For the Love of Physics (29 page)

What about all of the physical activity we do in a day? Don’t we also have to eat to fuel that? Going up and down stairs, say, or puttering around the house, or running the vacuum cleaner? Housework can be exhausting, so we must be expending a lot of energy, right? Well, I’m
afraid I have a surprise for you. It’s really very disappointing. The kind of activity that you and I do in one day uses so embarrassingly little energy that you can completely neglect it if you expect to balance out food intake, unless you go to the gym for a really hard workout.

Suppose you take the stairs to climb three floors to your office instead of taking the elevator. I know plenty of people who feel virtuous for taking the stairs, but do the math. Say those three floors cover a height of about 10 meters, and you walk up them three times per day. Since I don’t know you, let’s give you a mass of about 70 kilograms—154 pounds. How much energy does it take to walk up those stairs three times? Let’s be really virtuous—how about five times a day? Let’s assume you really go out of your way. Five times a day, three floors up. The energy you would have to produce is
mgh
, where
h
is the difference in height between the first and the fourth floor. We multiply the 70 kilograms (
m
) by 10 meters per second per second (
g
) by 10 meters (
h
) by 5, since you do it five times a day, and here’s what we get: 35,000 joules. Compare that to the
10 million
joules per day that your body radiates. You think you have to eat a little bit more for these lousy 35,000 joules? Forget it. It’s nothing: just one-third of 1 percent of the total. But that doesn’t stop marketers from making absurd claims about calorie-burning equipment. I just opened a mail-order catalog this morning that features high-end gadgets and found an ad for “wearable weights” that provide “extra calorie burning during normal daily activity.” You might enjoy the feeling of your arms and legs being heavier (though I’m not sure why), and wearing them will build up muscle, but don’t expect to lose significant weight by this kind of punishment!

Now a clever reader will note that of course we cannot go up the stairs five times a day without coming down. When you come down, those 35,000 joules will be released, in the form of heat in your muscles, your shoes, and the floor. If you were to jump, all of the gravitational potential energy you built up climbing the stairs would be converted to the kinetic energy of your body—and you’d probably break a bone or two. So while you had to come up with the 35,000 joules to get there, you don’t get
them back in a usable form when you come down, unless you can rig up a very clever device to take your kinetic energy and convert it to, say, electricity—which is exactly what hybrid cars do.

Look at it another way. Say you spread that stair climbing out over ten hours in a day, maybe once or twice in the morning, twice in the afternoon, and a final time in the early evening. In those ten hours, 36,000 seconds, you generated about 35,000 joules. This is, to be blunt, absurdly little—an average of about 1 watt. Compare that with your body, which radiates on average about 100 joules per second, or 100 watts. So, you can see, the energy burned by your stair climbing is completely negligible. It won’t do anything for your waistline.

However, suppose you climb a 5,000-foot mountain instead? To do that, you would have to generate and use a million joules on top of your regular output. And a million is no longer negligible compared to 10 million. After climbing that mountain you feel legitimately hungry, and now you really do need more food. If you walk up that mountain in four hours, the average power that you have generated (power is joules per second) is substantial, an average of 70 watts during those four hours, of course. And so now the body sends an emphatic message to your brain: “I need to eat more.”

You might think that since you’ve used 10 percent more energy over your normal 10 million joules that you would only have to eat 10 percent more (thus 240 Calories more) than you normally eat, because it’s pretty obvious that a million is only 10 percent of 10 million. But that’s not quite true, which you probably knew intuitively. You have to eat a good bit more than normal, because the body’s food-to-energy conversion system is not particularly efficient—in physics terms. The best human beings do, on average, is 40 percent—that is, we convert at most 40 percent of our caloric intake to usable energy. The rest is lost as heat. It has to go somewhere, since energy is conserved. So to generate an extra million joules of energy to feed your mountain-climbing habit, you’ll have to eat about 600 additional Calories, the rough equivalent of an extra meal per day.

Where Are We Going to Get What We Need?

The amount of energy required for our everyday life activities is astonishing to me. Suppose I wanted to take a bath, and I want to calculate how much energy it takes to heat the water. The equation is very simple; the amount of energy in kilocalories required is the mass in kilograms of the water times the temperature change in Celsius. So since a bath holds about 100 kilograms of water—that’s about 26 gallons—and if we assume that the temperature increase is about 50 degrees Celsius, it takes roughly 5,000 kilocalories, or 20 million joules, of energy to produce a hot bath. Baths are lovely, but they require quite a bit of energy. The remarkable thing is that energy is still so cheap in the United States, that the bath will only cost about $1.50. Two hundred years ago, bathwater was heated with a wood fire. Firewood contains about 15 million joules per kilogram, so a family would have to get all the energy out of a kilo of wood for a single bath. While modern woodstoves can burn at 70 percent efficiency, an open fire or the stoves of 200 years ago convert wood to heat much less efficiently, and over a longer period of time, so it would probably take 5 to 10 kilos of wood to heat that 26-gallon bathtub. No wonder our ancestors bathed a lot less frequently than we do, and an entire family used the same bathwater.

Here are some figures to give you a sense of household energy usage. A space heater uses roughly 1,000 watts, which means that in the course of an hour, you expend about 3.6 million joules, or, to use the common term for measuring electricity, 1 kilowatt-hour. An electric furnace in a cold climate can use roughly 2,500 watts. A window-unit air-conditioner typically uses 1,500 watts, while a central-air system will use about 5 to 20 kilowatts. At 350 degrees Fahrenheit, an electric oven will use 2 kilowatts, while a dishwasher will use about 3.5 kilowatts. Here’s an interesting comparison for you. A desktop computer with a 17-inch cathode-ray-tube monitor uses between 150 and 350 watts, while a computer and monitor in sleep mode only uses 20 watts or less. On the really
low end, a clock radio uses just 4 watts. Since a 9-volt alkaline battery stores a total of about 18,000 joules, or about 5 watt-hours, one battery would power your clock-radio for a little more than an hour.

There are more than 6.5 billion people living on Earth, and we are using about 5 × 10
²⁰
joules of energy per year. Forty years after the OPEC oil embargo, 85 percent still comes from fossil fuels: coal, oil, and natural gas. The United States, with only a little more than 300 million residents, one-twentieth of the world population, is responsible for one-fifth of world energy usage. There’s no way to get around this: we are energy spoilers, big energy spoilers. That’s one reason I was so happy that President Obama appointed a Nobel Prize–winning physicist, Steven Chu, as his secretary of energy. If we’re going to solve our energy problems, we’re going to need to pay attention to the physics of energy.

For example, there is much hope being placed in the potential for solar energy, and I am all for developing it vigorously. But we must beware of the limitations we are up against. There is no question that the Sun is a wonderful source of energy. It produces 4 × 10
²⁶
watts—4 × 10
²⁶
joules per second—of power, most of it in visible light and in the infrared part of the spectrum. Since we know the distance between the Earth and the Sun (150 million kilometers), we can calculate how much of that power reaches the Earth. It’s about 1.7 × 10
¹⁷
watts, or about 5 × 10
²⁴
joules per year. If you point a one-square-meter panel directly at the Sun (no clouds!), that panel would receive roughly 1,200 watts (I have assumed here that about 15 percent of the incoming power is reflected and absorbed by the Earth’s atmosphere). An easy number to work with is 1,000 watts (1 kilowatt) per square meter
pointed directly at the Sun
in the absence of clouds.

The potential for solar power would seem tremendous. It would take about 2 × 10
¹⁰
square meters to harvest enough solar energy for the world’s energy needs. That’s about five times the area of my home country, Holland—not a very big country at all.

However, there is a catch. There are day and night, which we haven’t allowed for yet. We just assumed that the Sun was always there. There
are clouds, too. And if your solar panels are not movable, then they cannot remain pointed at the Sun all the time. Where you are situated on the Earth also matters. Countries at the equator receive more energy (they are hotter, after all) than more northern countries (in the Northern Hemisphere) or more southern ones (in the Southern Hemisphere).

Then we need to take into account the efficiency of the units with which you capture the solar energy. There are lots of different technologies, more all the time, but the maximum efficiency of practical silicon solar cells (as opposed to those made with expensive materials) is about 18 percent. If you use solar energy to directly heat water (without first converting it to electric energy), the efficiency is much higher. An oil-fired furnace, by comparison, even one that’s not so new, can easily reach an efficiency of 75 to 80 percent. So if you take all those limiting factors into account, you would need an area more like a trillion square meters, roughly 400,000 square miles, an area about three times larger than Germany. And we haven’t even considered the cost of building the arrays to collect and convert all that solar power to electricity. At the moment it costs about twice as much to extract electricity from the Sun as it does to extract it from fossil fuels. Not only would the cost of converting to solar power be staggering, such a project is simply beyond our present technological capability or political will. That’s why solar power will play a growing but relatively small role in the world economy for some time.

On the other hand, if we start now, we could make enormous strides in the next four decades. Greenpeace International and the International Energy Agency estimated in 2009 that with very substantial government subsidies, solar power could meet “up to 7 percent of the world’s power needs by 2030 and fully one-quarter by 2050.”
Scientific American
magazine argued several years ago that a crash program and more than $400 billion in subsidies over the next forty years could result in solar power providing 69 percent of the United States’ electricity, and 35 percent of its total energy needs.

What about wind power? After all, wind power has been used as long
as humans have put sails into the wind. Windmills have been around way longer than electric power, maybe even a thousand years longer. And the principle of getting energy from nature and converting it into a different kind of energy for human use was exactly the same, whether it was in thirteenth-century China, even more ancient Iran, or twelfth-century Europe. In all of these places windmills helped do some of the hardest chores human beings took on: lifting water for drinking or crop irrigation, or grinding grains between large stones in order to make flour. It takes wind energy to power a windmill, whether or not it’s making electricity.

As a producer of electricity, wind energy is readily available, utterly renewable, and produces no greenhouse gas emission. In 2009, wind energy production worldwide was 340 terawatt-hours (a terawatt-hour is one trillion watt-hours), which is about 2 percent of the world’s electric consumption. And it is growing rapidly; in fact, electricity production from wind has doubled in the past three years.

What about nuclear energy? Nuclear energy is much more plentiful than we are generally aware. It is, in fact, all around us, every day. Window glass contains radioactive potassium-40, which has a half-life of 1.2 billion years, and energy produced by its decay helps to heat the Earth’s core. All the helium in the atmosphere was produced by the radioactive decay of naturally occurring isotopes in the Earth. What we call alpha decay is in fact the emission of a helium nucleus from a larger unstable nucleus.

I have a very special, very large collection of Fiestaware, which is American tableware—dishes, bowls, saucers, and cups—designed and manufactured starting in the 1930s. I love to bring a few of these plates into class and show them to my students. The orange ones, in particular, which are called “Fiesta red,” have uranium oxide in them, since it was a common ingredients in ceramic glazes. I hold a plate near a Geiger counter, and it begins to beep rapidly. The uranium in the plate emits gamma rays as a result of the process we call fission, which is the same process that drives nuclear reactors. After this demonstration, I always
invite students to come to dinner at my home, but strangely I have never gotten any takers.

Fission, or splitting of heavy nuclei, generates large amounts of energy, whether in a nuclear reactor, in which the chain reactions splitting uranium-235 nuclei are controlled, or in an atomic bomb, in which the chain reactions are uncontrolled and produce tremendous destruction. A nuclear power plant that produces about a billion joules per second (10
⁹
watts, or 1,000 megawatts) consumes about 10
²⁷
uranium-235 nuclei in a year, which amounts to only about 400 kilograms of uranium-235.