of blocks [click]. The blocks are absolutely indestructible, such that they cannot be
broken, or divided into any pieces. Each block, is the same as all the others. And, for
the sake of this analogy, let us suppose that he has, 58 [click] of these blocks. At the
beginning of each day, his Mother [click] puts him in his playroom, with his blocks,
and at the end of each day, she counts the blocks. And she discovers an amazing thing:
no matter what he does with the blocks, after he goes through all his tricks, there are
always 58! The number does not change!
This continues for a number of days, until one day, there are only, 57 blocks…but a
little bit of investigating shows, that there is one, under the rug. With a kid like
Dennis, the Mother has to look everywhere, so that she has not missed any. One day,
however, the number really does appear to change—there are only 56 blocks anywhere
in the room. But, her careful investigation indicates, that the window is open, and upon
looking outside, the other two blocks are found! Another day, careful count indicates,
that there are 60 blocks! Now this causes some considerable confusion, until it is
realized that Bruce came to visit, bringing his blocks with him, and leaving a few behind.
After disposing of the extra blocks, she closes the window, does not let Bruce in, and
everything is going all right, until the time she counts and finds only 55 blocks. There
are none under the rug, and none out the window. However, there is a toy box [slide 4]
in the room. So she goes over to look in the toy box, but when she gets close Dennis
starts hollering, “No, no, no, you stay away from my toy box!” See, the toy box is where
Dennis keeps all his treasures, and nobody else, is allowed to open the toy box. Ok, fair
enough. However, being curious, and smart, the Mother devises a scheme! She knows
that each block weighs 3 ounces. She weighs the toybox, at a time when she can see all
58 blocks, and it weighs 16 ounces. Then, the next time she wishes to check, she weighs
the box again, subtracts 16 ounces and divides by three. She discovers the following
[click]:
 number of  box weight   16 oz.

 
 58
3 oz.
 blocks seen 
This serves her well, but then, there appear to be some new deviations. But very careful
study indicates, that the dirty water in the mop bucket [click]is changing its level. It
seems that Dennis is throwing blocks, into the water, and she cannot see them because
it is so dirty. But, she can find out, how many blocks are in the water, by adding another
term to her formula. Since the original height of the water, was 6 inches, and each block
raises the water, a quarter of an inch, her new formula is [click]:
 number of  box weight   16 oz. water height   6 in.

 

 58
1 in.
3 oz.
 blocks seen 
4
We can see, that with the gradual increase, in the complexity of her world, the Mother
finds, a whole new series of terms [click], all representing ways, of calculating how many
blocks, are in places where she is not allowed to look. In the end, she finds a complex
formula, a way to compute this particular number, which always stays the same for her
situation.
So what is the analogy of this, to the conservation of energy? The most remarkable
thing that we must take from this picture is that there are no blocks. [slide 5] In all the
activity, that I have just described, it was energy, and not blocks, that remained constant.
Energy does not come in blocks. It is important to realize, that in Physics today, we
have no knowledge of what Energy is. Without any blocks to count, what we have, are
formulas, for calculating some numerical quantity, and when we add it all together, we
get “58” [click]—or whatever the number would be for our particular situation. The
analogy also has, the following points. First, when we are calculating the energy in a
system [click], sometimes, some of the energy leaves [click] the system and goes
away—like the blocks going out the window—or sometimes some energy comes in
[click]–like the blocks that Bruce brought and left behind. In order to verify the
conservation of energy, we must be careful, both, in defining just what our system is and
what its boundaries are, and in making sure, that we have not allowed any extra energy
to come in, or taken any of the energy out. The second point is, that energy has a
number of different forms, and there is a formula, for each one. When we total up the
formulas, for all of these contributions, the result will not change, except for the energy
going in, and out [click].
Then what are the different forms, [slide 6], that Energy can take, as we know them?
When we write, the Conservation of Energy equation, we must account, for the
contributions of Gravitational Energy [click], and Kinetic Energy [click], and Heat
Energy [click], Elastic Energy [click], Electrical Energy [click], Chemical Energy
[click], Radiant Energy [click], Nuclear Energy [click], and finally, Mass Energy
[click]. We’ll look closer at each of these forms in a moment, and at how Energy can
move from one of these forms to another. But first, it’s important to point out, that
these forms do not necessarily tell us anything, about the more fundamental nature of
Energy; these are simply the terms in our equation. These represent, the different
things that we can measure, the weights of toy boxes, and the water levels of mop
buckets. These are, in some ways quite arbitrary, and the forms of Energy, that one
chooses to consider, may depend on the kinds of problems that one is trying to solve. Your
textbook has some different terms, and a chemical engineer uses a terminology, different
than that of an electrical engineer. This is a way that scientists and engineers, like me,
can stake out territory, but it makes it difficult for the student!
When we look closer at each of the terms—and you will see this in a moment—we find
that there are, perhaps only three basic manifestations of energy. There are three
particular, things, about our Universe, that require, or contain, or are composed of,
Energy. [slide 7] It can be difficult to say just what causes what, since they are
inseparable. But for some reason, there is inherently, Energy in Force [click], Energy
in Mass [click], and Energy in Motion [click]. Wherever you see one of these, you see
Energy, and more of one means more of the other. I wonder, if any of you will
remember, in what equation you have seen these particular quantities together, before?
Referring back to the forms of Energy in our list, we will look at Mass Energy first
[slide 8]. We calculate mass energy, using Einstein’s famous equation [click],
E  m  c2 ,
which he published in 1905. Einstein figured out, that an object has energy, from its
sheer existence, and the proportion constant between an object’s mass, and the energy
from that mass, is the square of the absolute speed of light. So mass and energy are
equivalent—what a strange concept! And with this relationship, we can see that, the
Law of Conservation of Mass [click], and Law of Conservation of Energy [click] are
really one and the same [click]. In fact, the stars [click], powered by nuclear fusion,
are places where Mass is converted to Energy—where the Universe subtracts, from the
mass side of the ledger, and adds to the energy side. The Energy of Mass is one of our
fundamental manifestations.
Another of the fundamental manifestations, is the Energy of Motion [slide 9], also
known as Kinetic Energy. It is true that an object has energy, if it is in motion—or, to
put it another way, Energy is required to put an object in motion. The energy
associated with this motion, is given by the famous equation [click] for kinetic energy,
E
1
 m  v2 .
2
which says that kinetic energy is proportional to the square of its velocity, with the
proportion constant as one-half the object’s mass.
We calculate this term, for a particular object, but we also know that objects are made of
atoms, and so we are assuming that the collection of atoms that comprise that object,
are moving and acting as one [click]. But is this actually what happens, or rather, is
this all that can happen, within an object [click]? It is actually true that, the atoms
within any structure, can, and always do, jiggle around quite independently. When a bat
strikes a baseball, the atoms of the baseball, on average, take off at a particular velocity.
But they do not all, move at that velocity. It is quite possible that none are, because they
are all jiggling around against each other. We could calculate, the kinetic energy of each
atom, using formula (2). But that quickly becomes problematic when, for example
[slide 10], a single gram of carbon contains around 51022 atoms, in other words, 50
billion trillion atoms [click], or, 50,000,000,000,000,000,000,000(!) [click] atoms in it.
Since we can’t keep track of any, significant number, of atoms, we account for this
internal jiggling on average, as Heat Energy [slide 11]. Whenever objects are set in
motion, or contact one another, the atoms in the objects get jostled around. If the atoms
in a solid, shake hard enough, they can break free, and the solid melts. Now, the atoms
are bouncing around, against each other, and if they start to bounce hard enough, they
can fly off [click], and the liquid evaporates. When large collections of atoms are
moved, the individual atoms are excited. External kinetic energy, becomes internal
kinetic energy, until the objects finally slow down, and stop. What a drag! But we
should be thankful for this—otherwise, nothing would ever stay where we put it! Jokes
aside, we see that what we call Heat Energy, is really that fundamental Energy of
Motion.
The third fundamental category to discuss is then, the Energy of Force. Let me first
explain that, we understand there to be, Four Fundamental Forces [slide 12], that
govern all the interactions of matter. These are, in order of relative strength, the
Strong Nuclear Force, the Electromagnetic Force, the Weak Nuclear Force, and the
Gravitation Force. In broad terms [click], the Strong Nuclear Force, is the force that
binds, protons and neutrons together, in the nucleus of an atom. [click] The
Electromagnetic Force, is the attraction between positive and negative charges. [click]
The Weak Nuclear Force, causes the radioactive decay of a neutron, into a proton, an
electron, and an antineutrino. And of course [click], the Gravitation Force is, the
mutual force of attraction between all matter. As far as anyone has been able to
determine, these four forces, and these four forces alone, govern the observable behavior
of the Universe. We will not go into these forces in any more detail today; it is enough
that we know that they exist. Actually, it has been found that, at much higher
temperatures (or in other words, much higher energies!), that the Electromagnetic and
the Weak Nuclear Forces combine into a single, Electro-Weak Force. This would leave
us, with only three, fundamental forces. And it has been theorized, that at much higher
temperatures still, the Strong Nuclear Force will merge into the Electro-Weak Force,
leaving out only Gravity. At that point, we surely have to wonder, is there not some
way to combine them all?, and the search for such a “Grand Unified Theory” [click]
has long been underway. For now, let us see how all this talk, of forces, leads us to
Energy [slide 13].
Well, first we must come up with a way to describe what a Force does. We could say,
that a force simply, distorts or bends space [click], in such a way that, extra energy is
required to move against the force [click], while extra energy is released by moving
with the force [click]. We are made aware of this fact, whenever we climb up and
down stairs, for example, or drop something, or when we move two magnets together.
The formula for this energy is simply [click],
E  F d ,
that is, the strength of the force, times the distance moved through it. The inherent
energy, associated with one location, in a force field, compared to another, is most
commonly referred to, as Potential Energy [slide 14]. The example of Potential
Energy, with which we are most familiar [click], is Gravitational Energy, which is, of
course, associated with the Gravitation Force. But there is Potential Energy, likewise
associated, with the other three fundamental forces as well. When we speak of Nuclear
Energy [click], as in, nuclear reactors or nuclear bombs, we are speaking of that
energy, associated with the Strong and Weak Nuclear Forces, the binding and releasing
of nuclei and nuclear particles. Similarly, it is the Electromagnetic Force [click], that
is the associated with Chemical, Electrical, Elastic, and Radiant Energies. Chemical
Energy, is the energy that comes from binding atoms together, into molecules, and
Elastic Energy, is the energy that comes from stretching, but not breaking, those bonds.
Electrical Energy, has to do with moving around excesses of positive or negative
charges, and Radiant Energy, is in the form of coupled electrical and magnetic fields—
force fields.
We can see, that Energy is both a very simple, and a very complex, thing. [slide 15]
We start with, some fundamental concepts—mass, relative motion, a handful of forces,
space-time itself, and this thing called Energy—yet somehow, these few things combine,
to yield, for example, me, and you, and all of this. How does this happen? Or rather,
why does it happen, in this way, as opposed to some other way? Why does Energy, take
one form, over another, and why does it, change forms, from one to another? When
does it change forms? How quickly does it change forms? Whew! Well, the details of
these questions, not to mention any others you could imagine, could occupy (and indeed,
have occupied) many lifetimes, and we still don’t know all the answers! Since we do not
wish to spend a lifetime here (I have someplace to be later), it is therefore necessary
that, the things I leave out, will far outnumber the things I include, in today’s
discussion. Even so, there is one more idea, that I simply must pass along, and it is this:
Energy flows downhill [slide 16]. Allow me to explain [click].
It is another strange fact of our Universe, that things tend toward disorder. A messy
room will not clean itself up—our friend Dennis could tell us that!—and if left alone, it
would become dusty and moldy, the walls and roof themselves would eventually fall,
weeds would grow up through the floor, and at some point, we could hardly tell, that
there had ever been a room at all. This fact, is called Entropy [click], and, like
everything else really, it has to do with quantum mechanics and randomness, but the
name is not important. What we care about is Energy, and as it pertains to Energy, it
means that Energy, will tend to spread itself out, as Heat [click]. Any time, that
Energy changes forms, any time there are interactions of Matter, more and more
Energy is “lost” to Heat. For this reason, reactions, and transfers of Energy, must
naturally occur in this direction of increasing Heat, much the same as water must
naturally flow downhill. This is an interesting fact, since it is the only law of Physics, of
which I am aware, that gives Time a direction. Most laws of Physics, work equally well,
forwards or backwards. If I were to compress a spring, and then return it to its original
position, the only evidence, that anything had happened at all, is the slight increase in the
temperature of the spring. If we were to videotape the event for posterity, we could
watch the tape, backwards and forwards, and it would look the same, with only the
increase or decrease in Heat to give us the direction.
In this way, in every event that takes place, and in every event that has ever taken place,
heat has increased, and randomness has increased, and Energy has flowed, downhill.
Now, if this idea has sunk in, and if you can start to think through the implications, you
may wonder, How Can This Be? If Energy flows downhill, if randomness is increasing,
where does all this structure come from? All this complexity, all this Life? The answer is
that the Universe, and Space, have a shape, and that shape determines how the energy
flows, in the same way that the shape of a water slide determines how the water flows
[click]. Now, some remarkable things happen in the course of that flow. Sure, the
water flows downhill, and sure, it follows this curve or that curve. But, in some
particular spot, the water might splash upwards, or, a little whirlpool might form, spin
for a while, then dissipate, or, in our Universe of Energy, a person might be born, live,
and die. We see that, the shape of the waterslide, does not have to be very complex, and
in fact, even through a straight pipe, water will twist and tumble. Now, if we can
imagine, an enormous waterslide, stretching as far as the eye can see, with more twists
and turns than we can count, and through it all flows Energy, and it is not so difficult to
imagine that, all the Physical Universe, is but whirlpools and turbulence.
Now, if you have been paying attention, you must undoubtedly have, one more question
[slide 17]. How did the Energy get up the hill, to begin with? Ah, I said at the
beginning, that our discussion would take us to the limits, of our understanding—and
here they are. If you can one day answer, this question, then, in your Nobel prize
acceptance speech, I hope you will make reference to me. Science has no answer to this.
Oh sure, we might talk about something called a Big Bang, but what caused the Big
Bang? What came before it? With the laws of Physics that we have, scientists can
calculate what happened, back to a tiny fraction of a second, after, the Big Bang, but they
cannot get to it, and they cannot go before it. How it started, and why, may not even be
questions for scientists, and at the very least, it is not a question for us today. I hope
that this lecture, has been of some interest to you. Thank you, and good day.
[slide 18, optional, if time required] (Discussion of available energy; Energy sources
versus energy forms; Energy production and societal needs)