and the
physics of explosions
Comet Shoemaker-Levy
crashes into Jupiter[1]
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 a thousand Earth radii. Hitting the Earth is comparable to hitting an ant on a dartboard.
Although the probability of an asteroid impact during your lifetime is small, the consequences could be huge, with millions or maybe even billions of people killed. For this reason, the US government continues to sponsor both asteroid searches, to identify potential impactors, and research into ways to deflect or destroy such bodies.
But why should an asteroid impact cause an explosion? The asteroid was made of rock, not dynamite. And why would it cause such a big explosion? But then--what is an explosion, after all?
Explosions and energy
An explosion occurs when a great deal of stored energy is suddenly converted into heat in a confined space. This is true for a grenade, an atomic bomb, or an asteroid hitting the Earth. The heat is enough to vaporize the matter, turning it into an extremely hot gas. Such a gas has enormous pressure, that is, it puts a great force on everything that surrounds it. Nothing is strong enough to resist this pressure, so the gas expands rapidly and pushes anything near it out of the way. The flying debris is what does the damage in 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 the explosive TNT (trinitrotoluene). It is the rapid conversion of this energy into heat that is at the heart of most explosions.
You may have noticed that I used a lot of common terms in the previous paragraph that I didn’t explain. Words such as energy and heat have everyday meanings, but they also have precise meanings when used in physics. Physics can be derived in a deductive way, just like geometry, but it is hard to learn in that manner. So our approach will be to start with intuitive definitions, and then make them more precise as we delve deeper into the physics. Here are some beginning definitions that you may find helpful. The precise meanings of these definitions will become clearer over the next three chapters.
Definitions (don’t memorize)
Energy is the ability to do work. (Work is defined numerically as the magnitude of a force multiplied by the amount the force moves in the direction of the force.)
Alternative
definition for Energy: anything that can
be turned into heat. [2]
Heat is something that raises the temperature of a material, as measured by a thermometer. (It will turn out that heat is actually the microscopic energy of motion of vibrating molecules.)
These definitions sound great to the professional physicist, but they might be somewhat mysterious to you. They don’t really help much since they involve other concepts (work, force, energy of motion) that you may not precisely understand. I’ll talk more about all these concepts in the coming pages. In fact, it is very difficult to understand the concept of energy just from the definitions alone. Trying to do so is like trying to learn a foreign language by memorizing a dictionary. So be patient. I’ll give lots of examples, and those will help you to feel your way into this subject. Rather than read this chapter slowly, I recommend that you read it quickly, and more than once. You learn physics by iteration, that is, by going over the same material many times. Each time you do that, it makes a little more sense. That’s also the best way to learn a foreign language: total immersion. So don’t worry about understanding things just yet. Just keep on reading.
Amount of Energy
Guess: how much energy is there in a pound of an explosive, such as dynamite or TNT, compared to, say, a pound of chocolate chip cookies? Don’t read any more until you’ve made your guess.
Here’s the answer: it is the chocolate chip cookies that have the greater energy. Not only that, but the energy is much greater--eight times greater in the cookies than in TNT!
That fact surprises nearly everybody, including many physics professors. Try it out on some of your friends who are physics majors.
How can it be? Isn’t TNT famous for the energy it releases? We’ll resolve this paradox in a moment. First, let’s list the energies in various different things. There are a lot more surprises coming, and if you are investing in a company, or running the U.S. government, it is important that you know many of these facts.
To
make the comparisons, lets consider the amount of energy in one gram of various
materials. (A gram is the weight of a cubic centimeter of water; a penny weighs
3 grams. There are 454 grams in a
pound.) I’ll give the energy in several units: the Calorie, the calorie, the
watt-hour, and the kilowatt-hour.
Calorie
The unit you might feel most familiar with is the Calorie. That’s the famous “food calorie” used in dieting. It is the one that appears on the labels of food packages. A chocolate chip (just the chip, not the whole cookie) contains about 3 Calories. A 12-ounce can of Coca Cola™ has about 150 Calories.
Beware: if you studied chemistry or physics, you may have learned the unit called the calorie. That is different from the Calorie! A food Calorie (usually capitalized) is 1000 little physics calories. That is a terrible convention, but it is not my fault. Physicists like to refer to food Calories as kilocalories. Food labels in Europe and Asia frequently say “kilocalories”, but not in the U.S. So 1 Cal = 1000 cal = 1 kilocalorie.[3]
Kilowatt-hour
Another famous unit of energy is the “kilowatt-hour”, abbreviated kWh. (The W is capitalized, some say, because it stands for the last name of James Watt, but that doesn’t explain why we don’t capitalize it in the middle of the word kilowatt.) What makes this unit famous is that we buy electricity from the power company in kWh. That’s what the meter outside the house measures. One kWh costs between 5 and 25 cents, depending on where you live. (Electric prices vary much more than gasoline prices.) We’ll assume the average price of 10 cents per kWh in this text.
It probably will not surprise you that there is a smaller unit called the watt-hour, abbreviated Wh. A kilowatt-hour consists of a thousand watt-hours. This unit isn’t used much, since it is so small. Its main value is that a Wh is approximately 1 Calorie[4]. So for our purposes, it will be useful to know that:
Wh
= 1 Calorie (approximately)
1kWh
= 1000 Calories
Joule. Physicists like to the use energy unit called the joule (named after James Joule) because it makes their equations look simpler. There are about 4000 joules in a Calorie, 3600 in a Wh, 3.6 million in a kWh.
The energy table below shows the approximate energies in various substances. I think you’ll find that this table is one of the most interesting ones in this entire textbook. It is full of surprises. The most interesting column is the last one.
Energy per gram
|
object |
Calories (or Watt-hours) |
joules |
compared to TNT |
|
bullet (at sound speed, 1000 ft per sec) |
0.01 |
40 |
0.015 |
|
battery (auto) |
.03 |
125 |
0.05 |
|
battery (rechargeable computer) |
0.1 |
400 |
0.15 |
|
battery (alkaline flashlight) |
0.15 |
600 |
0.23 |
|
TNT (the
explosive trinitrotoluene) |
0.65 |
2,723 |
1 |
|
modern High
Explosive (PETN) |
1 |
4200 |
1.6 |
|
chocolate
chip cookies |
5 |
21,000 |
8 |
|
coal |
6 |
27,000 |
10 |
|
butter |
7 |
29,000 |
11 |
|
alcohol
(ethanol) |
6 |
27,000 |
10 |
|
gasoline |
10 |
42,000 |
15 |
|
natural gas
(methane, CH4) |
13 |
54,000 |
20 |
|
hydrogen gas or liquid (H2) |
26 |
110,000 |
40 |
|
asteroid or
meteor (30 km/sec) |
100 |
450,000 |
165 |
|
uranium-235 |
20 million |
82 billion |
30 million |
Note: many numbers in this table have been rounded off.
Stop reading now, and ponder the table of energies. Concentrate on the last column. Look for the numbers that are surprising. How many can you find? Circle them. My answers are below.
I think all of the following are surprises:
the very large amount of energy in chocolate chip cookies
the very small amount of energy in a battery (compare to gasoline!)
the high energy in a meteor, compared to a bullet or to TNT
the enormous energy available in uranium, compared to anything else in the table
Try some of these facts on your friends. Even most physics majors will be surprised. These surprises and some other features of the table are worthy of much further discussion. They will play an important role in our energy future.
Discussion of the table of energies
Let’s pick out some of the more important and surprising facts shown in the energy table and discuss them in more detail.
TNT vs. chocolate chip cookies
Both TNT and chocolate chip cookies store energy in the forces between their atoms. That’s like the energy stored in compressed springs; we’ll discuss atoms in more detail soon. Some people like to refer to such energy as chemical energy, although this distinction isn’t really important. When TNT is exploded, the forces push the atoms apart at very high speeds. That’s like releasing the springs so they can suddenly expand.
One of the biggest surprises in the energy table is that chocolate chip cookies (CCCs) have eight times the energy as the same weight of TNT. How can that be true? Why can’t we blow up a building with CCCs instead of TNT? Almost everyone who hasn’t studied the subject assumes (incorrectly) that TNT releases a great deal more energy than cookies. That includes most physics majors.
What makes TNT so useful for destructive purposes is that it can release its energy (transfer its energy into heat) very, very quickly. The heat is so great that the TNT becomes a gas that expands so suddenly that it pushes and shatters surrounding objects. (We’ll talk more about the important concepts of force and pressure in the next chapter.) A typical time for 1 gram of TNT to release all of its energy is about one millionth of a second. Such a sudden release of energy can break strong material.[5] Power is the rate of energy release. CCCs have high energy, but the TNT explosion has high power. We’ll discuss power in greater detail later in this chapter.
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 that occur during digestion, such as the mixing of food with acid in the stomach and with enzymes in the intestines. Finally, the digested food reacts 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 sledgehammers, 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.
Note that we have cheated a little bit. When we say there are 5 Cal per gram in CCCs, we are ignoring the weight of the air that combines with the CCCs. In contrast, TNT contains all the chemicals needed for an explosion, CCCs need to combine with air. Although air is “free” (you don’t have to buy it when you buy the CCCs), part of the reason that CCCs contain so much energy per gram is that the weight of the air was not counted. If we were to include the weight of the air, the energy per gram would be lower, about 2.5 Calories per gram. That’s still almost four times as much as for TNT.
The surprisingly high energy of gasoline
As the energy table shows, gasoline contains significantly more energy per gram than cookies, butter, alcohol or coal. That’s why it is so valuable as fuel. This fact will be important when we consider alternatives to gasoline for automobiles.
Gasoline releases its energy (turns it into heat) by combining with oxygen, so it must be well mixed with air to explode. In an automobile, this is done by a special device known as a fuel injector; older cars use something called a carburetor. The explosion takes place in a cylindrical cavity known, appropriately, 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.[6] 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 can 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. We’ll talk more about the gasoline engine in the next chapter.
The high energy per gram in gasoline is the fundamental physics reason why it is so popular. Another reason is that when it burns, all the residues are gas (mostly carbon dioxide and water vapor) so there is no residue to remove. In contrast, for example, most coal leaves a residue of ash.
The surprisingly low energy in batteries
A battery also stores its energy in chemical form. It can use its energy to release electrons from atoms (we’ll discuss this more in Chapters 2 and 6). Electrons can carry their energy along metal wires and deliver their energy at another place; think of wires as pipes for electrons. The chief advantage of electric energy is that it can be easily transported along wires and converted to motion with an electric motor.
A car battery contains 340 times less energy than an equal weight of gasoline! Even an expensive computer battery is about 100 times worse than gasoline. Those are the physics reasons why most automobiles use gasoline instead of batteries as their source of energy. Batteries are used to start the engine because they are reliable and fast.
Battery-powered
cars
A typical automobile battery is also called a lead-acid battery, because it uses the chemical reaction between lead and sulfuric acid to generate electricity. The table shows that such batteries deliver 340 times less energy than gasoline. However, the electric energy from a battery is very convenient. It can be converted to wheel energy with 85% efficiency; put another way, only 15% is lost in running the electric motor. A gasoline engine is much worse: only 20% of the energy of gasoline makes it to the wheels; the remaining 80% is lost as heat. When you put in those factors, the advantage of gasoline is reduced from 340 down to a factor of 80. So, for automobiles, batteries are only 80 times worse that gasoline. That number is small enough to make battery-driven autos feasible. In fact, every so often you’ll read in the newspaper about someone who has actually built one. A typical automobile fuel tank holds about 100 pounds of gasoline. (A gallon of gasoline weighs about 6 pounds.) To carry that much energy in car batteries would take 80 times that weight, 480 pounds. But if you are willing to halve the range of the car, from 300 miles to 150, then the weight is down to 240 pounds. If you only need 75 miles to commute, then the weight is only 120 pounds.
But why would you do that? The usual motivation is to save money. Electricity bought from the power company, used to charge the battery, costs only 10 cents per kWh. Gasoline costs (as of this writing) about $2.50 per gallon. When you translate that into energy delivered to the wheels, that works out to about 40 cents per kWh. So electricity is 4 times cheaper! Actually, it isn’t quite that good. When m