PHYSICS FOR FUTURE PRESIDENTS

2003 Richard A. Muller

Chapter 1. Energy and Power

> At the end of the Cretaceous period, the golden age of dinosaurs, an
> asteroid or comet about 10 miles in diameter headed directly towards
> the Earth with a velocity of about 20 miles per *second*, over ten
> times faster than our speediest bullets. Many such large objects may
> have come close to the Earth, but this was the one that finally hit.
> It hardly noticed the air as it plunged through the atmosphere in a
> fraction of a second, momentarily leaving a trail of vacuum behind it.
> It hit the Earth with such force that it and the rock near it were
> suddenly heated to a temperature of over a million degrees Centigrade,
> several hundred times hotter than the surface of the sun. Asteroid,
> rock, and water (if it hit in the ocean) were instantly vaporized. The
> energy released in the explosion was greater than that of a hundred
> million megatons of TNT, 100 *teratons*, more than ten thousand times
> greater than the total U.S. and Soviet nuclear arsenals.. . . Before a
> minute had passed, the expanding crater was 60 miles across and 20
> miles deep. It would soon grow even larger. Hot vaporized material
> from the impact had already blasted its way out through most of the
> atmosphere to an altitude of 15 miles. Material that a moment earlier
> had been glowing plasma was beginning to cool and condense into dust
> and rock that would be spread world wide.. . .
>
> \-- adapted from Nemesis (1987)

Few people are surprised by the fact that an asteroid, the size of Mt.
Everest, could do a lot of damage when it hits the Earth. And it is not
really surprising that such bodies are out there. The danger has been
the subject of many movies, including *Deep Impact,* *Meteor,* and
*Armageddon*. Asteroids and comets frequently come close to the Earth.
Every few years, there is a newspaper headline about a \"near miss\" in
which an object misses the Earth by \"only a few million miles.\" (That
is hardly a near miss. The radius of the Earth is about 4000 miles. So a
miss by, say, four million miles would be a miss by 1000 Earth radii.)

But why should an asteroid impact cause an explosion? The asteroid was
made of rock, not dynamite. And why such a big explosion? But then \--
what is an explosion, after all?

**Explosions and energy: asteroids, TNT, and cookies**

An explosion occurs when a great deal of stored energy is suddenly
converted into heat in a confined space. The hot gas has enormous
pressure, that is, it puts a great force on everything that surrounds
it. The gas expands rapidly and pushes anything near it out of the way.
The flying debris is what we call an explosion. It doesn\'t matter what
the original form of the energy is; it could be kinetic energy (the
result of motion) like the energy of the asteroid, or chemical energy
like the energy in TNT. It is the rapid conversion of this energy into
*heat energy* that is at the heart of the explosion.

So far, I have explained almost nothing, because I haven\'t explained
what energy is, or what it means for it to occur in different forms, or
what heat is, or why the sudden production of heat should cause the
great forces that lead to destruction. But that is where we are headed
in this chapter, and in the next. These concepts are not self-evident,
and they were only understood in the 1800s. For now, let\'s define
energy as something that can be converted into heat. Heat is something
that raises the temperature of material, such as water. For now, you can
take the definition of energy to be *anything that can be converted to
heat*.[^1]

Before we get too abstract, let\'s get a sense of the *amount* of energy
in different objects. To make the comparison fair, I\'ll let each object
weigh one gram. [^2] Table 1.1 shows the masses of some common objects
in grams. The metric system is reviewed in Appendix 00; for now you
should try to remember that a penny weighs about 3 grams; a nickel
weighs about 5 grams.

Table 1.2 Now look at Table 1.2. This table will be very important in
this chapter, and it contains some numbers that surprise surprise most
people when they first see them. As I mentioned, all the examples are
assumed to weigh 1 gram. The table gives the energy in *Calories* (Cal),
also known as \"food Calories.\" These are the Calories that are listed
on containers of food. A typical human eats food every day that contains
about 2000 Calories of food energy.

More technically, a Calorie is defined as the amount of energy that it
takes to heat a thousand grams (1 kilogram) of water by 1 degree Celsius
(or \"Centigrade\"), a temperature change equal to 1.8 degrees
Fahrenheit. To make comparisons easier, the Table 1.2 lists not only the
amount of energy per gram, but its ratio to the energy contained in the
explosive TNT (trinitrotoluene).

Beware: If you have taken a course in biology, chemistry, or physics,
you may have encountered an energy unit called a *calorie* spelled with
a small c. One calorie (cal) is 1/1000 of a food Calorie (Cal). This is
a terrible convention, but I can\'t change it.[^3] It\'s not my fault.
To distinguish the two, the food Calorie should always be capitalized,
although in popular writing---including the nutrition information on
food-can labels---it often is not. But for us, 1 Cal = 1000 cal.

# Table 1.1 Masses of common objects in grams

+-----------------------------------------+----------------------------+
| **1 cubic centimeter of water**         | **1 gram**                 |
+-----------------------------------------+----------------------------+
| **1 penny**                             | **3 grams**                |
+-----------------------------------------+----------------------------+
| **1 nickel**                            | **5 grams**                |
+-----------------------------------------+----------------------------+
| **cup of water**                        | **227 grams**              |
+-----------------------------------------+----------------------------+
| **a pound of anything**                 | **454 grams**              |
+-----------------------------------------+----------------------------+
| **small elephant, small car**           | **1,000,000 grams**        |
|                                         |                            |
|                                         | **= 1 metric ton**         |
|                                         |                            |
|                                         | **= 1.1 English tons**     |
+-----------------------------------------+----------------------------+

**Table 1.2. Relative energies**

  ---------------------------- -------------------- ---------------------
  **object**                   **Calories in one    **compared to TNT**
                               gram**               

  bullet (moving at speed of   0.01                 0.015
  sound, 1000 ft per second)                        

  battery (flashlight)         0.01                 0.015

  battery (computer)           0.1                  0.15

  TNT (trinitrotoluene)        0.651                1

  modern High Explosive (PETN) 1.06                 1.6

  chocolate chip cookies       5                    8

  gasoline                     10                   15

  methane gas (CH~4~)          13                   20

  hydrogen gas (H~2~) for fuel 26                   40
  cell                                              

  asteroid or meteor (30       100                  154
  km/sec)                                           

  uranium-235                  20,000,000           30,000,000
  ---------------------------- -------------------- ---------------------

Ponder the table of energies. I think all of the following are
surprises: the very large amount of energy in chocolate chip cookies,
compared to TNT; the very small amount of energy in a battery, compared
to gasoline; the high energy in a meteor, compared to a bullet; the
enormous energy available in uranium, compared to anything else on the
table.

*TNT vs. chocolate chip cookies*.

Both TNT and chocolate-chip cookies have *chemical energy*, which is
energy contained in the forces between its atoms. When TNT is detonated,
these forces push the atoms apart at very high speeds. Yet chocolate
chip cookies contain eight times as much energy as the same weight of
TNT. How can that be true? Why can\'t we blow up a building with cookies
instead of TNT?

What makes TNT so useful for destructive purposes is that it can
*release* its energy---transfer its energy to the surroundings---very
very quickly. The chemical energy is transformed into heat and kinetic
energy. The TNT is converted into hot gas, and this expands so suddenly
that it shatters surrounding objects. A typical time for 1 gram of TNT
to release all of its energy is about one *millionth* of a second.
Sudden release of energy can lead to the greater forces that are
necessary to break strong material. [^4]

Even though chocolate chip cookies contain more energy than a similar
weight of TNT, the energy is normally released more slowly, through a
series of chemical processes that we call metabolism. This requires
several chemical changes (e.g. resulting from mixing the food with acid
in the stomach and with enzymes in the intestines), and finally the
reaction of the food with oxygen (taken in by the lungs and stored in
red blood cells). In contrast, TNT contains all the molecules it needs
to explode; it needs no mixing, and as soon as part of it starts to
explode, that triggers the rest. If you want to destroy a building, you
can do it with TNT. Or you could hire a group of teenagers, give them
sledge hammers, and feed them cookies. Since the energy in chocolate
chip cookies exceeds that in an equal weight of TNT, each gram of
chocolate chip cookies will ultimately do more destruction than would
each gram of TNT.

## Gasoline

Gasoline releases its energy (turns it into heat) by a chemical reaction
with oxygen, and so it must be well-mixed with air to explode. In an
automobile, this is done by the carburetor or the fuel injector. The
explosion takes place in a cylindrical cavity known as the cylinder. The
energy released from the explosion pushes a piston down the axis of the
cylinder, and that is what drives the wheels of the car. An \"internal
combustion engine\" can be thought of as an \"internal explosion
engine.\"[^5] The *muffler* on a car has the job of making sure that the
sound from the explosion is muffled, and not too bothersome. Some people
like to remove the muffler (especially some motorcyclists) so that the
full explosion is heard; this give the illusion of much greater power.
(Removing the muffler also lowers the pressure just outside the engine,
so that the power to the wheels is actually increased, although not by
very much.)

## Batteries vs. gasoline

A battery stores its energy in the chemical form, and converts it
directly to electric energy. (Electric energy is in the form of
electrons moving through wires; we\'ll discuss this further in Chapter
??.) The chief advantage of electric energy is that it can be easily
transported along wires, and converted to motion with an electric motor.

Table 1.2 shows that gasoline contains 1000 times as much energy per
gram as does a flashlight battery, and 100 times as much as does an
expensive computer battery. That observation explains why most
automobiles use gasoline instead of batteries as their source of energy.
A typical car carries about 100 lb of gasoline. Carrying 100 times that
in battery weight (10000 lb = 5 tons) is not a viable option, even if
the batteries were cheap. But batteries have advantages in some
circumstances. In World War II, when submarines had to submerge (and
could not obtain oxygen), their energy source was a huge number of
batteries stored beneath the decks. (When on the surface, or
\"snorkeling depth\", the submarines ran on diesel fuel, a form of
gasoline. The diesel fuel also ran generators that recharged the
batteries.)

Nevertheless, there is a fascinating new technology called \"hybrid
automobiles\". In a hybrid, a small gasoline engine provides energy to
charge a battery; the car then gets its energy from the battery. This
has more value than you might guess: the gasoline engine can be run at a
constant rate, under ideal conditions, and so it is two to three times
as efficient as the engine in ordinary cars. In addition, hybrid engines
can convert some of the mechanical motion of the automobile (e.g. its
extra speed picked up when descending a hill) back into stored chemical
energy in the rechargeable battery. Hybrid engines are becoming very
popular, and in a few years, they may be the most common type of
automobile, particularly if gasoline prices rise.

## Hydrogen gas vs. gasoline

Notice from Table 1.2 that hydrogen gas has 2.6 times more chemical
energy per gram than gasoline. Popular articles about the future
\"hydrogen economy\" are partially based on this fact. The other
attractive feature is that the only waste product from hydrogen fuel is
water, created when the hydrogen is chemically combined with oxygen from
the air to make H~2~O (water). This can be done using an advanced
technology called a fuel cell. to convert the chemical energy directly
into electricity.[^6]

A fuel cell looks very much like a battery, but has a distinct
advantage. In a battery, once the chemical is used up, you have to
recharge it with electricity produced elsewhere, or throw it away. In a
fuel cell, all you have to do is provide more fuel (e.g. hydrogen and
oxygen). Perhaps you\'ve seen a demonstration of \"electrolysis\" in
which electricity is passed between two terminals through water, and
hydrogen and oxygen gas are produced at the terminals. A fuel cell is a
very similar device, but run backwards. Hydrogen and oxygen gas are
compressed at the electrodes, they combine to form water, and
electricity flows through wires that connect one terminal to the other.

The main technical difficulty of the hydrogen economy is that hydrogen
is not very dense. Even if liquefied, it has a density of only 0.071
grams per cubic centimeter, a factor of 10 less than gasoline. Per gram,
hydrogen is 2.6 as good as gasoline. Put these together, and we find
that a gallon of liquid hydrogen stores about four times less energy
than one gallon of gasoline. Most experts say the factor is closer to
three times worse, since hydrogen can used more efficiently than
gasoline. Nevertheless, it is possible we will be driving
hydrogen-driven cars in the near future. It is also possible that
hydrogen will be more valuable as a fuel for airplanes, since for these
the low weight of the hydrogen may be more important than the fact that
it takes more volume than gasoline.

Where does the hydrogen come from? There is virtually no free hydrogen
gas (or liquid) in the environment; it must be manufactured, and that
takes energy. A typical hydrogen production plant of the future would
start with a power plant fueled by coal, gasoline, nuclear fuel, or
solar energy. That power plant uses this energy to convert ordinary
water into hydrogen and oxygen (through a process called electrolysis).
Then, for example, the hydrogen could be cooled until it is turned into
a liquid, and then transported to the consumer.

Thus hydrogen is not a *source* of energy; it is a means for
*transporting* energy. Although the fuel cell produces no pollution
(only water), it is not quite right to say that a hydrogen-based economy
is pollution-free unless the plant that used energy to produce the
hydrogen is also pollution-free. Nevertheless, the use of hydrogen as a
fuel is expected to be environmentally less harmful than gasoline for
two reasons: power plant can, in principle, be made more efficient than
the automobiles; and the power plant can have more elaborate
pollution-control devices than an automobile. Other people like the idea
of hydrogen as fuel because it moves the sources of pollution away from
the cities, where the high concentration of pollutants can be more
dangerous to human health.

## Gasoline vs. TNT

On Nov. 6, 2002, the US started dropping 15,000 lb \"fuel-air
explosives\" on Taliban soldiers in Afghanistan. What is a fuel-air
explosive? You can probably guess: mostly gasoline. The gasoline is
dropped from an airplane, and descends slowly on a parachute. As it near
the ground, a small charge of high explosive (probably only a few pounds
worth) explodes in the center, dispersing the gasoline and mixing it
with air -- but not initially igniting it. Only when the gasoline is
spread out and well-mixed with air, it is ignited by a second explosion.
The explosion is spread out over a large area, so it doesn\'t exert the
same kind of intense force that it takes to break though a concrete
wall. But it has enough energy released to kill people and other
\"soft\" targets. What makes it so devastating is the fact that 15,000
lbs of gasoline contain the energy equivalent of 225,000 lbs of TNT. So
although 15,000 lbs sounds bad, in fact it is much worse than it sounds.
Once the soldiers had seen the fuel-air explosive from a distance, the
mere approach of a parachute could induce panic.

Discussion question: In the Spanish revolution, the rebels invented a
device that later became known as a \"Molotov cocktail.\" It was a
bottle filled with gasoline, with a rag stuck in the neck. The rag
soaked with gasoline, ignited, and then the bottle was thrown at the
enemy. It broke upon impact. What happened next? Why did such a weapon
quickly achieve a strong reputation as an ideal weapon for
revolutionaries?

In most movies, when a car crashes, it explodes. Does this happen in
real life? Have you ever witnessed the scene of a car crash? Had an
explosion taken place? (Hint: if gasoline is not well-mixed with air, it
can not explode, but can only burn.)

*uranium vs. TNT*

The most dramatic entry in the table is the enormous energy in
uranium-235: 30 million times that of TNT. We will discuss this in
detail in chapters 3 and 4. For now, there are only a few important
facts to know. The source of energy is the enormous forces inside the
atom\'s nucleus. For most atoms, this energy cannot be easily released,
but for uranium-235 (a special kind of uranium that makes up only 0.7%
of natural uranium), the energy can be released through a process called
a \"chain reaction\". This enormous energy release is the principle
behind nuclear power plants and atomic bombs. Plutonium-239 is another
atom capable of releasing such huge energy.

Compared to gasoline, U-235 can release 1.5 million times as much
energy. Compared to Chocolate-chip cookies, it releases about 0.75
million times as much. The following approximation is so useful that it
is worth memorizing:

> A nuclear chain reaction releases about a million times as much energy
> as a chemical reactions.

**What *is* energy?**

We have talked about many different kinds of energy: chemical energy (in
food) and heat energy (in explosions and in water). The energy in a
moving bullet or asteroid is called \"kinetic\" energy. The energy
stored in a compressed spring is called \"potential energy.\" Despite
its name, potential energy does *not* mean that it is something that can
\"potentially\" be converted to energy; potential energy *is* energy.
Nuclear energy is the energy stored in a nucleus, released when the
nucleus is broken. Gravitational energy is the energy that an object has
at high altitude; when it falls, this energy is converted into kinetic
energy. As the table shows, all these energies can all be measured in
Calories.

Many physics texts like to refer to chemical, nuclear, and gravitational
energy as different forms of potential energy. This definition lumps
together in one category all the kinds of energy that depend on shape
and position, e.g. whether the spring is compressed, or how the atoms in
a chemical are arranged. This lumping is done in order to simplify
equations; there is no real value in doing it in this text, as long as
you realize that all energy is energy, regardless of its name.

I keep on talking about energy, but I still haven\'t said what energy
*is*. I have been deliberately avoiding that question, because energy is
better understood through examples than through definition. However, in
case you really want to know, here are the formal definitions in
physics:

> **Energy** is defined as \"the ability to do work.\" (So now we have
> to define *work*.)
>
> **Work** is defined as a force times the distance through which the
> force moves. (The only distance that counts, in the physics
> definition, is the distance moved in the same direction as the force.)

I don\'t consider these definitions to be very useful for a future
President. In fact, they may not be very useful to anybody. What does
\"ability\" mean? Does a compressed spring have \"ability\"? Is negative
energy *inability*? Yet I wanted to give you these definitions since you
will see them if you look at other physics texts. These definitions are
equally obscure to the beginning physics major as they are to you (as I
well remember from my first physics course). Physicists learn the
meaning of energy by familiarity with numerous examples, from seeing how
energy is converted, and from the law of \"conservation of energy\"
which we will soon discuss. In physics texts, you\'ll see the definition
of energy E written as E = W. Then you\'ll see the definition of work
written as W = F x, where F is the force, and x is the distance. These
are useful equations for calculations, but I don\'t think they really
help you to *understand*. That comes with experience, just as
understanding other people comes only as you get to know them.

There is, however, one formal definition that you will find very useful:
Power is the rate of energy release, i.e. it is the energy per second.
In equation form:

> **P = E/t**

where **P** is the power, **E** is the energy, and **t** is the time to
release it (or to convert it to another form, e.g. heat or motion).

TNT may have less energy than an equal mass of chocolate chip cookies,
but it can deliver more power. Of course, it can\'t deliver this power
for very long, because it runs out of energy. TNT delivers all the power
it contains in just one millionth of a second.

# ENERGY IS CONSERVED. SO WHY CONSERVE ENERGY?

When the chemical energy in gunpowder is suddenly released (turned into
heat energy), the gases that come out are so hot that they expand
rapidly and push the bullet out of the gun. In doing this pushing, they
lose some of their energy (they cool off); this energy goes into the
kinetic energy of the bullet. One form of energy is being converted into
other forms.

One of the most useful discoveries in science is that, when you add up
all the different kinds of energy, the total amount doesn\'t change.
When a bullet hits a target and stops, some of the kinetic energy is
transferred to the object (ripping it apart), and the rest is converted
back into heat energy. (The target and the bullet each get a little bit
warmer when they collide.) This fact, that the total energy is always
the same, is called \"The conservation of energy.\" It is one of the
most fundamental and most useful laws of physics.[^7]

But if energy conservation is a law of physics, why are we constantly
admonished (by our teachers, our political leaders, and by our children)
that we should conserve energy? Isn\'t energy automatically conserved?

Yes it is, but not all forms of energy have equal economic value. It is
easy to convert chemical energy into heat, and very difficult to convert
it back. When you are told to conserve energy, what is really meant is
\"conserve useful energy.\" The most useful kinds are chemical (e.g. in
gasoline) and in potential energy (e.g. the energy stored in water that
has not yet run through a dam to produce electric power).

**Measuring Energy**

The easiest way to measure energy is to convert it into heat, and see
how much it raises the temperature of water. As mentioned earlier, the
Calorie is defined as the amount of energy that it takes to raise one
kilogram of water by one degree Celsius (also known as one degree
Centigrade; one degree Celsius is 1.8 degrees Fahrenheit.) Another unit,
the joule, is frequently used. There are 4182 joules in one Calorie. A
kilojoule = 1000 joules. Another unit of energy that we will discuss
shortly is the kilowatt-hour, abbreviated kwh. This is the unit that you
pay for when you buy electric energy from a utility company. A kwh is
the energy delivered when you get one thousand joules per second for
3600 seconds (an hour), i.e. it is 3.6 million joules = 861 Calories.

# TABLE 1.3 ENERGY UNITS

+-----------------------------+----------------------------------------+
| **Energy Units**            | **Definition or Equivalent**           |
+-----------------------------+----------------------------------------+
| Calorie                     | heats 1 kg of water by 1 C             |
|                             |                                        |
|                             | 1 Cal = 1/4182 joules                  |
+-----------------------------+----------------------------------------+
| joule                       | 4182 Calories                          |
|                             |                                        |
|                             | ≈ Energy to lift 1 kg by 10 cm         |
|                             |                                        |
|                             | ≈ Energy to lift 1 lb by 9 inches      |
+-----------------------------+----------------------------------------+
| kilojoule                   | 1000 joules                            |
|                             |                                        |
|                             | 4.18 megaCalories = 4.18 x10^6^        |
|                             | Calories                               |
+-----------------------------+----------------------------------------+
| megajoule                   | 1000 kilojoules = 10^6^ joules         |
|                             |                                        |
|                             | costs about 5c from electric utility   |
+-----------------------------+----------------------------------------+
| kwh (kilowatt-hour)         | 861 Calories                           |
|                             |                                        |
|                             | 3.6 megajoules                         |
|                             |                                        |
|                             | costs about 20 cents from electric     |
|                             | utility                                |
+-----------------------------+----------------------------------------+

**Calories per second, watts and horsepower**

You can destroy a building using cookies, teenagers, and hammers, but
you can do the job a lot faster with TNT. A gram of TNT has less
chemical energy than a gram of chocolate chip cookies, but it can
transfer its energy to the building much faster*.* Another way of saying
this is that TNT can deliver a lot more power.

As I mentioned earlier, *power* means the rate of energy transfer.
Recall that the *rate* at which something happens is the \"something\"
divided by the time---for example, miles/hour = miles per hour, or
births/year = births per year. Power is the *energy transferred per
second*. Thus, when 1 gram of TNT releases 0.651 Calories in 0.000001
sec (one millionth of a second) the power is 651,000 Calories per
second.

Although power can be measured in Calories per second, there are two
other units that are far more common: the watt (one joule per second)
and the horsepower. The horsepower was originally defined as the power
that a typical horse could deliver, i.e. how much work the horse could
do every second. These days, the most common use of the term is to
describe the power of an automobile engine; a typical auto delivers 100
to 400 horsepower. James Watt, in the 1700s, was the first to actually
determine how big one horsepower is. One horsepower turned out to be
0.18 Calories per second. (Does that sound small to you? Or does it
illustrate that a Calorie is a big unit?) The other common unit today is
the *watt*, was named after him. A watt is one joule per second. It is
the unit that is commonly used to measure electric power. It is common
to capitalize the unit, since it is also the name of a person.

Other common units are the kilowatt (1 kW = 1000 watts), the megawatt (1
MW = 1 million watts), and the gigawatt (1 GW = one billion watts =
10^9^ watts). The abbreviation for million is capital M, and for billion
(giga) is capital G. So, for example, 1000 kW = 1 MW = 0.001 GW. One
Calorie per second is approximately 4 kilowatts (see Table 1.3).[^8]

If you need to do engineering calculations, then you need to know that
one horsepower is 0.746 kilowatts. I do not recommend you try to
remember this; you can always look it up if you really need it. Instead,
remember the approximate equation:

1 horsepower ≈ 1 kilowatt

( ≈ means \"approximately equals\"). It is far more useful to remember
this approximate value than it is to forget the exact value.

**Table 1.3 Power examples**

+-----------------------+----------------------+-----------------------+
| **value**             | **equivalent**       | **example of that     |
|                       |                      | much power use**      |
+-----------------------+----------------------+-----------------------+
| watt                  | one joule per second | flashlight            |
+-----------------------+----------------------+-----------------------+
| 100 watts             |                      | bright lightbulb;     |
|                       |                      |                       |
|                       |                      | heat from a human     |
+-----------------------+----------------------+-----------------------+
| horsepower            | 746 watts            | human running fast up |
|                       |                      | flight of stairs      |
|                       | ≈ 1 kilowatt         |                       |
+-----------------------+----------------------+-----------------------+
| 1 kilowatt (1 kW)     | 1.3 horsepower       | small house (not      |
|                       |                      | including heat);      |
|                       | ≈ 1 horsepower       |                       |
|                       |                      | power in 1 square     |
|                       |                      | meter of sunlight     |
+-----------------------+----------------------+-----------------------+
| 100 horsepower        | 74.6 kW              | automobile            |
+-----------------------+----------------------+-----------------------+
| 1 megawatt (MW)       | 10^6^ watts          |                       |
+-----------------------+----------------------+-----------------------+
| 45 megawatts          | 60,000 horsepower    | 747 airplane;         |
|                       |                      |                       |
|                       |                      | small power plant     |
+-----------------------+----------------------+-----------------------+
| 1 gigawatt            | 10^9^ watts          | large coal, gas, or   |
|                       |                      | nuclear power plant   |
+-----------------------+----------------------+-----------------------+
| 3000 gigawatts        |                      | total average power   |
|                       |                      | use of United States  |
+-----------------------+----------------------+-----------------------+

-   Nonscientists often use the words *power* and *energy*
    interchangeably. They have the right to do that, since the terms
    pre-dated science. Science adopted these words and defined them more
    narrowly, to allow greater precision in scientific discussions and
    publications. But scientists were never given the \"rights\" to
    redefine these words. So when newspaper articles \"confuse\" power
    and energy, it is a valid defense to say that they are just using
    the words in their original imprecise meaning. When precision is
    needed (e.g. when the electric company sends you a bill, or when
    people specify the power of an automobile engine) people tend to use
    the more precise scientific definitions. In this book, and in this
    class, you should use the more precise scientific definitions. Think
    of it as if you are learning a second language, Scientific English,
    to be used when precision is important.

**power: HUMANS, Power plants, batteries**

Since energy is conserved, the entire energy industry never actually
produces or generates energy, it only converts it from one form to
another and transports it from one location to another. Nevertheless,
the popular term for this is \"generating power.\" (It is an interesting
exercise to read the words used in newspaper articles, and then
translate them into a more precise physics version.)

Here is a brief example of what happens between the power plant and the
lighting of a light bulb in your home. The original source of the energy
may be chemical (oil, gas, or coal), nuclear (uranium), or kinetic
(falling water). In a power plant, energy is converted into heat, which
boils water, creating hot compressed steam. The steam is allowed to
expand through a series of fans called a turbine. The turbine rotates
the crank of a device called an electric generator. We\'ll discuss how
electric generators work in more detail in a later chapter, but they
turn the mechanical motion into electric current, that is, into
electrons that move through metal. The main advantage of electric energy
is that it is easily transported over thousands of miles just using
metal wires, to your home.

Note again that, strictly speaking, power plants don\'t *create* energy;
they only *convert* it from one form to another. Nonetheless, the
typical English usage is that they \"produce\" power or energy.

A typical large power generating station produces electric power at the
rate of about one gigawatt = one billion watts = 10^9^ watts. This is a
useful fact to remember. It is true for both nuclear and oil/coal
burning plants. If each house or apartment required one kilowatt, then
one such power plant could provide the power for one million houses.
Small power plants typically produce 50 to 100 MW (megawatts). These are
often built by small towns to supply their own local needs. 100 MW will
provide power for about 100,000 homes (fewer if we include heating or
air conditioning).

In an electric power plant, not all the fuel energy goes into
electricity; in fact, about two thirds of the energy is lost into heat.
That\'s because much the steam does not cool completely, and because
much of the heat escapes into the surroundings. Sometimes this heat is
used to warm surrounding buildings. When this is done, the plant is said
to be \"co-generating\" both electricity and useful heat.

**Light bulbs.** Ordinary household light bulbs (sometimes called
\"incandescent\" or \"tungsten\" bulbs) work by letting electricity heat
a thin wire (called the filament) until it glows white hot. The filament
is protected by the glass bulb that gives the device its name. All of
the visible light comes from the hot filament, although the bulb itself
can be made frosted so that it spreads the light out, making it less
harsh to look at. The glass bulb protects the filament from touch (it\'s
temperature is over 1000 Celsius) and keeps away oxygen, which would
react with the hot tungsten and weaken it.

The brightness of the bulb depends on how much power it uses, that is,
on how much electricity is converted into heat each second. A bulb that
uses 100 watts is brighter than one that uses 60 watts. Because of this,
many people mistakenly believe that a watt is a unit of brightness, but
it isn\'t. A 13 watt *fluorescent* light bulb is as bright as a 60 watt
conventional (incandescent) bulb. Does that mean that a conventional
bulb wastes electricity? Yes. The extra electric power used does little
good; it just heats the bulb. That\'s why tungsten bulbs are hot, and
fluorescent bulbs relatively cool.

One kilowatt, the amount of power used by ten 100-watt bulbs, will
illuminate your home brightly, assuming you have an average-size house
and are using conventional bulbs. *Memory trick*: imagine that it takes
one horse to light your home (one horsepower ≈ 1 kilowatt).

**Sunlight.** How much power is in a square meter of sunlight? You know
from experience that it is much greater than that in an electric light.
The energy of sunlight is about 1 kilowatt per square meter. So the
sunlight hitting the roof of your car (about 1 square meter) is about 1
kilowatt ≈ 1 horsepower. And all of that energy is in the form of light.
When the light hits the surface, some bounces off (that\'s why you can
see it), and some is converted into heat.

Discussion question: Suppose you placed a kilowatt tungsten bulb in
every square meter of your home. Would the home then be as brightly lit
as it would be by sunlight? (Hint: a watt is not a unit of brightness,
but of energy delivered per second. In sunlight, all of that energy is
in the form of light. In an electric bulb, most of the energy goes into
heat.) Does your answer match your experience?

**Solar-generated power** . Many environmentalists believe that the best
source of energy for the long term future is solar. It is \"renewable\"
in the sense that sunlight keeps coming as long as the sun shines (and
the sun is expected to have many billions of years left). Solar energy
can be converted to electricity by using silicon solar cells, which are
crystals that convert sunlight directly into electricity. The power
available in sunlight is about one kilowatt per square meter. So, if we
could harness all of the solar energy falling a square meter for power
production, that energy would generate one kilowatt. But an inexpensive
solar cell can only generate about 15% of this amount, or about 150
watts per square meter. (The rest is converted into heat, or reflected.)
A more expensive solar cell (such as used on satellites to generate
power) is about 30% efficient, i.e. it can produce about 300 watts per
square meter.

You will sometimes hear someone say that solar power is not practical,
since to get enough power you would have to cover the entire country
with solar cells. Is this true? As we said in the previous paragraph,
from solar cells we get a kilowatt from 7 square meters. We would get a
gigawatt (a typical nuclear power plant equivalent) from 70 square
kilometers. This may sound big, but it really isn\'t. California has a
typical peak power use of about 50 gigawatts of electricity; to produce
this would take 350 square kilometers of solar cells. This would take
less than one thousandth (one tenth of one percent) of the 400,000
square kilometer area of California. That hardly counts as \"plastering
the state.\" (Besides, the solar plants would probably be placed in a
nearby state, such a Nevada, that gets less rain.)

Others argue that solar energy is available only during the day. Of
course, it is during the day that we have the peak power demand. But if
we are to convert completely to solar cells, then we will need an energy
storage technology. Many people think that large fuel-cells might
provide that.

Research topics: Why are we not using solar energy today? See what you
can find about the costs of solar cells and the cost of building such a
plant. (I\'ve talked to contractors who have told me that installation
of anything costs \$10 per square foot.) Would solar power be more
feasible in underdeveloped regions of the world?

-   **Solar powered automobiles and airplanes**. There is an annual race
    across Australia for solar powered automobiles. The fundamental
    problem with such a vehicle can be seen from the fact that one
    square meter of sunlight gives has about 1 kilowatt of power, which
    is equal to about one horsepower. Since expensive solar cells are
    only about 30% efficient, that means that you need more than three
    square meters of solar cell just to get one horsepower. (Typical
    automobiles use 100 hp or more.) To read more about the annual race,
    go to their homepage http://www.wsc.org.au/index.shtml.) The race is
    obviously among very low-powered vehicles!

> Given that low power, it is surprising to discover that a solar
> powered aircraft has successfully flown. Actually, the vehicle isn\'t
> truly an airplane \-- it doesn\'t have a pilot or passengers, so it is
> called an aircraft, a drone, or an UAV (for \"unmanned air vehicle\").
> The aircraft was named the *Centurian*. The solar cells are on the
> upper and lower surfaces of the wings; the cells on the undersides use
> light reflected off the earth. The solar cells have to be big, to
> gather enough solar power to run the engines, that give the aircraft
> lift, and yet light in weight. The Centurian has a wingspan of 206
> feet, greater than for a Boeing 747. The total power from the solar
> cells is only 28 horsepower. The entire weight of the Centurian is
> 1100 pounds. It has already set an altitude record for airplanes of
> 96,500 feet. (Conventional airplanes fly at about 40,000 ft.) The
> Centurian was built by AeroVironment, a company started by engineer
> Paul McCready, who designed the Gossamer Condor and the Gossamer
> Albatross. For more information, see the AeroVironment web page:
>
> http://www.aerovironment.com/area-aircraft/unmanned.html.

**Human power**. If you weigh 140 lbs, and run up a 12 foot flight of
stairs in 3 seconds, your muscles are generating about 1 horsepower.
(Remember: \"generating\" means converting from one form to another. The
muscles store energy in chemical form, and convert it to energy of
motion.) If you can do this, does that make you as powerful as a horse?
No. One horsepower is about as much power as most people can produce,
and only briefly---just try to keep it up for a minute. A horse can
produce 1 horsepower for a sustained period and more than 1 horsepower
for short bursts.

Over a sustained period of time, a typical person riding a bicycle can
generate power at the rate of about 1/7 = 0.14 of a horsepower. (Does
that seem reasonable? How much does a horse weigh compared to a person?)
A trained cyclist in excellent physical condition can do better: about
0.4 horsepower for several minutes. In 1979, cyclist Bryan Allen used
his own power to fly a super-light airplane, the Gossamer Albatross,
across the 23 mile wide English Channel. The Gossamer Albatross is that
it had to be made extremely light and yet stable enough to control. A
key aspect of the design was that it had to be made easy to *repair*.
Paul McCready, the engineer who designed it, knew that such a
light-weight airplane would crash frequently, for example, whenever
there was a large gust of wind. It flew only a few feet above the ground
(or water).

**Wind power**.

Wind is generated from solar energy, when different parts of the surface
of the earth are heated unevenly. (Uneven heating can come from many
causes, such as difference in absorption, differences in evaporation,
and differences in cloud cover.) Windy places have been used as sources
of power for nearly a thousand years. The \"windmill\" was originally a
mill (factory for grinding flour) driven by wind power, although early
windmills were also used by the Dutch for pumping water out from behind
their dykes. Many people are interested in wind power again these days
as an alternative source of electricity. Pilot wind generation plants
were installed at the Altamont Pass in California in the 1970s.

A \"forest\" of windmills has been proposed for construction on the
ocean, off the coast of Massachusetts, to supply commercial power. In
case you are interested, here are some of the details: there will be170
large windmills in a 5 mile by 5 mile square, connected to land via an
undersea cable. Each windmill would rise 426 feet from water level to
tip of the highest blade (the height of a 40 story building). They would
be spaced 1/2 mile from each other. The maximum power this forest would
be 0.42 gigawatt. The major opposition to the idea appears to be coming
from environmentalists who argue that the array destroys a wilderness
area, would kill birds, and creates noise that could disturb marine
animals. (Reference: New York Times, \"Offshore Harvest of Wind is
Proposed for Cape Cod\", Karen Lee Ziner, April 16, 2002.)

Wind power ultimately derives from solar, since it is difference in
temperature that drive the winds. The windmills cannot be spaced too
closely, since when a windmill takes energy from the wind, the wind
velocity is decreased, and the wind is made turbulent, i.e. it is no
longer flowing in a smooth pattern.

**Cost of Energy**

As stated earlier, a typical price for electric energy from an electric
utility is \$0.20 per kwh,. If we obtain our electric energy instead by
buying batteries, the price goes way up -- far more than most people
guess: \$1000 per kwh! [^9] That\'s 5000 times as expensive as the 20
cents per kWhr charged by the power company. Many people are astonished
when they first hear this. But everybody knows batteries are expensive.
That\'s why people who leave their lights on when they leave their
house, will be very careful to turn off their flashlight when they are
not using it.

Rechargeable batteries are much less expensive per kwh, since they can
be used over and over again. If I take into account the limited lifetime
of such batteries, then a typical rechargeable computer battery (one
that I own) costs about \$3 per kwh. [^10] In contrast, gasoline is
cheap. The net cost of useful energy from gasoline is about \$0.15 per
kWh, similar to the cost of electric energy.[^11]

Discussion question: is it a coincidence that energy from gasoline costs
about the same as energy from an electric power plant?

**The California \"energy crisis\" of 2001.**

That year, the state of California was unable to obtain the electricity
that the customers wanted. \"Rolling blackouts\" were instituted by the
state government, with different regions taking turns losing their
electric power. A lot has been written about this crisis, including the
possibility that companies such as Enron artificially worsened it. But
there is an aspect of the crisis that must be understood by anyone who
is trying to prevent similar crises, in California or anywhere. If you
know the technical difference between energy and power, then you can
understand that the crisis was due to an inability to obtain the
required *power*, not due to a shortage of energy.

Here is a paradox that might confuse you at first, but will ultimately,
deepen your understanding of the crisis. During the crisis, experts
realized that it made excellent sense to send electric energy from
California to the state of Washington! This was done at night. During
the day, Washington sent Calfornia electric energy. But the amount
California sent at night was twice as much as Washington sent during the
day. As a result, both states benefited. How can that be?

The answer is that California had plenty of gasoline to use as fuel in
electric generating plants. But it didn\'t have enough electric
generating plants -- industrial plants that convert gasoline to
electricity. California was limited in the electric power that it could
produce. The crisis hit each day during the hot afternoon, when people
throughout the state were using their air conditioning systems at full
power. There wasn\'t enough electric power being generated to provide
that demand.

So California imported electric power from the state of Washington.
Washington gets much of its electricity from hydro power, i.e. from
power generated by water flowing downhill through turbines near dams.
They had a limited amount of water (generated by the winter snows) and
once Washington used it all up, it would have to use more expensive
gasoline-generated power. Yet they still decided to generate more power
than they needed during the day, using up their dammed water, to send to
California (over power lines). It was not due to generosity. In the
evening and night, they shut down their dams and saved water, as
California supplied their energy needs. The deal was simple: California
borrows energy during the day, when it needed the high power, and pays
back energy during the night, giving Washington back twice what it had
loaned. Washington saved its precious water, and California got the peak
power it needed.[^12]

**Kinetic energy: The Death of the dinosaurs**

Let\'s go back to Table 1.2 again, and discuss another surprising fact
from that table: the energy of motion of a typical meteor is150 times
greater than the chemical energy of an equal mass of TNT.

Unlike chemical energy, which usually has to be measured (not
calculated), there is a simple equation for kinetic energy:

$E = \frac{1}{2}{mv}^{2}$ \-- kinetic energy equation

To use this equation, *v* must be in meters per second, and *m* in
kilograms. The energy *E* then comes out in joules. To convert to
Calories, divide joules by 4128.

Notice how similar the kinetic equation is to Einstein\'s famous
equation of special relativity:

$$E = {mc}^{2}$$

In this equation, *c* is the velocity of light. The similarity is not a
coincidence, as you will see when we discuss relativity later in this
book. Einstein\'s equation states that the energy hidden in the mass of
an object is approximately equal to the classical kinetic energy that
object would have if it moved at the speed of light. For now,
Einstein\'s famous equation might help you to remember the less famous
kinetic energy equation.

Let\'s take a closer look at what the kinetic energy equation tells us
about the relation of kinetic energy to mass and speed. First, the
kinetic energy of a moving object is directly proportional to the
object\'s mass. This is very useful to remember, and can give you
insights even without using the equation. For example, In a 2-ton SUV
has twice as much kinetic energy as a 1-ton Volkswagen Beetle traveling
at the same speed.

In addition, the object\'s kinetic energy is proportional to the
*square* of its velocity. This is also a very useful thing to remember.
If you double your car\'s speed you will increase its kinetic energy by
a factor of *four*. A car moving at 60 mph has 4 times the kinetic
energy as a similar car moving at 30 mph.

**Discussion topic: automobile and plane crashes.** When an automobile
crashes, the kinetic energy of the vehicle is converted into heat,
crushed metal, injury and death. From what you have seen (in real life;
in movies) consider two crashes, one at 35 mph, and another at 70 mph.
Is it plausible that a crash of the faster automobile is four times
worse? What other factors besides speed could affect the outcome of the
crash? Airplane velocities are typically 600 mi/hr, except during
take-off and landing, when they are closer to 150 mph. Does the kinetic
equation explain why there are few survivors in an airplane crash?

Now let\'s plug some numbers into the kinetic equation and see what we
get. We will express mass in kilograms and velocity in meters/second.
We\'ll do the calculation for a one gram meteor traveling at 30 km/sec.
First must convert these numbers: the mass m = 0.001 kg; the velocity 30
km/sec = 30,000 meters/sec. Plugging in to the equations, we get:

$$\begin{array}{r}
E = \frac{1}{2}{mv}^{2} = \frac{1}{2}(0\text{.}\text{001})(\text{30000})^{2} \\
\text{450000}\text{joules} = \text{107}\text{Cal}»\text{100}\text{Cal}
\end{array}$$

That\'s the answer given in Table 1.2.

**Smart rocks.**

For over two decades, the U.S. military has seriously considered a
method of destroying nuclear missiles that would not involve explosives.
Instead, the missile is intercepted by a rock, or any chuck of heavy
material, that is simply placed in the missile\'s path. In some systems,
the rock is made \"smart\" by putting a computer on it, so that if the
missile tries to avoid it, the rock will maneuver to stay in the path.

How could a rock destroy a nuclear warhead? The warhead is moving at a
velocity of about 7 kilometers per second, i.e. v = 7,000 meters/sec.
From the point of view of the missile, the rocket is approaching it at
7,000 meters per second. The kinetic energy of each gram (0.001 kg) of
the rocket is

E = (1/2)(0.001)(7000)^2^ = 25000 joules = 6 Cal

Thus the kinetic energy of the rock (seen from the missile) is 6
Calories, 9 times what it would have if it were made from TNT. It is
hardly necessary to make it from explosives; the kinetic energy by
itself will destroy the missile. In fact, making the rock out of TNT
would provide only a little additional energy, and it would have very
little additional effect. The military likes to refer to this method of
destroying an object as \"kinetic energy kill\".

A later invention that used even smaller rocks and smarter computers,
was called \"brilliant pebbles\". (I\'m not kidding. Look up brilliant
pebbles on the internet.)

# The Demise of the Dinosaurs

Now let\'s think about the kinetic energy of the asteroid that hit the
Earth and killed the dinosaurs. The velocity of the Earth around the Sun
is 30 km/sec[^13], so it is reasonable to assume that the impact
velocity was about that much. (It would have been more in a head-on
collision, and less if the asteroid approached from behind.)

If the asteroid had a diameter of 10 kilometers, its mass would be about
1.6 x10^12^ tons (1.6 teratons)[^14]. Now we can do a calculation in our
heads: the energy released upon impact was equal to this much TNT
times150, i.e. 2.4 x10^14^ tons of TNT = 2.4 x10^8^ megatons of TNT.
Taking one typical nuclear bomb to be 1 megaton of TNT[^15], this says
that the impact released energy equivalent to over 10^8^ nuclear bombs.
That\'s 10,000 times the entire Soviet-US nuclear arsenal at the height
of the cold war.

The asteroid makes a mess, but it stops. The energy is all turned to
heat, and that resulted in an enormous explosion. However, an explosion
of this size is still large enough to have very significant effects on
the atmosphere. (Half of the air is within three miles of the surface of
the Earth.) For a description of the environment effects that scientists
imagine for that event, see the Appendix \"Nemesis\" to this chapter.

Would the impact knock the Earth out of its orbit? We assumed that the
asteroid was about 10 km across; that\'s about one thousandth the
diameter of the Earth. A reasonable comparison is between a mosquito and
a truck. The impact of a mosquito doesn\'t change the velocity of the
truck (at least not very much), but it sure makes a mess on the
windshield. (In this analogy, the windshield represents the Earth\'s
atmosphere.)

# But what is heat?

In this chapter, we discussed a lot about energy, and how it is
converted from one form to another. We measure energy by turning it into
heat. Heat was measured by seeing how much it caused the temperature of
water to rise. But what is temperature? What is heat? We said that when
a gas gets very hot, it expands rapidly, creates great pressure, and
that is what causes an explosion. But why does high temperature cause
expansion and great pressure? These are the questions we will address in
the next chapter.

(END OF CHAPTER)

Additional material and discussion items

When the numbers matter, the confusion between energy and power can be
problematical. For example, here is a quote I found on the web site for
Portland General Electric:
(http://www.portlandgeneral.com/about_pge/news/archives/western_power_supply_california_issues_briefing.asp?bhcp=1)

\"One very large industrial plant can use as much power in one hour as
50 typical residences use in a month.\"

Can you see the reason for confusion? What is meant by the \"amount of
power in one hour\"? Do you suppose they really meant the \"amount of
energy in one hour\"?

Let\'s assume they do. Since there are typically 30 days per month, that
means there are 30x24 = 720 hours per month. So the industrial plant
uses 720 times as much energy as 50 houses. We stated in the text that
50 houses typically use 50 kilowatts. So this would imply that the power
plant uses 720x50 kilowatts = 36 megawatts.

Recall that a typical large power plant produces 1 GW = 1000 megawatts.
The usage of the industrial plant seems quite small compared to this.
Yet the original statement made the usage appear quite large (at least
that was my interpretation).

Automobiles carry, typically, 100 lb of gasoline. That has the energy
content of 1500 lb of TNT. Is gasoline really as dangerous as this makes
it sound? If so, why do we accept it in our automobiles? If not, why
not? Do we accept gasoline only because it is a \"known\" evil?

According to Table 1.2, a 1-gram bullet moving at the speed of sound
(1000 feet per second) has a kinetic energy of 0.01 Calories. Verify
this by using the kinetic energy calculation. Hint: most of the work is
in getting the units right.

Appendix -- selection from *Nemesis*

**Selection from book Nemesis (1987):**

> **. . .** Before a minute had passed, the expanding crater was 60
> miles across and 20 miles deep. It would soon grow even larger. Hot
> vaporized material from the impact had already blasted its way out
> through most of the atmosphere to an altitude of 15 miles. Material
> that a moment earlier had been glowing plasma was beginning to cool
> and condense into dust and rock that would be spread world wide. The
> entire Earth recoiled from the impact, but only a few hundred feet.
> The length of the year changed by a few hundredths of a second.
>
> The deep crater may have reached through the crust of the Earth to the
> mantle. The rock at this depth is very hot due to the natural
> radioactivity of trace amounts of potassium, uranium and thorium. The
> hot rock turned to liquid as soon as the weight of the rock above it
> had been removed. Great pressures from the earth\'s interior quickly
> filled in most of the crater with melted rock from below. . . .
>
> Shock waves from the impact rattled the Earth with energy much greater
> than that of the largest earthquakes humans have experienced, probably
> a million times more energetic than the earthquake that devastated San
> Francisco in 1906. The shock may have triggered other earthquakes,
> causing aftershocks lasting for months or years. However this is
> speculation, for we don\'t know enough about the crust of the Earth to
> say with any certainty. Weak points in the earth\'s crust may have
> opened and sprouted new volcanoes. It is impossible to guess all the
> effects, or how long they lasted.
>
> . . . If the asteroid did strike the ocean, it quickly punched through
> the water layer much as a rock would through a puddle, since in most
> places the depth of the ocean is less than the hypothesized 5 mile
> diameter of the asteroid. The splash created a great tsunami, or tidal
> wave, which grew hundreds of feet high as it swept towards shore. The
> giant wave swept around the Earth many times, inundating the coastal
> regions. The inner parts of the continents were spared.
>
> Rock from the crater, mixed with vaporized comet material, cooled to
> several thousand degrees centigrade as it rose in a great fireball up
> through the atmosphere. It was then about as hot and bright as the
> surface of the sun, the greatest fireball ever seen by living
> creatures. But they didn\'t watch it for long, for the intense heat
> radiated from the glowing cloud burned everything within sight. The
> heat of the fireball also fused nitrogen and oxygen in the air to make
> nitrous oxides, a constituent of modern smog. Some of this gas would
> later combine with water in the atmosphere to make nitric acid.
> Likewise sulfur dioxide from burning plant material eventually formed
> sulfuric acid, which together with the nitric acid eventually fell to
> Earth. This acid rain may have been strong enough to dissolve the
> shells of creatures that lived near the surface of the oceans.
>
> Some of the material ejected from the crater flew out of the
> atmosphere in ballistic trajectories and, like intercontinental
> ballistic missiles, rained havoc on distant continents. Some escaped
> into space, perhaps to hit the Earth on an anniversary of the impact
> when both the Earth and the ejecta returned to the same part of their
> orbits around the sun. As the fireball reached the top of the
> atmosphere it bobbed like a cork, floating on the cooler air beneath
> it, but it had nothing to hold it together and it began to spread out
> over the entire globe. As it spread, its color cooled from a glowing
> red to an impenetrable black. The surviving creatures below probably
> thought that night had come early. But it was a night without a moon,
> without stars. The dinosaurs could not see their own claws in front of
> their faces. Morning would not come for several months.
>
> A few animals had avoided the initial destruction, and at first they
> seemed to manage surprisingly well. Most of the plant eaters could
> still find food, although the settling dust added a gritty taste to it
> all. Some of the carnivores were accustomed to hunting in the dark,
> although they had never experienced blackness such as this. But the
> ultimate source of all food, the sun, had been effectively blocked
> out. Without sunlight there was no photosynthesis, no creation of
> sugar and starch from carbon dioxide and water. Unseen by the
> creatures, the plants were turning from green to yellow, and then to
> brown. Except for the darkness, it would have been a beautiful autumn
> scene. The larger herbivores began to starve, followed soon afterwards
> by the large carnivores. Similar death occurred in the oceans.
> Phytoplankton, the first link in the food chain for the oceans, died
> from the acid rain and lack of sunlight, and the higher organisms
> quickly followed.
>
> Without sunlight, the temperature of much of the Earth began to drop.
> On much of the land the temperature soon fell below freezing. Only
> those fortunate few animals that had already begun to hibernate
> didn\'t notice. Warm blooded creatures had an advantage in their
> ability to live with the cold, but they also required more food. Only
> the coastal regions had the cold moderated by the oceans, but these
> were the areas that had been devastated by the tsunamis. Tremendous
> storms were generated by the great temperature differences between the
> oceans and the land masses. The storms rained out the nitrous and
> sulfuric acids on to land and sea.
>
> The tiny particles of dust began to stick to each other, agglomerating
> into larger particles that fell to Earth more quickly. All over the
> Earth the dust settled to form a layer about a half-inch thick. One
> day Walter Alvarez would puzzle over a section of this layer in an
> outcropping near Gubbio, Italy, where it had been brought up to the
> surface as the crust of the Earth folded during the creation of the
> Apennine mountains. Walter would cut a piece of it out to give as a
> gift to his father.
>
> As the dust settled, sunlight began to filter through to the Earth\'s
> surface. Virtually every animal and plant had died. The plants were
> probably the first to revive. Many spores and seeds had been left
> behind. Life can be incredibly robust. For some plants the three month
> period of darkness and cold was no worse than a severe winter; these
> resprouted from seeds and roots. It was a miracle that any of the
> higher life forms made it through. Indeed virtually every land animal
> that weighed more than about 50 pounds had been extinguished, probably
> because they were most vulnerable in their high position on the food
> chain. The reptilian dinosaurs, both on land and on sea, had vanished
> forever. The nearest relatives of the dinosaurs to survive were the
> birds. We don\'t really know why. Perhaps it was their mobility, their
> ability to search for warmth and food. Perhaps they were better able
> than other dinosaurs to feed off decaying matter and seeds. Perhaps it
> was because they were warm blooded. We can\'t be sure, because we
> don\'t even know if the other dinosaurs were warm blooded or cold
> blooded. There was no obvious pattern that explained why certain
> creatures had survived, and others not. Life is both very robust, and
> yet very fragile.
>
> With plant life suddenly sprouting all around, the few creatures that
> had made it through the catastrophe found themselves in a virtual
> Garden of Eden. Their natural enemies had been removed, and food from
> plants was abundant. However their species would not continue unless
> they could find mates. Those that could quickly spread out over the
> Earth, like (much more recently) the rabbits let loose in Australia.
> They filled the ecological niches that had been denied them by their
> previously \"fitter\" enemies. The slate of evolution had been wiped
> nearly clean. Now there was plenty of room for Nature to try new
> inventions. In fact, the great catastrophe was not only marked in the
> paleontological record by the disappearance of species, but also by
> the great proliferation of new species that followed. Like a forest
> fire clearing the brush, the destruction may have been necessary to
> clear the world of weak creatures who had nevertheless held on to a
> niche simply by virtue of being there first. In evolution, possession
> really is 9/10 of the law. The catastrophe had cleared out whatever
> stagnation there had been in the process of evolution. Once again
> there was room for free experimentation.
>
> In this picture, evolution wasn\'t exactly what we had once thought it
> to be, creatures fighting other creatures to determine which one was
> best. To survive creatures also had to be adapted to endure
> catastrophe. Maybe that\'s why the mammals made it through. They had
> put up with trauma for 100 million years, the trauma of attempting to
> live with the dinosaurs.

[^1]: It is likely, as the Universe evolves, that virtually *all* energy
    will be converted into heat. This idea has spawned numerous essays
    by philosophers and theologians. It is sometimes called the \"heat
    death\" of the Universe, since heat energy cannot always be
    converted back to other forms.

[^2]: Technical note, that can be skipped by the students: I am not
    going to distinguish between mass and weight until we discuss
    gravity. By a weight of one gram, I mean the weight of an object
    whose mass is one gram. This is the conventional usage, e.g. in
    Europe, for selling food by the \"kilo\".

[^3]: There is a similar convention in cooking, which I learned about
    the hard way (when baking a cake). The abbreviation for teaspoon is
    \"tsp\" but the abbreviation for tablespoon is Tsp. 1 Tsp = 3 tsp.

[^4]: To calculate the force, you can take the energy and divide it by
    the distance over which it is released (from chemical to kinetic
    energy).

[^5]: Engineers like to make a distinction between an *explosion*, in
    which an abrupt front called a \"shock wave\" is generated which
    passes through the rest of the material and ignites it, and a
    \"conflagration\", in which there is no shock wave. There is no
    shock wave in the detonation of gasoline in an automobile, so by
    this definition, there is no explosion in an automobile engine.
    Newspapers and the general public do not make this fine distinction,
    and in this book, neither will I.

[^6]:

[^7]: When Einstein predicted (with his Theory of Relativity; see
    chapter ??) that mass can be converted into energy, the law was
    modified to say that the total of mass and energy is conserved.

[^8]: Some people believe that the unit should be capitalized, since
    Watt was a person. They tend to do this when using abbreviations,
    e.g. 1 kW stands for 1 kilowatt.

[^9]: A typical D-cell flashlight battery lights a 1.5 watt bulb for
    about an hour, so the energy contained is about 1.5 watt-hours. It
    costs about \$1.50, so it delivers energy at a cost of \$1.00 per
    watt-hour. That means that the cost of one kWhr from batteries is
    \$1000.

[^10]: My laptop battery can run a 20 watt computer for about 2 hours,
    so the energy it stores is 40 watt-hours = 0.04 kWhr. The battery
    costs about \$100, can be recharged about 1000 times (I hope; my
    last one failed after 300). That means that it costs me 10 cents =
    \$0.10 each time I charge it, just to cover the cost of buying the
    battery (and not including the cost of the electricity from the
    utility company that I use to recharge it). So it costs \$0.10 per
    0.04 kWh, equal to \$2.50 per kWh. If I add in the \$0.20 the
    electric utility charges me for the electricity I use to recharge
    it, the price becomes \$2.70 ≈ \$3 per kWh.

[^11]: Gasoline costs (2003) about \$1.50 per gallon. Using the value of
    10 Calories per gram (from Table 1.2), we can calculate that energy
    from gasoline costs about \$0.05 per kWh. But automobiles do not
    convert all this energy into useful locomotion; about 2/3 is lost to
    heat (in the exhaust, from the radiator that cools the engine, and
    from the direct heating of air in contact with the engine). Thus the
    net cost of *useful* energy from gasoline is about \$0.15 per kWh

[^12]: Note that the return on investment amounted to rate of 100% per
    day. If you use the formula for compound interest, you can show that
    that works out to an effective interest rate of 7x10^107^ % per
    year. Even the Mafia, at its most extreme, never charged interest
    that high. Was some legal limit on permissible usury exceeded? We'll
    leave that to the law students. Yet both sides were very happy with
    the deal. (The energy was actually borrowed for only 1/2 day. Can
    you work out the true effective interest rate, taking into account
    that fact?)

[^13]: The Earth-Sun distance is *r* = 93 x10^6^ miles = 150 x10^6^ km.
    The total distance around the circumference is *C* = 2 π *r*. The
    time it takes to go around is one year *t* = 3.16 x10^7^ seconds.
    Putting these together, we get the velocity of the Earth is *v* =
    *C/t* = 30 km/sec. (Note that the number of seconds in a year is
    very close to *t* ≈ π x10^7^. That is a favorite approximation used
    by physicists.)

[^14]: Taking the radius to be 5 km = 5 x10^5^ cm, we get the volume V =
    (4/3) π *r*^3^ = 5.2 x10^17^ cubic centimeters. The density of rock
    is about 3 grams per cubic centimeter, so the mass is about 1.6
    x10^18^ grams = 1.6 x 10^12^ metric tons.

[^15]: The Hiroshima bomb had an energy equivalent of 13 kilotons of TNT
    = 0.013 megatons TNT. The largest nuclear weapon ever tested was a
    Soviet test in 1961 that released 58 megatons of TNT equivalent.