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Why don’t I feel the miles of air above me that are crushing me down? — This article explains why the force of atmospheric pressure (100,000 N per square meter!) doesn’t crush us.
Video Transcript
Hello there! Welcome to lecture 14: gases!
Gas is a state of matter where molecules are very free to move about and are arranged in a very loose manner. This means that the shape and volume of a gas is free to change. A gas will assume the same shape as the container that it’s in, AND it can be compressed to take up less space, or expanded to take up more space.
Learning about gases helps us to understand a lot of fascinating and important topics: what properties the Earth’s atmosphere has, how balloons float, how airplanes fly, and more!
Each of the following concepts will be discussed in this video: the Earth’s atmosphere, atmospheric pressure, Boyle’s law, Archimedes principle, Bernoulli’s principle, and plasma.
The Earth’s atmosphere
The Earth’s atmosphere is a layer of gases that surrounds the planet. The atmosphere doesn’t just allow us to breathe, it also protects us from UV radiation, traps moisture and heat, and exerts forces on every surface it touches.
The composition of the Earth’s atmosphere is approximately 80 percent nitrogen and 20 percent oxygen. There are also trace amounts of some other gases in our atmosphere: argon, carbon dioxide, water vapor and other gases.
Because gas molecules can be compressed, we can think of our atmosphere as being sort of like a giant layer cake. The molecules closest to sea level have a lot of other molecules pushing down on them from above, making the density of the atmosphere higher the closer to sea level we are. The molecules at the upper levels of the atmosphere have relatively few molecules pushing down on them, making the density lower. If we were to take a ride from sea level up and up and up, we would notice the density of the atmosphere decrease with our altitude. At a certain point, we would require an oxygen tank to allow us to breathe. Though the composition of the atmosphere remains constant for about 100 kilometers, meaning that we still have 20% oxygen, the total amount of molecules decreases when density decreases. This is why commercial airplanes have pressurized cabins as they fly through the stratosphere, and why many mountain climbers summiting Mount Everest will take oxygen with them.
The atmosphere of our planet has no real height to it. There is no point in our journey up and up to higher altitudes where the atmosphere stops. Instead, it is more of a gradient. There are a lot of atmospheric molecules close to the surface of the Earth, and fewer and fewer as altitude increases. Most of the mass of the Earth’s atmosphere exists below 100 kilometers, known as the Karman line. This altitude is used as the designation of where “space” begins and the people who go beyond that altitude are considered to be astronauts. However, atmospheric phenomena such as auroras can still occur above this point.
Atmospheric pressure
At sea level, the pressure we experience due to the atmosphere is approximately 100,000 pascals. That means over a one square meter area, the force exerted by the atmosphere is equal to 100,000 newtons!
A device called a barometer is used to measure atmospheric pressure. Old barometers were made of tubes filled with mercury. As atmospheric pressure increased, more force was exerted on the mercury, which would rise up a vacuum tube and indicate higher pressure. If you’ve ever heard the units “millimeters of mercury” or “inches of mercury”, this is where those units of atmospheric pressure come from. Standard sea level pressure is 29.92 inches of mercury.
Aneroid barometers use compressible cells connected to a pointer to indicate pressure. As pressure increases, the cells are squished and the needle moves to higher values. As air pressure decreases, the cells expand and the needle indicates lower pressure values.
Today, many devices such as smartphones and watches use tiny barometers made of micrometer-sized electronics. Barometers are extremely useful devices in forecasting weather, and are an essential instrument in airplane control panels.
Our atmosphere is capable of amazing things. Because we are constantly experiencing our atmosphere, we may not realize just how powerful atmospheric pressure is. Suction cups are capable of holding things up. Where does the counterforce to gravity come from? When air molecules are forced out from under the cup, there are many molecules pushing on the suction cup from the side, but very few molecules inside to push back. A really good suction cup can hold up quite a bit of weight.
Let’s see a more dramatic example of the power of atmospheric pressure. In this demo, I’ve taken a metal can and removed the lid. I poured some water inside and placed it onto a hot plate. The water heats up and begins to boil. Due to buoyancy, the hot water vapor rises and displaces the air, forcing most of the air molecules out of the can and into the surrounding room. At this point, I screw the cap back on tightly, and remove the can from the hot plate. Over time, the water vapor molecules inside the can cool down and convert back to their liquid form. When all of the water has condensed, there are very few molecules left inside the can, so very little pressure is being exerted outward on the can, but a lot of pressure is being exerted inward on the can. This causes it to collapse very dramatically!
Boyle’s law
Boyle’s law describes the relationship between pressure and volume of a gas when the temperature and number of molecules in a system is held constant. It states that the pressure times the volume is a constant. In a closed system, if the volume decreases, it will cause the pressure to increase. If the volume increases, it will cause the pressure to decrease. We can state that in equation form as saying P one times V one equals P two times V two. In other words, the product of pressure and volume before the change is equal to the product of pressure and volume after the change.
In this demo, I have a cylinder and a piston. I can control the volume of the cylinder by moving the piston up and down. A pressure gauge shows the pressure inside the cylinder, subtracting out the background atmospheric pressure. As I decrease the volume of the cylinder, the pressure increases. It actually becomes hard to decrease the volume of the cylinder once it starts getting very small, due to the large amount of pressure that has built up in the cylinder.
Once I’ve compressed the cylinder all the way down, I released the air. This causes the pressure gauge to indicate zero again. Now as I increase the volume of the cylinder, the pressure decreases, indicating negative on the pressure gauge. This relationship continues until I increase the volume back up to maximum again.
A more general version of Boyle’s law is the ideal gas law, which also considers temperature and the number of molecules involved. We will not go into details of this law, other than to say that the ideal gas law tells us that volume and pressure are proportional to temperature. In other words, as the temperature decreases, the product of volume and pressure decreases as well. If you have a car with an automatic tire pressure sensor, you may notice that it goes off in the winter due to the cold weather causing tire pressure to decrease.
Archimedes’ principle
As discussed in lecture 13, Archimedes’ principle discusses the buoyant force that exists when a fluid is displaced by another object. The buoyant force is equal to the weight of the displaced fluid. In liquids, this makes us feel lighter when we go swimming, for example. Both Archimedes’ principle and the principle of flotation exist in gases, too.
Any gas that is more dense than air will sink; any gas that is less dense than air will rise. Because the density of air decreases as the height above the surface of the Earth increases, any object that experiences a buoyant force will rise up until its density matches the surrounding density of the atmosphere.
In this video, I lit three candles in a large beaker. The beaker is initially just filled with air. I place a piece of solid carbon dioxide inside the beaker. The solid carbon dioxide sublimes, turns directly into a gas, using a process we’ll discuss in lecture 17. The gaseous form of carbon dioxide is more dense than air. As the CO2 builds up, it displaces the air. Eventually the level of CO2 rises up in the beaker and causes the candles to snuff out. Fire requires oxygen to burn, and when the CO2 displaces it, there is no more fuel for the candles to remain lit.
Hot air balloons use buoyancy to fly. Hot air is less dense than cold air. Therefore, by heating up an envelope with hot air, we can achieve flight. Blimps achieve flight by using a gas that’s less dense than air, usually helium, inside their envelope.
If all it takes to rise up in our atmosphere is a less dense gas than air, why not use balloons to go to outer space? Let’s consider a balloon filled up with helium gas. At sea level, helium is much less dense than the atmosphere. If you’ve ever let go of a helium-filled balloon, you’ve probably watched as it flew up into the sky. As the balloon rises, two things happen. The surrounding atmospheric pressure decreases with altitude. So the balloon will expand, and the difference in density between the balloon and the surroundings decrease.
In this demo, I have a jar with an uninflated balloon. In the beginning, the surrounding pressure is relatively high and the volume of the balloon is low. We’ll assume the balloon is a closed system and that no molecules can either enter or exit through the balloon in any way. As I pump air out of the jar, the volume of the balloon increases. The pressure in the balloon causes it to inflate because there are fewer molecules pushing in on it from outside.
If we picture this balloon on a journey upward through our atmosphere, one of two things will limit the balloon’s flight. Either the balloon will rise up to the point where its density is equal to the surrounding atmosphere’s. Or the balloon will expand to the point where the envelope of the balloon bursts. Balloons are certainly used for a lot of high-altitude research and weather measurements, but they are not a feasible method to achieve space flight. For that, we require rocketry.
Bernoulli’s principle
We just learned about two methods to fly around in our atmosphere: hot air balloons and blimps. What about airplanes and gliders? How do they work?
Bernoulli’s principle states that as the speed of a fluid increases, the pressure decreases. Another related principle is the venturi effect, which states that as the area of fluid flow decreases, speed must increase. Let’s discuss both of these properties and see how they relate to airplane flight.
The venturi effect comes about due to conservation of mass. If I have some fluid flowing through some pipes, if I decrease the area of the pipe, then in order to get the same amount of mass flowing through, the fluid has to speed up in the smaller area. If you’ve ever heard of a carburetor, which is how gasoline and air were mixed together in car engines prior to fuel injection systems, this is how a carburetor works.
On the other hand, Bernoulli’s principle comes about due to conservation of energy. That fluid that speeds up now has more kinetic energy than the surrounding fluid. But energy can’t come from nowhere! As a result, the pressure of the fluid decreases in order to compensate. Whenever we have a difference in pressure on one side of an object compared to the other, we get a net force.
In this demo, I have a hair dryer and a foam ball. At first, I blow the air directly upward on the foam ball, pushing it up. As I tilt the hair dryer, I redirect the air flow, causing the air to flow faster above and slower below. I use a string to show the air flow, which is moving very fast above the ball, and pretty much not at all below. This creates a pressure differential. The air pressure is lower on the top side of the ball, and higher on the bottom side of the ball. This causes a force of lift that counteracts gravity to keep the ball flying in the air. This is exactly the same physics that causes airplanes to fly!
In an airplane, a wing is angled with respect to air flow, causing this decrease in space and making air speed up over the top of the wing compared to the bottom of the wing. Bernoulli’s principle states that the fast air on the top of the wing has less pressure than the slow air on the bottom of the wing. This pressure difference leads to a force, which we call lift. As long as lift is initially greater than the weight of the airplane, the airplane will accelerate up into the air and fly! When the airplane is level in the air, the lift and weight vectors are equal and the airplane will maintain steady flight.
Plasma
The fourth of the four fundamental states of matter is plasma. Plasma is ionized gas. Recall from lecture eleven that ions are atoms with an unequal number of protons and electrons. They contain a charge. Plasma is a gas where so much energy is present that electrons are removed from the atom. The resultant atoms have a positive charge. This electric charge makes plasma capable of conducting electricity.
Plasma is the most abundant state of matter in the universe, as stars are made of plasma. Lightning, gas discharge lamps (such as neon lights), and the aurora lights are all examples of plasma that we may experience here on Earth.
Plasma is particularly valuable as a method of creating light. We’ll discuss this application of plasma in much greater detail in lecture thirty on light emission. For now, it’s enough to know that plasma is how many different types of lighting work: fluorescent light, neon light, and sodium street lights.
Thanks for taking the time to learn about gases. Until next time, stay well.