For the Love of Physics (12 page)

In our case, we take the weight and density of our invisible atmosphere for granted. We live, in truth, at the bottom of a vast ocean of air, which exerts a great deal of pressure on us every second of every day. Suppose I hold my hand out in front of me, palm up. Now imagine a very long piece of square tubing that is 1 centimeter wide (on each side, of course) balanced on my hand and rising all the way to the top of the atmosphere. That’s more than a hundred miles. The weight of the air alone in
the tube—forget about the tubing—would be about 1 kilogram, or about 2.2 pounds.
*
That’s one way to measure air pressure: 1.03 kilograms per square centimeter of pressure is called the standard atmosphere. (You may also know it as about 14.7 pounds per square inch.)

Another way to calculate air pressure—and any other kind of pressure—is with a fairly simple equation, one so simple that I’ve actually just put it in words without saying it was an equation. Pressure is force divided by area:
P
=
F
/
A.
So, air pressure at sea level is about 1 kilogram per square centimeter. Here’s another way to visualize the relationship between force, pressure, and area.

Suppose you are ice-skating on a pond and someone falls through. How do you approach the hole—by walking on the ice? No, you get down on your stomach and slowly inch forward, distributing the force of your body on the ice over a larger area, so that you put less pressure on the ice, making it much less likely to break. The difference in pressure on the ice when standing versus lying down is remarkable.

Say you weigh 70 kilograms and are standing on ice with two feet planted. If your two feet have a surface area of about 500 square centimeters (0.05 square meters), you are exerting 70/0.05 kilograms per square meter of pressure, or 1,400 kilograms per square meter. If you lift up one foot, you will have doubled the pressure to 2,800 kilograms per square meter. If you are about 6 feet tall, as I am, and lie down on the ice, what happens? Well, you spread the 70 kilograms over about 8,000 square centimeters, or about 0.8 square meters, and your body exerts just 87.5 kilograms per square meter of pressure, roughly thirty-two times less than while you were standing on one foot. The larger the area, the lower the pressure, and, conversely, the smaller the area, the larger the pressure. Much about pressure is counterintuitive.

For example, pressure has no direction. However, the force caused by pressure does have a direction; it’s perpendicular to the surface the pressure
is acting on. Now stretch out your hand (palm up) and think about the force exerted on your hand—no more tube involved. The area of my hand is about 150 square centimeters, so there must be a 150-kilogram force, about 330 pounds, pushing down on it. Then why am I able to hold it up so easily? After all, I’m no weight lifter. Indeed, if this were the only force, you would not be able to carry that weight on your hand. But there is more. Because the pressure exerted by air surrounds us on all sides, there is also a force of 330 pounds upward on the back of your hand. Thus the net force on your hand is zero.

But why doesn’t your hand get crushed if so much force is pressing in on it? Clearly the bones in your hand are more than strong enough not to get crushed. Take a piece of wood of the size of your hand; it’s certainly not getting crushed by the atmospheric pressure.

But how about my chest? It has an area of about 1,000 square centimeters. Thus the net force exerted on it due to air pressure is about 1,000 kilograms: 1 metric ton. The net force on my back would also be about 1 ton. Why don’t my lungs collapse? The reason is that inside my lungs the air pressure is also 1 atmosphere; thus, there is no pressure difference between the air inside my lungs and the outside air pushing down on my chest. That’s why I can breathe easily. Take a cardboard or wooden or metal box of similar dimensions as your chest. Close the box. The air inside the box is the air you breathe—1 atmosphere. The box does not get crushed for the same reason that your lungs will not collapse. Houses do not collapse under atmospheric pressure because the air pressure inside is the same as outside; we call this pressure equilibrium. The situation would be very different if the air pressure inside a box (or a house) were much lower than 1 atmosphere; chances are it would then get crushed, as I demonstrate in class. More about this later.

The fact that we don’t normally notice air pressure doesn’t mean it’s not important to us. After all, weather forecasts are constantly referring to low-and high-pressure systems. And we all know that a high-pressure system will tend to bring nice clear days, and a low-pressure system means some kind of storm front is approaching. So measuring
air pressure is something we very much want to do—but if we can’t feel it, how do we do that? You may know that we do it with a barometer, but of course that doesn’t explain much.

The Magic of Straws

Let’s begin with a little trick that you’ve probably done dozens of times. If you put a straw into a glass of water—or as I like to do in class, of cranberry juice—it fills up with juice. Then, if you put a finger over the top of the straw and start pulling it out of the glass, the juice stays in the straw; it’s almost like magic. Why is this? The explanation is not so simple.

In order to explain how this works, which will help us get to a barometer, we need to understand pressure in liquids. The pressure caused by liquid alone is called hydrostatic pressure (“hydrostatic” is derived from the Latin for “liquid at rest”). Note that the total pressure below the surface of a liquid—say, the ocean—is the total of the atmospheric pressure above the water’s surface (as with your outstretched hand) and the hydrostatic pressure. Now here’s a basic principle:
In a given liquid that is stationary, the pressure is the same at the same levels. Thus the pressure is everywhere the same in horizontal planes.

So if you are in a swimming pool, and you put your hand 1 meter below the surface of the pool at the shallow end, the total pressure on your hand, which is the sum of the atmospheric pressure (1 atmosphere) and the hydrostatic pressure, will be identical to the pressure on your friend’s hand, also at 1 meter below the surface, at the deep end of the pool. But if you bring your hand down to 2 meters below the surface, it will experience a hydrostatic pressure that is twice as high. The more fluid there is above a given level, the greater the hydrostatic pressure at that level.

The same principle holds true for air pressure, by the way. Sometimes we talk about our atmosphere as being like an ocean of air, and at the bottom of this ocean, over most of Earth’s surface, the pressure is about 1 atmosphere. But if we were on top of a very tall mountain, there would
be less air above us, so the atmospheric pressure would be less. At the summit of Mount Everest, the atmospheric pressure is only about one third of an atmosphere.

Now, if for some reason the pressure is not the same in a horizontal plane, then the liquid will flow until the pressure in the horizontal plane is equalized. Again, it’s the same with air, and we know the effect as wind—it’s caused by air moving from high pressure to low pressure to even out the differences, and it stops when the pressure is equalized.

So what’s happening with the straw? When you lower a straw into liquid—for now with the straw open at the top—the liquid enters the straw until its surface reaches the same level as the surface of the liquid in the glass outside the straw; the pressure on both surfaces is the same: 1 atmosphere.

Now suppose I suck on the straw. I will take some of the air out of it, which lowers the pressure of the column of air above the liquid inside the straw. If the liquid inside the straw remained where it was, then the pressure at its surface would become lower than 1 atmosphere, because the air pressure above the liquid has decreased. Thus the pressure on the two surfaces, inside and outside the straw, which are
at the same level
(in the same horizontal plane) would differ, and that is not allowed. Consequently, the liquid in the straw rises until the pressure in the liquid inside the straw at the same level as the surface outside the straw again becomes 1 atmosphere. If by sucking, I lower the air pressure in the straw by 1 percent (thus from 1.00 atmosphere to 0.99 atmosphere) then just about any liquid we can think of drinking—water or cranberry juice or lemonade or beer or wine—would rise about 10 centimeters. How do I know?

Well, the liquid in the straw has to rise to make up for the 0.01-atmosphere loss of air pressure above the liquid in the straw. And from the formula for calculating the hydrostatic pressure in a liquid, which I won’t go into here, I know that a hydrostatic pressure of 0.01 atmosphere for water (or for any comparably dense liquid) is created by a column of 10 centimeters.

If the length of your straw was 20 centimeters, you would have to suck
hard enough to lower the air pressure to 0.98 atmosphere in order for the juice to rise 20 centimeters and reach your mouth. Keep this in mind for later. Now that you know all about weightlessness in the space shuttle (
chapter 3
) and about how straws work (this chapter), I have an interesting problem for you: A ball of juice is floating in the shuttle. A glass is not needed as the juice is weightless. An astronaut carefully inserts a straw into the ball of juice, and he starts sucking on the straw. Will he be able to drink the juice this way? You may assume that the air pressure in the shuttle is about 1 atmosphere.

Now back to the case of the straw with your finger on top. If you raise the straw slowly up, say 5 centimeters, or about 2 inches, as long as the straw is still in the juice, the juice will not run out of the straw. In fact it will almost (not quite) stay exactly at the mark where it was before. You can test this by marking the side of the straw at the juice line before you lift it. The surface of the juice inside the straw will now be about 5 centimeters higher than the surface of the juice in the glass.

But given our earlier sacred statement about the pressure equalizing inside and outside of the straw—at the same level—how can this be? Doesn’t this violate the rule? No it does not! Nature is very clever; the air trapped by your finger in the straw will increase its volume just enough so that its pressure will decrease just the right amount (about 0.005 atmosphere) so that the pressure in the liquid in the straw at the same level of the surface of the liquid in the glass becomes the same: 1 atmosphere. This is why the juice will not rise precisely 5 centimeters, but rather just a little less, maybe only 1 millimeter less—just enough to give the air enough extra volume to lower its pressure to the desired amount.

Can you guess how high water (at sea level) can go in a tube when you’ve closed off one end and you slowly raise the tube upward? It depends on how much air was trapped inside the tube when you started raising it. If there was very little air in the straw, or even better no air at all, the maximum height the water could go would be about 34 feet—a little more than 10 meters. Of course, you couldn’t do this with a small
glass, but a bucket of water might do. Does this surprise you? What makes it even more difficult to grasp is that the shape of the tube doesn’t matter. You could make it twist and even turn it into a spiral, and the water can still reach a vertical height of 34 feet, because 34 feet of water produces a hydrostatic pressure of 1 atmosphere.

Knowing that the lower the atmospheric pressure, the lower the maximum possible column of water will be, provides us with a way to measure atmospheric pressure. To see this, we could drive to the top of Mount Washington (about 6,300 feet high), where the atmospheric pressure is about 0.82 atmosphere, so this means that the pressure at the surface outside the tube is no longer 1 atmosphere but only about 0.82 atmosphere. So, when I measure the pressure in the water inside the tube at the level of the water surface outside the tube, it must also be 0.82 atmosphere, and thus the maximum possible height of the water column will be lower. The maximum height of water in the tube would then be 0.82 times 34 feet, which is about 28 feet.

If we measure the height of that column using cranberry juice by marking meters and centimeters on the tube, we have created a cranberry juice barometer—which will indicate changes in air pressure. The French scientist Blaise Pascal, by the way, is said to have made a barometer using red wine, which is perhaps to be expected of a Frenchman. The man credited with inventing the barometer in the mid-seventeenth century, the Italian Evangelista Torricelli, who was briefly an assistant to Galileo, settled eventually on mercury for his barometer. This is because, for a given column, denser liquids produce more hydrostatic pressure and so they have to rise less in the tube. About 13.6 times denser than water, mercury made the length of the tube much more convenient. The hydrostatic pressure of a 34-foot column of water (which is 1 atmosphere) is the same as 34 feet divided by 13.6 which is 2.5 feet of mercury (2.5 feet is 30 inches or 76 centimeters).

Torricelli wasn’t actually trying to measure air pressure at first with his device. He was trying to find out whether there was a limit to how high suction pumps could draw up a column of water—a serious problem
in irrigation. He poured mercury to the top of a glass tube about 1 meter long, closed at the bottom. He then sealed the opening at the rim with his thumb and turned it upside down, into a bowl of mercury, taking his thumb away. When he did this, some of the mercury ran out of the tube back into the bowl, but the remaining column was about 76 centimeters high. The empty space at the top of the tube, he argued, was a vacuum, one of the very first vacuums produced in a laboratory. He knew that mercury was about 13.6 times denser than water, so he could calculate that the maximum length of a water column—which was what he really wanted to know—would be about 34 feet. While he was working this out, as a side benefit, he noticed that the level of the liquid rose and fell over time, and he came to believe that these changes were due to changes in atmospheric pressure. Quite brilliant. And his experiment explains why mercury barometers always have a little extra vacuum space at the top of their tubes.