Pressure and the simple mercury barometer

We typically consider matter to exist in three distinct states. We've got solids, we've got liquids and we've got gases. And of those three, probably the least often considered are gases. And maybe that's because we can't often see or hold gases too well, but it doesn't mean that gases aren't important. In fact, the very air that you're breathing right now is a gas. So the macroscopic, kind of big picture level, the gas phase refers a system in which the molecules don't have a definite shape or volume. So, I've got kind of a cloud of gas here and it doesn't have a shape or volume to it. And at the nitty-gritty, microscopic level, we're talking about a substance with molecules that are freely moving through space. So these particles are moving freely through space. And this means that the energy of their motion, which is their kinectic energy, is greater than the potential energy of the intermolecular forces that might hold these molecules together as a solid. Now, one of the more intuitive properties of a gas is that it exerts pressure on its surroundings. So gas exerts pressure on the surroundings. And for example, when you inflate a balloon the gas inside exerts a pressure on the elastic sides, making them grow taut and then eventually causing them to expand. So what is this pressure that's causing the gas in the balloon to expand? Well, pressure is actually a measure of force per unit area. So what's actually going on here is that the little particles in here are moving around the container. So they have a velocity. They're moving around the container. And when they collide against the container they exert a force on the area of collision. And while one little particle collision might not have a huge amount of pressure, when you think about the huge amount of particles and the huge number of collisions, we pretty easily get enough pressure to fill the balloon. And the neat thing about balloons is we typically don't just fill them up a little bit, we can fill them up a lot. And the more we fill them up the tauter the sides get, indicating that they have more pressure. So what might cause the pressure to increase? Well, according to our little pressure formula here, pressure is directly proportional to the force. So let's think about what would cause the force to increase. We know that force is equal to the mass times acceleration. So if we increase the magnitude of the acceleration, we can increase the force. Because force and acceleration are also directly proportional. That means if we have a greater change in velocity- because that's what acceleration is, it's a change in velocity. So if we have a greater change in velocity during the collision, we can increase the force. And that means that the faster our little particles are moving, the greater the force. And thus the greater the pressure. And if you remember from our last video, we said that temperature was a measure of the average kinetic energy of the particles. So really what we're saying, is that when we increase the temperature, we're increasing the pressure that the gas exerts. So what else might cause the pressure to increase? Well, if the total pressure is the sum of those little individual collisions, more collisions would mean more pressure. But how do we increase the number of collisions? One method might be to add more particles, because more particles means more collisions. So more moles of gas- remember that moles is simply referring to the number of particles. More moles of gas means more pressure. Now we could also increase the frequency of these collisions by making the container smaller. Because the particles would have less space to move around, and would therefore hit the sides of the container more frequently. So if we decrease the volume- If we decrease the space of the container, we're going to increase the pressure. So we can change the pressure of a gas. But how do we measure those changes? Well, a long time ago in 1643 a former student of Galileo named Evangelista Torricelli asked the same question while he was trying to measure the changing pressure of the gas in our atmosphere. And he solved the problem by inventing the Torricellian Barometer. A barometer is a device that measures pressure. And so he took a glass tube, and he filled it up with mercury. So he took a glass tube and he filled it up with mercury. And he quickly flipped the tube over, and he stuck the open end into an open dish of mercury. So he stuck the tube into an open dish of mercury, open end down, and interestingly enough, most of the mercury stayed in the tube. And the mercury stayed in the tube, even though it was trying to flow out, because as it tries to flow out it exerts a pressure on the mercury in the dish, which then causes the mercury in the dish to push upward against the air. And when the pressure of the rising mercury meets the pressure of the atmosphere pushing down on the liquid's surface, the mercury that's in the tube, it can't flow anymore. So the pressure in the atmosphere traps some of the mercury inside the tube. And we see that at sea level the height of the mercury that's left in the column is about 760 millimeters. Now if we were to measure the height of the column on top of a giant mountain, the column would be shorter. Because there isn't as much air pushing down on the open liquid. So more mercury from the column can escape. In fact on the ski slopes of Breckinridge, Colorado, the height of the column would only be about 520 millimeters. So with less weight of the atmosphere pushing down on the surface of the mercury in the dish, more can escape so that the amount in the column is shorter. And in order to get a baseline for comparison, we say that the pressure of the atmosphere at sea level is one standard atmosphere or one ATM And because of a lot of manometers, which are kind of generic devices that measure pressure using mercury, pressure is often measured in millimeters of mercury. Which we know that one atmosphere, because it's at sea level, would equal 760 millimeters of mercury. And in honor of Torricelli, this millimeters of mercury unit is often called a tor. So one atmosphere equals 760 millimeters of mercury, which equals 760 tor. Now because pressure is a measure of force-per-area, and the SI unit for force is the newton, and the SI unit for area is the square meter, we have another unit of pressure which is the newton-per-square-meter. And we call that the pascal. But if we measure the pressure of the atmosphere at sea level in pascal, we get one atmosphere is equal to 101,325 pascals. And so it's worth quickly mentioning pascals, because it might be a unit of pressure that allows us to translate into other standard units, but mostly, because this number is annoyingly large, we typically measure pressure in atmosphere or tor. Especially when we're dealing with the pressure of gases.