 In Chapter 2, we had just dipped our toe into the water of energy analysis by considering a simple setup. And by simple, I mean the least complicated that we could. We narrowed our scope to looking at closed and isolated systems first, and the only substances we were considering were ideal gases. The next step to trying to get a little bit more accuracy in our analysis is to allow for substances that aren't ideal gases, that includes substances that are gases, but we can't treat as being ideal, and also substances that aren't gases. So Chapter 3 is dedicated to properties of substances. And before we get into it, let's establish some ground rules, some of the default assumptions that we're making here. First of all, we are talking only about pure substances. And a pure substance, for our purposes, is one that has a fixed chemical composition throughout. We have a homogenous mixture of one thing. That could be a mixture of different gases, but the mixture itself has to be fixed everywhere. So if you have a mixture of say, oxygen and nitrogen, we are talking about the same mixture in every corner of the box that is our system. Or if we have water, it's okay to have liquid water and vaporous water, but we can't have a mixture of water and air unless it's evenly distributed. So right now, we are narrowing our scope to one mixture, one pure substance at a time. The next distinction we have to make is between phases. The reason that we have to do that is because our material properties are sorted by phase. So we have to determine the phase of our substance before we can determine properties about it. And to do that, we are going to be assuming that the phases are neatly organized, that there are clear distinctions between them, and that they are very simple and predictable in their behavior. So we are collapsing the reality of trying to distinguish between different generalizations of materials, i.e. phases into neat and orderly boxes with solid lines between them. And I think it's easiest to start this conversation by imagining a plot of energy. If you consider a substance, let's say water, for the sake of conversation, the lowest energy phase that we will consider for water is the solid phase. If you had solid water or ice and you added energy to it, you would be increasing the sensible energy of the ice, i.e. the energy would go into increasing the temperature. Remember that sensible and latent energy make up thermal energy and thermal energy is one of the components inside of the internal energy and internal energy is one of the components inside the energy of our substance. As we increase the sensible energy, we are increasing the temperature until we reach a point at which that water can contain no more energy without changing phase. At that point, it becomes saturated with energy. At that point, any additional energy will go into the latent energy of the substance instead of the sensible energy of the substance. At that point, a phase transition occurs. And here, we are describing that phase transition as going from a solid to a liquid. And this gap between solid and liquid is intentional. This is the latent energy associated with that phase transition. Going from solid to liquid requires an investment of energy. Going from liquid to solid gives off energy. That's why ice is so much more effective as a cooling mechanism for my coffee than adding liquid water because the ice requires energy in order to go from the solid phase to the liquid phase. The source of that latent energy is going to be the sensible energy of the surrounding coffee. It has to absorb enough energy to change phase before it can even begin to change temperature to try to reach some sort of thermal equilibrium. The latent energy is the same in both directions. It takes the same amount of energy to go from solid to liquid as it gives off going from liquid to solid. Then as we add energy to the sensible energy of the liquid, we are increasing the temperature again until it reaches a point at which it becomes saturated with energy. Then any additional energy will go into changing the phase from liquid to vapor. And I will point out that we can use vapor and gas interchangeably here. I will stick to vapor because that allows us to distinguish between a vapor and gas phase and gasoline when we start to talk about combustion and heat engines. So again, there is a gap in our energy chart here that is associated with the latent energy between the liquid and vapor phases. That latent energy is the same in that it requires energy to go from liquid to vapor and going from vapor to liquid gives off or requires an extraction of energy. But the actual quantity here is going to be different or isn't necessarily the same as going from solid to liquid. Therefore, we give them separate names. The one that refers to specifically the transition between liquid and vapor is called latent energy of vaporization, which is something that you can look up for a substance. And the transition between solid and liquid is latent energy of fusion. Again, something that you can look up. Then all three of these regions between the latent energies are the sensible energy associated with that phase. Again, for our purposes, the phase transitions are all neat orderly lines. There are solid boundaries between what is and is not a certain type of phase. And I will also point out that this is a very broad simplification of the reality of phases. I mean, we could throw in more, we could throw in different types of solids. There's like seven different types of ice depending on the crystalline structure, etc. But for our purposes, we're just talking about the solid phase as a general category. Furthermore, while there is another box up here for plasma, we aren't even going to touch that. We are looking only at this region here and more specifically, we're going to be zooming in on this region, because that is the one that is the most relevant to our analyses. But hold up, we're not quite there yet. First, while we are talking about terminology associated with phases, we have special names for the phase transitions between these, going from solid to liquid is melting. Going from liquid to solid is freezing. Going from liquid to vapor is evaporation. And note, for right now, you can think of evaporation and boiling as the same thing. When you get to heat transfer, you will start to distinguish between the two, because there are several types of boiling and they behave differently, etc. But right now, they are one and the same. And going from vapor to liquid is condensation. And if we have a process that involves a phase transition from solid all the way up to vapor, we call that sublimation. And if we go from vapor all the way to solid, forgive that terrible arrow, try that again, we call that deposition. For our three phases, our solid liquid and vapor, we have names for the amount of energy between the phases, we have names for the energy associated with the phase itself, we have names for the phase transitions, specifically based on direction. And we are zooming in on the phase transition between liquid and vapor, because that's where we spend the majority of our time. So much time will we spend here that it is handy for us to have more specific names within this region. So liquid and vapor are accurate, but not quite precise enough for what we want. I want to have a special name for this part of the liquid and this part of the liquid. I want to have a special name for this part of the vapor and this part of the vapor. So the names we associate with the borders of the phase itself are saturation. This border on the edge of the liquid is called a saturated liquid. It is liquid that is about to change phase. It has become saturated with energy and it can contain no more energy without changing phase. Similarly, the border itself here for vapor is called saturated vapor, because it is at saturation conditions still. Then the region between the two is called saturated liquid vapor mixture. The saturated liquid vapor mixture is the region between the two borders. That doesn't actually include the borders themselves, because on the borders you either have 100% liquid or 100% vapor at saturation conditions. So it's not technically a mixture of the two if there isn't some amount of both in there. Then anything to the left of a saturated liquid within the liquid phase is called a compressed liquid. And anything to the right of the saturated vapor within the vapor phase is a superheated vapor. And I'm not sure, I don't remember enough line theory. I don't remember if it's the curly brackets or the square brackets that represent up to the line, but not including the line, but whatever the correct abbreviation for that is, I'm going to draw a curly bracket for now. The superheated vapor region is the vapor region except without the boundaries. And the compressed liquid region is the liquid region up to but not including the boundaries. And again, I'm drawing that as a curly bracket, despite the fact that I don't actually remember if it's curly or square. So by using terminology like compressed liquid, saturated liquid, saturated liquid vapor mixture, saturated vapor, and superheated vapor, we have a better idea of where specifically within this transition we are. A compressed liquid is a liquid that is not about to change phase. A saturated liquid is a liquid that is about to change phase. A saturated liquid vapor mixture is a mixture of saturated liquid and saturated vapor. A saturated vapor is a vapor that is about to change phase. And a superheated vapor is a vapor that is not about to change phase. Make sense? Cool. And we have tables corresponding to these phases. We have a table full of superheated vapor properties of water. We have a table full of compressed liquid properties for water. The table that includes saturated liquid properties of water, saturated vapor properties of water, and saturated liquid vapor mixture properties of water. And knowing which table to use is dependent on our understanding of how the properties are going to change between the phases. So just like how we have an idea of how the energy of the substance is related to the phase, we should try to develop an understanding for how the other big properties are going to change between the phases. Those three big properties, for our purposes right now, are pressure, specific volume, and temperature. And those three properties were related to one another in a very reliable way when we were talking about the ideal gas law. Pressure times volume was equal to mass times specific gas constant times temperature, i.e. pressure times specific volume was equal to specific gas constant times temperature. That was the relationship between pressure, specific volume, and temperature. They were related on a linear basis with a constant that we called specific gas constant. But for real substances, the relationship between them is not quite so cut and dry. Instead, we have to look at them one by one and we have to keep track of the changes on a very general basis. So if we start by looking at the temperature and volume of water specifically, we have a relationship that looks like this. If you increase the energy of water at a constant pressure, you are increasing the temperature, which is also increasing the volume or specific volume for a given amount of mass. This trend continues until the water is saturated with energy, at which point it changes phase. During the phase transition process, the temperature remains the same, but the specific volume or volume increases. Once it has increased enough to change the phase, it becomes a vapor and you can increase the temperature again. So for a line of constant pressure, the temperature increases along with specific volume in the liquid phase. The temperature remains constant as the specific volume increases for the phase transition. And then, once we have changed phase, the temperature increases with specific volume again. So on this plot, one represents a compressed liquid, two represents a saturated liquid, three represents an arbitrary saturated liquid vapor mixture, four represents a saturated vapor, and five represents a superheated vapor. That horizontal line is the saturation condition corresponding to the phase change between liquid and vapor. If we can look up the saturation condition, we can use our properties to determine the phase. So here, we must be looking at water because at one atmosphere, water boils, i.e. water changes phase, at the saturation temperature, the boiling point, of 100 degrees Celsius. So if we knew that we had water at one atmosphere and we knew that the temperature was 90 degrees Celsius, that must be less than the saturation temperature, meaning we must be in the compressed liquid region. Or if we had water at one atmosphere and 120 degrees Celsius, we would know that we would be in the superheated vapor region because our temperature is higher than the saturation temperature. So we can use the saturation conditions corresponding to the phase change and an understanding of how the properties relate across that phase transition to place our state point on a phase and look up the correct properties. So the general relationship between temperature and specific volume for a line of constant pressure is up in the liquid phase, horizontal line to the right for the phase transition, up into the right for the vapor phase. This is true for a line of constant pressure and different lines of constant pressure will have different temperatures corresponding to a specific volume and a different saturation temperature corresponding to the phase change. If I were to show multiple lines of constant pressure, you can see how much the temperature is going to increase for a given specific volume and you can also recognize that the gap between liquid and vapor gets closer together as the pressure increases. On this plot, we can compare the specific volume associated with a phase transition for multiple pressures and we could also determine an approximate temperature corresponding to a line of constant pressure and that would give us our saturation temperature for that pressure. Note when we are talking about a substance, it is often useful to combine all of these saturated liquid state points together and all of these saturated vapor points together at which point you create a dome shape and we know everything to the left of the dome is going to be a compressed liquid, everything to the right of the dome is going to be a superheated vapor and everything under the dome is going to be a saturated liquid vapor mixture. If we are directly on the left side of the dome on that line specifically, we have a saturated liquid, if we are on the right side of the dome, we have a saturated vapor and the very tippy top of the dome is the critical point for that substance which is the point at which the saturated liquid and saturated vapor states are identical. So everything above their critical point has a blurry region between the compressed liquid and superheated vapor region. As a result, most of our focus is going to be on conditions less than the critical point or up into the right or down into the left of our dome. It is going to be useful for you to remember that a line of constant pressure on a plot of temperature versus specific volume i.e. a TV diagram goes up into the right. Easy way to remember that, you want to turn the TV up because you are young people and young people are always what with the turning up of the TV. A line of constant pressure on a TV diagram goes up into the right. This is different from a line of constant temperature on a PV diagram. On a plot of pressure versus specific volume, the saturated liquid and saturated vapor lines make the same general shape, but a line of constant temperature goes down into the right. So if you are holding the temperature constant and you are adding energy, you are going to be decreasing the pressure until you reach the point at which you can contain no more energy without changing phase, at which point you cross the dome, you accomplish the phase transition. Once it is a vapor, you can decrease the pressure again. Of course, holding the temperature constant and affecting the energy is a little bit of a complicated setup, but what this means for us is that we can use the relative position of our pressure to the saturation pressure corresponding to a temperature to place our state point. If we look up the saturation pressure corresponding to a given temperature and place our pressure above that, then we know that our substance must be a compressed liquid. If we place our pressure below that, then we know that we must have a superheated vapor. Think of this like if you imagine a beaker of water sitting in a vacuum chamber. You start with liquid water, and as you pull air out of that vacuum chamber, the pressure drops and eventually you begin to boil the water. Think of it like you are expanding the molecules enough that they begin to transition from the liquid phase to the vapor phase. And if you drop the pressure enough, eventually the water will entirely vaporize into a vapor. There are videos of that process out on the internet. You can watch them. You can boil water at room temperature by dropping the pressure. And that is how we place the phase of our state point if we know the pressure and enough information to determine the saturation pressure. Again, it will be useful for you to remember that a line of constant temperature goes down into the right on a PV diagram. An easy way to remember that would be to remember the phrase, it's going down, I'm yelling Timber. Timber is a song by Kesha performed with Pitbull, and Pitbull starts with the letter P. Pitbull, P, it's going down. The line of constant temperature goes down into the right on a PV diagram. Or, you know, you can use whatever method you use to remember which line goes down into the right on which diagram and which line goes up into the right on which diagram. Since pressure, specific volume, and temperature are all related, it's also sometimes useful for us to look at a plot of temperature versus pressure. This plot, called the PT diagram, can allow us to visualize where our phases are for a given combination of pressure and temperature. Note that we have a special name for the interface between the solid, vapor, and liquid regions. That point is the triple point. And that's where our solid and vapor and liquid phases can all coexist at the same temperature and pressure. Furthermore, I will point out that all three of these plots, that's temperature and specific volume, pressure and specific volume, and pressure and temperature, are all three perspectives of the same thing. This pressure, specific volume, and temperature surface, also known as the PVT surface, is what we are using to position the phase of our state points. We're just looking at it two dimensions at a time. So when we look at it from this perspective, what we are seeing is the PV diagram, and the plot of the saturated liquid and saturated vapor lines looks like a dome, because remember, we are looking at the transition between the liquid and vapor phases specifically. We see the same general dome shape when we look at this from above, because it is the same dome, but we are looking at a plot of temperature versus specific volume then. And when we look at this from the right side, we see our plot of pressure versus temperature, and we see the transition between liquid and vapor as a line that goes up into the right, because we are looking at the dome from the right. The first step in determining the phase corresponding to our substance properties is to consider the saturation conditions. Let's try an example.