The Science of Everything Podcast - Episode 42: Gases and Gas Laws

Episode Date: December 28, 2012

A discussion of the properties and behaviour of gases, focusing on the kinetic theory of gases and the ideal gas law. I also discuss the thermodynamic behaviours of gases, gas partial pressures, and PV diagrams. Recommended prerequisites are Episode 9: Matter and Molecules and Episode 13: Newtonian Mechanics.

You're listening to The Science of Everything podcast, episode 42, gases and gas laws. Now, I'm your host, James Fodor. In this episode, we're going to look at the properties and behavior of gases, focusing on the kinetic theory of gases and also the ideal gas law. I'll talk about some of the thermodynamic behaviors of gases. I'll talk about partial gas pressures, and also I'll introduce the concept of PV diagrams and how those are useful for understanding gas behaviors. Recommended prerequisites for this episode are episode 9, matter and molecules,

and episode 13 on Eutonian Mechanics. or basically just a little bit of background on atoms, molecules, nature of matter, and forces and things like that. It should be helpful for this episode. Okay, let's get started. So, first of all, we'll talk about the properties of gases and what we mean when we say gas. So gases are, a gas is one of the fundamental states of matter, along with liquid and solid and plasma and some other more exotic ones as well. Gases consist of tiny particles. Okay, all matter consists of tiny particles, but the key thing is gases in gases the particles are widely spaced.

So there's a lot of space in between them, empty space. and it's important to understand when we say empty space, you don't mean air, because air is itself a gas. That is air itself is composed of tiny particles with lots of space in between them. That space is essentially vacuum, like there's literally nothing there. Well, I mean, there are some atomic particles and various something. But basically, for our purposes, it's literally empty space. Under typical conditions, the average distance between gas particles is about 10 times a diameter of the particles themselves. The individual particles could be atoms or there could be molecules.

Generally, they're fairly small molecules like H2O. So when that's gas form, that's just a water molecule, two hydrogens and one oxygen, or air. For example, it's a common gas which is composed of about 80% nitrogen, which is N2, two nitrogen atoms bonded together, about 20% O2, which is two oxygen atoms bonded together, plus some carbon dioxide, CO2, and a few other bits and pieces. So, but anyway, as I said, the average distance between the particles in a gas is about 10 times the diameter of particles, so that means that most of the gas is empty space and it's just, just a bunch of particles sort of bouncing around with large, a lot of space in between them. For a gas at room temperature and pressure, so that's one atmosphere in roughly 25 degrees Celsius, the gas particles themselves only occupy about 0.1% of the total volume, so that's 1,000th of 1%. The rest of it, as I said, is empty space.

In liquids and solids, it's more like 70% of volume is occupied by particles, with only the remaining 30% being empty space, so that means that gases are much less dense than other forms of matter, and that'll become important in their properties, which we'll talk about a bit later on. Because there's so much space between gas particles, the forces that act between them, basically the electromagnetic force, are relatively weak. So even if you have charged gas particles, although often they're neutral, but even if they're charged, the forces between them will still be relatively weak, and that will be important for understanding some of their properties a bit later on. So these particles in a gas, they're not just sort of floating around. They're actually in

constant and rapid, constant, continuous and rapid motion. So, for example, the average velocity of nitrogen molecules, so remember there's in two molecules in air about 20 degrees, is roughly 500 metres per second. So the average nitrogen molecule is moving half a kilometre every second in the air that you're breathing now, possibly faster if it's hot wherever you are. The reason that you don't feel a, you know, a massive wind brushing past you is because the nitrogen molecules are constantly smashing into things, partly solid objects, partly just either nitrogen molecules or oxygen molecules in the air, and so they're constantly sort of jiggling around and changing direction and bumping off each other. So there's no overall net motion of the molecules

unless there is actually a wind. So wind would be overall net motion of the molecules, and that's much smaller in terms of speed, maybe a few dozens of kilometers per hour at most, whereas at a microscopic scale, the individual molecules are moving in hundreds of meters per second. The molecules are not all moving at the same speed, by the way. There's a distribution of different speeds. The average is around 500 meters per second, so that means that many are moving faster than that, many are moving slower than that, and that will change as they bump into each other and against solid objects and so on. An important fact to understand about gases, as with all substances, is that as the temperature of the gas increases, the average velocity of the

particles increases. So that's why I had to say before, at roughly 20 degrees, it's about 500 minutes per second. If you increase the temperature, it would be faster than that. Okay, so those are some of the basic properties of gases. Particles, widely separated from each other, in constant motion, bashing into each other and into the walls of the container and moving around. Now we'll move on to look at some important definitions of concepts that are crucial to understand before we can talk about the kinetic theory of gases and the ideal gas law. So specifically, these concepts are the mole, temperature, volume, pressure. First of all, we'll start with the mole or amount. So amount is actually the concept. Mole is a measurement or a unit of measurement of that concept, and I'll explain what I'm in

a second. So we can think about distance is a concept, like how far away you are from something. meter or mile or whatever, those are units that measure distance. So amount is a concept. Mole is a unit that measures amount. So amount, well, that sounds like just an ordinary word. Like, how is that a technical term? Well, the technical term is that it refers to the actual number of particles or molecules or atoms or whatever in a given substance. Usually we refer to like particles, so molecules or atoms, depending on what kind of substance it is. So if we were talking about, say, a bunch of pure oxygen, a certain quantity of pure oxygen, O-2 molecules, the amount of oxygen would be the actual number of O-2 molecules in

that quantity. Now, how do we measure that? Well, we can measure it just in literal number, like the physical number of oxygen molecules. However, that number is going to be very, very large. And so instead, we have a concept called the mole, which is spelled M-O-L-E, as in the creature that digs, but not the same thing, it's just the same word. A mole is a certain number of molecules or particles, and I think we've talked about this in a previous episode. It's one mole is six 0.02 by 10 to the 23. So it's a very large number, but that's not really very important. The crucial thing to understand is that a mole is just like a really big number. It's kind of like a dozen. You know, when we say we have a dozen eggs, we've got 12 eggs. If you say we have

one mole or something, it means we've got 6.022 by 10 to the 23, particles or particles or whatever, of that substance. And the reason we use a mole is because, so we don't have to use these massive numbers of things all the time. And a mole is a convenient amount, like your mole or something might fit into the palm of your hand or something like that. I mean, obviously it depends on how dense the substance is, but like it's a convenient macro size amount we can talk about. So, mole amounts just refers to the physical amount, like number of things you've got there, number of particles you have in a given substance.

Temperature. So here the concept is temperature and the measurement are degrees. Degrees Celsius or degrees Fahrenheit or more commonly in science, degrees Kelvin. Degrees Kelvin are the same as degrees Celsius except that they start at a different level. So in degrees Celsius, the zero point is, well, zero degrees Celsius, but that refers to the melting temperature of water. So water, by definition, melts at zero degrees Celsius, under one atmosphere. pressure, the zero point of Kelvin is instead defined as absolute zero. And again, I think

we talk about this in the thermodynamic episode, the lowest possible temperature is defined as zero Kelvin, which is equivalent to, I think, negative 273 degrees Celsius. So, Kelvin scale is basically the same as Celsius except shifted down 273 degrees, so that negative 273 Celsius is zero Kelvin and so on. So that means ordinary room temperatures, which are like 20, 30 degrees Celsius, are, you know, like 300 Kelvin or something like that. Kelvin is what's commonly used in science, because it basically just avoid. it's negative temperatures, which are a bit annoying. And Fahrenheit, well, no one uses Fahrenheit.

Sorry, American listeners. You need to start using Celsius. But anyway, as I referred to before, temperature refers to the degree of hotness of an object. And it can be shown, of course, we won't do that here, but hotness, as that sort of vague concept, really is referring to, is directly proportional to the average kinetic energy of the particles in that substance. As I discussed earlier, that is how fast those molecules are moving on average. Now, they're not all moving at that velocity, but there's a distribution, you get the average, that is the temperature. So as an object gets hotter or a substance gets hotter, the average kinetic energy of its molecules is increasing.

So, moving up to our third concept, volume. The unit here is litres in the standard international units. Now, the volume refers to basically the amount of three-dimensional space that's occupied by a substance, in our case a gas. I mean, the larger the volume of something, the more space it's taking up. So this is different from the concept of amount or mole, because you can have a small amount of something, taking up a large space, or a large amount of something taken up a small space. And that leads onto the concept of density. So density essentially refers to the mass divided by the volume,

the mass being essentially the weight of something, which is usually related to mole of the amount of something there. So if you cram a lot of stuff into a small space, it's going to have high density, because lots of mass, lots of moles, are in a small amount of volume. Conversely, if you have lots of volume and only a small amount of stuff in there or the stuff in that doesn't weigh very much, so air would be an example of that, you have a very low density. and that's an important concept for gases, which we'll talk about later on.

Fourth concept we're going to talk about is pressure. Pressure is force divided by area. So it's literally defined by that fraction there. And the unit for pressure is Pascal's, after a famous scientist. So force divided by area, what do we mean by that? Well, force is, in terms of a gas, force is the force that's exerted by the particle collisions with the walls of the container that the gas is in.

So if you imagine, let's say, a bottle filled with air, Remember, all of those air molecules are moving around and colliding with each other and also the walls of the bottle, the sides of the bottle, and bouncing around and bouncing off one wall and onto another wall and so on. Each of those collisions with the wall exerts a force, in each of those collisions, the particle is exerting a force on the container. If we added up all of those forces in any given time and divided it by the area of all of the sides of the bottle, that would be equal to the pressure that the gas is exerting on the walls of the container. So pressure will increase if the force goes up and the area stays the same, or if the force stays the same and the area goes down. So that, again, means if you cram lots of gas into a small area, you'll get lots of force because essentially more gas means more collisions, but the area obviously stays the same, and so therefore the pressure goes up. And you can think about that's what happened when you're pumping up tires or pumping up a basketball or something like that. You're cramming more gas into the same area, or the surface area if it's going to be roughly the same. So therefore,

the pressure is increasing. Pressure doesn't just apply to gases as well. It applies to all objects. So when you push on, say if I'm pushing a pin onto a table, that's exerting a large pressure because although the force of my thumb onto the pin is fairly small, the area is really tiny because obviously it's just the tip of the pin. So therefore, fairly small force divided by really small area gives actually a fairly big answer. So therefore the pressure is high and that's how pins can push into fairly, you know, tough objects like wood. Okay, so now that we've got those important conceptual definitions out of the way, we will apply these concepts in terms of understanding the kinetic theory of gases, the ideal gas law, and then a bit about the thermodynamics

of gases. But first we're going to start with the kinetic theory of gases. So this is a theory of gas, you know, how they behave and how they work, which is a model, which is, you know, like all models in science, not perfect, but it's very useful for understanding and predicting its behavior, so we'll use it as a first approximation. So the kinetic theory of gases basically states that a gas consists of very small particles, the average distance of which is much larger than the size of the molecules. Now, this is what I said before. It doesn't always necessarily hold. Some gas molecules are actually quite large compared to the distances between them, especially if the gas is very dense, that is the pressure has been increased a lot, but generally

it is the case that in a gas, the average distance between the gas particles is very large of the distance between the, compared to the size of the particles themselves. Another sort of postulate of the kinetic theory of gases is the particles all have the same mass. Again, that will hold if the molecules all the same. Obviously, it doesn't hold for something like air, which is comprised of a number of different types of molecules that don't all have the same mass. Another assumption is that the number of molecules is so large that statistical treatments can be applied to the gases. So this is important because remember I said about the concept of a mole earlier on, one mole, which is a fairly small amount of gas. Like if you had a, you know, just a glass of water would be, I don't know, a couple of mole of water probably.

One mole is 6.02 by 10 to the 23, which is a very large number. You know, that's like a billion billion or something like that. That very large number of gas molecules that we have is important because it means that we can apply statistical analyses to the behavioural. of gases and sort of predict what they're going to do. So although we don't know, for example, the kinetic energy of each particular gas molecule, because they're all different, there's such a large number of them, we can get a very accurate distribution of them and, you know, averages and so on, and we can predict quite accurately how likely is it that a given particle will have greater

than this sort of threshold amount of kinetic energy and so on. Again, this obviously won't hold if the gases, there's only very small a matter of the gas is particularly sparse, for example. So kinetic theory of gases also posits that the molecules are in constant rapid motion, well, we already talked about that. The motion is also held to be random, so that there's no preference for the molecules moving in one direction or the other, or they don't want to like it to move up and down and things like that.

Again, obviously, that's not going to hold. If, for example, you have the gas in a gravitational field, there would be a tendency for them to be pulled down by the force of gravity, or if there's a temperature or pressure difference in a large amount of gas, which is what happens in the Earth's atmosphere and leads to winds, the air is essentially moving from areas of high pressure to low pressure. That would lead to a preferential movement, in other words, a non-random movement of the gas molecules.

So we're assuming that away in the kinetic theory of gases. And another, probably the crucial element of the kinetic theory of gases is that except when the molecules collide with the walls of the container or with each other, so apart from those, the interactions among the molecules are negligible. And this is crucial because remember before I said that if the molecules or particles are charged, there will be electromagnetic interactions with them and also magnetic interactions as well. The kinetic theory of gases assumes those away on the basis that

because the distance between the particles is so large compared to the size of the particles, those interactions will be negligible. Again, this will not always hold, especially if we have a highly charged gas that's relatively dense. The interactions may become significant. So those statements, to summarize, gas particles are small, the distance between them are large compared to their size. There are very many of them. Their interactions between each other are insignificant except for when they collide with each other.

Their motions are random and rapid, and they're constantly colliding with each other in walls of their container. That model there is the kinetic theory of gases, and it doesn't always hold, but it's the basic model of gases that, you know, scientists will normally have in their head. It's, you know, the basic model would be taught in, like, first year chemistry and that sort of thing, and physics too. Okay, so, from the kinetic theory of gases, we can sort of develop a more quantitative

analysis of the behavior of gases, and we call this the ideal gas law. So the ideal gas is a theoretical gas composed of a set of randomly moving, non-interacting point particles. So you can see here how the assumptions we had before from the kinetic theory of gases are applying here, so they're randomly moving, they're not interacting, so they don't interact with each other except for their collisions, and their point particles. This means we assume that the particles and the gas are, have literally zero size, like they're just points, the mathematical points.

This is obviously not realistic because, you know, all particles have some size, well, at least non-elementary particles, as gases are all non-elementary particles. Unless you had a gas of electrons, which would be quite interesting, but I don't think that's possible. So, yeah, so we take these assumptions, and we then can mathematically describe how the gas will behave, given these assumptions. as these assumptions are quite restrictive, you know, point particles, completely randomly moving, non-interacting, and so on, the ideal gas model fails in a large number of circumstances, like low temperatures, for example, when the interaction forces between the particles can become

large compared to their kinetic energies, because at low temperatures you have low kinetic energies, and so other forces become predominant within the gas, or higher pressures, when the gases are crammed in really tight, and so the space between the particles actually becomes much smaller than it usually is, or when the gas particles actually become quite large, and so the point particle assumption becomes quite unrealistic. So, yeah, it does fail for a number of circumstances. However, in many important circumstances, especially dealing with things like air and so on, it does hold. So the ideal gas law is a simplification, but it's a really good one, and it applies or nearly applies to many common and important circumstances. So that's why we still use it.

So gases that can be accurately modeled in ordinary circumstances by the ideal gas law include air, nitrogen, oxygen, hydrogen, all the noble gases, and carbon dioxide, and many other things as well. So, what does the ideal gas law actually say, although I've said so far as the assumptions that it makes and when it applies and when it doesn't apply? Well, the ideal gas law is really summarized by an equation. PV equals N-R-T, which is something you may have heard before in high school chemistry or something. Let's break this down. So literally it's saying P times V, where those are two variables, equals N times R times T. So two things times together equals three things times together, that's it. And so this is an equation which will always hold for an ideal gas

if those assumptions about non-interacting, randomly moving point particles are, if they hold. Now, what do these things mean? Let's break it down. So, P is the pressure of the gas, and we defined this before. It's force divided by unit area. V is the volume of the gas. So that's left-hand side, PV. Pressure times volume equals. N is the amount of the substance in moles, so, you know, that's like the number of molecules you have. R is a constant, which depends on the particular gas you're using. So, I mean, there's a universal gas constant, which is sort of what people usually mean when they talk about R. But in order to make predictions for a particular type of gas, you need to basically divide that by the molar mass of the molecules in that particular gas.

So we can just think about R as being a constant for the type of gas you're using. And if we have a mixture of different gases, then we need to just get an average R value, essentially. So R is just a constant, which means it's just a number. It's nothing special. It's not a measurement of anything in particular. And finally, T refers to the temperature of the gas. So that's the average kinetic energy of the molecules in the gas. So to summarize again, PV equals NRT is saying that the pressure of the gas times the volume of the gas is equal to some constant number multiplied by the number of moles of the gas you have,

multiplied by the temperature. That's literally what the ideal gas loss says, but let's try and understand what it means. Well, what it means is if you have a certain quantity of gas, so that means we're holding R constant, because the gas is constant, you know, like it's the same stuff. And we're also holding N constant because the amount of molecules isn't changing. So we can essentially just ignore N and R

because those aren't changing in our imaginary version of the equation here. So just imagine those away. So basically what we've got left is PV is proportional to T. So what does this tell us? Well, it tells us that if the pressure goes up and the volume stays the same, then the temperature has to go up as well

because PV is proportional to T. And this kind of makes sense because if the pressure of a gas is going up, that means that the force that the average molecules of the gas is exerting on the sides of the container is increasing. Well, how can that happen? Well, one way it could happen is if there's more molecules in the substance, but we know that's not happening in this imaginary case, because we've said N is constant. The only other way it could happen is if the average force of each collision increased.

And the other way that in turn could happen is if the velocity of the gas molecules had increased, so that each collision exerted a larger force on the walls of the container. And how can that happen? Well, if that does happen, that's equivalent to an increase in temperature. What about if the volume fell? Well, if the volume fell and the pressure stayed the same, that would mean that the temperature would have to decrease. Why?

Because if the volume fell, but the pressure was the same, that means that the same amount of gas is packed into a smaller space. But apparently, the pressure hasn't changed. If we did pack the same amount of gas into a smaller space, what we'd normally expect to happen is the pressure would increase, because now there's more collisions essentially per unit of space. more force per area, so higher pressure. However, we're assuming that pressure has stayed the same, but volume has fallen.

So, you know, we're packing more gas into this, well, the same amount of gas into a smaller space, yet the pressure is staying the same. How could that happen? The only way it could happen is if the temperature fell so that each collision of a gas particle with the walls of the container exerted a less force on the walls of the container, and therefore there are more collisions per unit area, but each collision exists a smaller force, and so therefore that they balance out. So the point is you can apply this equation to understand

the wide variety of circumstances. And it's a really useful mental model because whenever you're thinking you've got a gas and the volume increases or you add more gas or the temperature changes or anything like that, you can just imagine, well, okay, we change this one variable in the equation, what has to happen as a result? And generally, you know that N and R

are constant because that's just the amount of stuff you have and the type of stuff you have. If those are constant, then those don't change, then N and R don't change. And so it's just PV and T that you have to worry about. So p times V equals N times R times T. Very useful law to remember. That is the ideal gas law. Moving on now, we'll talk a bit about the thermodynamics of gases.

So thermodynamics essentially refers to the movement of heat and energy, and we've done an episode on this in the past. When a gas is compressed, work is done on the gas. Conversely, when the gas expands, negative work is done. Or in other words, the gas does work on its surroundings. So to say that again, when a gas is compressed, the environment or the surroundings do work on the gas. That essentially means they're exerting a force and pushing. across a distance. Remember, work is basically just force times distance applied. That's remember

Newtonian mechanics episode, or it might have been the follow-up to that. So when a gas is compressed, an outside force has to be exerted on it, and then the force has to push inwards. And so that's, you know, force times a distance. That's a positive force done on the gas. When the gas expands, it's the opposite. The gas is now doing work on its surroundings. Or we could say that that's being negative work being done on the gas. I mean, you can think about it as the gas does work on the surroundings or the surroundings does negative work on the gas. It's the same thing. Now, why do we care about this. Well, we know from the first law of thermodynamics, again see the episode, we did on that, episode six, that energy must always be conserved, and work is a form of energy. So if work is done on the gas,

let's say in the case the gas is compressed, work is being done on the gas. So that means energy is being extracted from the surroundings, essentially, and going into the gas. But where does it go exactly? Like, we know that work is a form of energy, so if the surroundings are doing work on the environment, sort of energy is being transferred from the environment in the form of doing the work, but it's got to go somewhere because energy has to be conserved. So where does it go? Well, I said before, it goes into the gas. But, like, what does that mean? How does it actually get into the gas? The answer is that the energy from the surroundings that is imputed into the gas by doing work on the gas, goes into the internal energy of the gas, internal energy of the system, which means, in the case of the gas,

an increase in the average kinetic energy of the gas molecules, as they, you know, bump around. And what is the average kinetic energy of the gas molecules? If you said temperature, you are correct, because that's, you know, the same, that's what temperature is. it's the average kinetic energy of the gas molecules. So in other words, when we do work on a gas, we are transferring energy into that gas in the form of increased kinetic energy of the molecules in the gas, or equivalently an increase in the temperature of the gas. So the conclusion to be drawn from this sort of thought experiment is that when we compress a gas, its temperature will increase. Again, other things being equal. We can also imagine the reverse situation. The gas expands. Negative work is

being done on the gas. Or in other words, the gas is doing work on its surroundings. So that means energy has to be coming out of the gas and going into the surroundings, reducing the average kinetic energy of the gas. So that means when a gas expands, it cools. The temperature goes down, the average kinetic energy of the gas molecules goes down because that energy is going into doing work on the environment that surrounds the gas. Oh, by the way, the surroundings of the gas could refer to another gas, or it could refer to a solid object or anything. It doesn't really matter what the surroundings are, just some physical object. Actually, it doesn't even have to be a physical object, because it could just be a vacuum. The gas expands into a vacuum, it'll still cool as it does

that. And this process, when a gas expands and it cools, when a gas compresses it heats up, is actually very important for many phenomena, including weather, and it is also visible, for example, if you pump up, pumping up bicycle tires, for example, you'll find that the tire will get hot after a while. The reason that's happening is because you're doing work on the air inside tire by pumping in, pumping in the air from the outside. By doing work, you're transferring energy into the tire, which is manifested by an increase in the average kinetic energy of the gas molecules within the tire, of the air in the tire, and therefore that's felt by us as an increase in the temperature. Next concept we want to look at after having examined the thermodynamics

of gases is the concept of partial pressures. This is a fairly sort of just a side issue, but it's an important one too. So so far I've just been talking about pressure P as just a sort of a broad concept, the force of the gas molecules on the walls of the container divided by the area of that container. However, what happens when you have multiple different types of gases? So air is a good example of that. of nitrogen gas, oxygen gas, carbon dioxide, some xenon, and a few other things. When working with a mixture of gases, we're sometimes only interested in the pressure of one particular type of gas. In other words, a common one is air, for example. We might just be interested in how much oxygen there is in the air. So we could talk about the partial

pressure of oxygen. Partial pressure, therefore, just refers to the portion of the total pressure of the gas that's contributed by that particular molecule or that particular type of gas. So in air, for example, we might have one atmosphere of air pressure, but maybe only about 20% of that pressure will be contributed by oxygen, because oxygen is only about 20% of the volume of the air. And therefore, the partial pressure of oxygen will be maybe 0.2 atmospheres. And a good application for this might be if we're interested in how the partial pressure of oxygen changes with altitude, because the Earth's atmosphere is thicker, the closer you go to the surface of the Earth. So that means if you go further away from the surface of the Earth, like high up on a mountain, for example, the atmospheric pressure declines. Now, that's a problem, but it's not so much a problem in and of itself. The partial pressure of the total atmosphere is not that important,

as long as it doesn't get really low. What's really important is the partial pressure of oxygen, because the partial pressure of oxygen is what determines essentially how much oxygen you can get into your bloodstream via your lungs. And if the partial pressure of oxygen falls too low, you're not going to be able to get enough oxygen into your bloodstream, and therefore basically you die, which is obviously bad. And so we can make measurements of the partial pressure of oxygen

to find out how much pressure oxygen has, even if total atmospheric pressure, you know, it would be possible that total atmospheric pressure could still be high enough, but the partial pressure of oxygen could be too low, maybe, because for some reason there was just a lot of nitrogen in the air and not much oxygen. So remember, if we can think of pressure as the total force of all of the molecules hitting the sides of the container, divided by the air of the container, you can think of the partial pressure is just subtract out all of the nitrogen and all of the xenon and all the carbon dioxide collisions, and just look at the force of the oxygen gas collisions with the walls of the container and divide that by the air of the container.

that would be the partial pressure of the oxygen, and you know, you could do that again for nitrogen and do it again for carbon dioxide. You add up all the partial pressures, you get the total pressure again. And an interesting phenomenon is that all gases in a mixture actually have the same average kinetic energy in equilibrium. And so again, this is assuming the ideal gas flow and assuming the gases in equilibrium,

so there's not like dramatic changes in the state of the gas or anything like that. Now, you might think this is being rather odd because, you know, the gas molecules could be different sizes or different masses. Well, it turns out the size doesn't matter at all. mass does matter, so, you know, big gas molecules take a larger amount of force to move or to accelerate a given amount than a small gas molecule. However, it turns out that that sort of exactly cancels out with the fact that more massive molecules have a larger kinetic energy. So, in other words, if you apply a given force to a big particle, you change its kinetic energy by the same amount as the given force applied to a small particle. The velocity of the big particle doesn't change as much because it has more inertia, basically.

but it still has more kinetic energy because it's more massive. So like the given amount of velocity that it increases goes further because of its larger mass essentially. So kinetic energies of the molecules in a given gas will be the same, even if their masses and velocities aren't the same. Again, this applies in equilibrium. This means that the partial pressure of a gas is simply equal to the percentage of that gas by volume, sorry, by amount of the gas in the container. So literally, if 22% of the mass of air is oxygen,

I don't know if that's exactly right, it's roughly that, then exactly 22%, then the partial pressure of oxygen will be exactly 22% of the total pressure of air in that given area. Again, this only applies in equilibrium for an ideal gas, but it can be very useful because then we can just look at the relative amounts of different substances and from that directly infer their partial pressures without having to try and measure their partial pressure directly.

So, having discussed partial pressures, we'll now move on to PV diagrams. PV is short for pressure volume, which you may have guessed, because these are the same symbols that we have in the PV equals NRT ideal gas law. Now, PV diagrams, like, they're literally diagrams on two axes. The vertical axis gives pressure, the horizontal axis gives volume. Now, the reason we'd want to graph like this is because it's a very useful way of summarizing

gas processes and how gases can change. Remember from the ideal gas law, PV equals NRT, if we assume that the amount of gas is constant and, of course, the type of gas is constant, so R doesn't change either. We can basically just say that there are only three variables, PV, and T. So only three things that could change. However, because we have this ideal gas law equation, if we specify two variables, then the third remaining variable is already specified, because, for example, if we stated that the pressure was such and such and the volume was such and such, then we times the pressure and the volume

together, we know what the temperature is. That's given by the equation. So that means we only have two, what we might call, degrees of freedom. That's things we can change independently of each other. We can't change temperature volume and pressure, because when we have two of those, the third one is given to us. So we can't just arbitrarily set three. We can only arbitrarily set two.

So that means we only need a two-dimensional axis in order to plot useful graphs, because if we plotted pressure and volume, then we already know what temperature must be. So we don't need a three-dimensional graph to have that because, you know, the information's already there. So that's why the P and the V is fine. I mean, we could put temperature on it as well,

but the, or we could put, you know, it could just be a P-T diagram or a T-V diagram, but PV is the convention, so that's what we go with. So as it said before, P is on the vertical axis, and V is on the horizontal axis. So that means that if we're close to the axis, you know, low P, low V. If we're far away from the axis in both dimensions, we've got a high P and a high V, and then we could have a low P and high V and so on. Now, PV diagrams are really

useful because essentially what you'll have is you put a point on there, which corresponds to a given pressure and a given volume of the gas at a given time, and then you see how the gas changes of time. So it might move from one point to another point, which is, you know, lower and to the right, or higher into the left, or something like that. And you get a bunch of these curves that mark out the transitions along the PV diagram. And some of these curves are given special names, because, for example, if we just went in a vertical line straight down or straight up, that would represent the fact that pressure has changed, because, you know, we've moved along the vertical axis, but volume is the same, because, you know, V, the horizontal axis has changed. And so a constant

volume process, which is called an isochoric process. We could also have a horizontal line, which would be constant volume, but varying, sorry, constant pressure, but varying volume. And that's referred to an isobaric process. The third type is an isothermal process, which is a constant temperature. So that would be represented by a, basically, a curved line with a very particular slope, such that the, sort of like

the ratio between pressure and volume was always the same. That's a little bit higher to understand, because temperature is not directly represented on the PV graph, and so it's not just going to be a straight line, vertical, or horizontal, but you can still represent an isothermal process on the graph. And these names, isochoric, isobaric, and

isothermal are a little bit technical, but they're sort of useful to understand. So ISO just means the same, and then we just say, you know, same volume, same pressure, same temperature, basically. Another interesting thing about PV diagrams is the area under the diagram from left to right is equal to the work done by the gas on its environment. So let's think about this. Remember that we said that if a gas expands, it does work on its environment, so that should be positive. If we work out the area of a graph, sorry, if we work out the area of a pv graph as the volume is increasing and the pressure is decreasing, we're moving from left to right, because the volume along the horizontal axis is increasing,

so we're getting a higher volume, but the pressure on the vertical axis is decreasing, so it's sort of like a downward sloping curve. It doesn't have be a straight line, can be probably a curve. And so we work at the area under that curve. That gives us the work done by the gas. Alternatively, if the gas was expanding, we'd have to move from right to left.

So we'd start with a relatively high volume and low pressure, and we'd get a higher pressure and lower volume as we moved in the opposite direction, and an upward sloping curve, you know, from right to left. In that case, because we're moving in the lower, opposite direction, basically the area becomes negative, because the direction you go in on the light, so it represents the sign of the area. And so that makes sense, because we know that an expanding gas, an expanding gas does positive work on its environment, so positive area, a contracting

gas does negative work on its environment, and therefore a negative area. One important thing to understand about PV diagrams is, apart from the fact that they assume the ideal gas laws, so they only apply when that applies. They're also only valid in thermal equilibrium, which means that no heat is being exchanged between the gas and its surroundings. So basically temperature is staying the same. Temperature doesn't have to be saying the same because it doesn't have to be an isothermal process, but temperature can't be changing due to an exchange of heat. And remember from the thermodynamics episode that heat is the exchange in thermal energy between objects through convection, conduction, or radiation, gases can change temperature because

of, say, changes in volume or so on, that's okay, but that's not the same as the transfer of heat. So the gas can change in temperature, if, for example, it's expanding, therefore losing energy, that's fine. But if there's a transfer of heat through convection or radiation, that's not okay, and if that happens, the PV diagram won't hold, so you won't be able to work. So when there's no change, when there's no exchange in heat, that's called thermal equilibrium. And that's the only time when the PV diagram actually holds, like when you can only legitimately use it. But it's

often used when, on systems that are only sort of roughly in thermal equilibrium or sort of a quasi-equilibrium, because it's sort of close enough. That PV diagram section is a little bit hard to understand without actually seeing the graphs. I'll post some of these on the Facebook page, but hopefully you get the idea of how we can basically use the changes in the relationships between the PV and T variables to visually represent processes, and it's used a lot in engineering, especially in terms of understanding the operation of heat engines and so on. The very last thing that I want to talk about quickly is what's called an adiabatic process,

which is very important in weather systems. An adiabatic process is any process that occurs without input or output of heat within the system, that is any process where there's no exchange in heat, no exchange in thermal energy. So this is directly what I was referring to before when I talked about thermally equilibrium. So PV diagrams only apply basically to adiabatic processes where there's no exchange in heat. Another place where adibati processes apply, though, is adibatic cooling in the atmosphere. So when gas rises in the atmosphere, the pressure on it falls, because remember gas, the atmosphere is denser at lower altitudes and less dense at higher altitude, so the pressure

on the parcel of gas decreases. As that happens, it expands. And as it expands, it's doing work on the surrounding gas. And as a gas expands and it does work, it loses energy, and it cools down. This all comes out from the ideal gas log, we talked about before. So basically, rising gases are expanding gases, which are therefore cooling gases. This is why air cools down as it rises, basically. There can also be exchanges in heat as well, because of thermal contact or whatever and a bit of radiation.

But if we ignore those and assume that those transfers in heat are minimal, then we can call this adiabatic cooling. It's cooling that is a result of an antibiotic process. That is the cooling down as the gas expands, does work on its surroundings, and therefore loses internal kinetic energy, the ideal gas law, PV equals NRT. So that's an interesting application of these gas laws and the PV diagrams that comply to adiabatic processes like antibiotic cooling in the atmosphere. And the same thing happens by the way when air comes down, it gets compressed, work is done on the air, and therefore

the air heats up. So that would be adibatic warming. And this will come into play later on when I finally get around doing an episode on weather and climate science and so on. So that's all I have for this episode. Hope you enjoyed it. If you did, we have a Facebook page, which I'd love you to go on. Just go to Facebook and search for The Science of Everything podcast. Give us a like. On that Facebook page, we have links to some supporting visual materials for past episodes, and also I'll be posting some up for this episode too, and additional links and other information. You can also visit the website for the podcast, FODS12.Foddbondbean.com. Give us an email at FODS12 at gmail.com and give us some feedback. Please spread the word, invite other people,

people to listen to the show that you think might be interested. Thanks for listening, and I'll talk to you next time.