Okay, welcome back. So when we left we had gone through an introduction to all the different state phases on our state diagram for the pressure volume diagram. So I'm going to orient you again here. So we had the solids on the leftmost. We have liquids and then as we move through the saturation dome, or the vapor dome, we come out the other side and we have vapors or gasses. Between the liquids and the vapors, we have the vapor dome where both phases are present. Between the solid and a liquid, we have the solid-liquid region where both phases are present. So Last time I said I labelled two isotherms, those are lines of constant temperature, as T B and T A, and our question to you was which temperature is higher if we were to label this arrow as being the direction. In this direction, what is happening to the temperature? Is the temperature increasing or is the temperature decreasing? So, the, you could use anything that works for you, in terms of understanding these state diagrams, is fine. But one thought process you might have gone through would be to say okay, well I'm going to sit at a fixed volume here. And as I moo, specific volume, or, or inverse density if you prefer. But, as I said at a specific volume and as I increase the pressure, what's going to happen to the fluid, what's going to happen to the temperature of the fluid. So, again, at a fixed specific volume, as you increase the pressure, you're going to have to (no period) Increase the temperature of a fluid. So the correct answer is that TB is greater than TA, that's not true, and that this is the direction of increasuing temperature. Again, so whatever thought process you went through or thought exercise or thought experiment you went through, that's great, that's the best way for you to understand. And if some of you came up with the correct correct response, that's fine. So, however you do it is fine. So, what I wanted to do, one last, make this just a little bit more complicated this figure is I want to add this the triple line which I did not have on their before and the triple line here is where you have all 3 phases present hence the name. Triple line not triple line. all three phases present. And what's kind of a neat thing to just understand is that the drawing that I showed for you, where there's the solid liquid region actually bumps to the left here, is for a fluid where it contracts unfreezing. And this interface would actually move to the dotted line if we had a fluid that expands on freezing. [NOISE] Now in energy systems we typically need to have fluids that move, so solids don't work so well for us. But their really fun for lot's of other systems that we might consider, so. I'll say that in thermodynamics, our working fluids, the fluids that actually do the work in terms of power generation, are typically liquids and vapors. So we typically don't operation in this region, most of our fluids are up here on the upper-right hand quadrant of the PD diagram. So this is kind of getting into detail that's fun, but not really neseccary for a lot of what we do. Okay, but I did want to introduce, so that was the PV diagram that again we've looked at that for awhile. Let's add another diagram to our list of tools. and it's, we use this one, mostly just to remind ourselves of all those definitions that we talked about before. So what am I talking about? The pressure temperature diagram. Again, this is the most tactile diagram, the most tactile variables in terms of our understanding. It's very intuitive for us to understand processes and state conditions on P-T, pressure-temperature, diagrams. And so, what I just wanted to do was remind you; I'm going to sketch here again a Two dimensional rendering here of the pressure-temperature diagram. And here's my critical point, and here's the vapor region, and here's the solid region, and here's the liquid region. So, now we have the three phases as identified on our P-T diagram: solid, liquid, vapor. So, this is just again a reminder of, well, if I take a liquid and I transition from a liquid to a vapor, that that process is referred to as vaporization. or if you prefer it's evaporation. Mm-kay. And if I move from a vapor or a gas, remember I use those interchangeably, to a liquid, then I have a process that's referred to as condensation. [SOUND] If I go from a solid to a vapor, that process is sublimation. [SOUND] And the one that everybody's familiar with or most everybody's familiar with, is when you take dry ice, which is carbon dioxide. And if you, usually people use that for shipping things that need to be kept cold for a long period of time. And if you ever pulled out a bar of dry ice you could see the vapor coming off it, and that's a very common sublimation example. and of course if you take a solid and change it into a liquid you're melting it. You're not melfing it, you're melting it. and that gives you again some orientation in terms of. The a PT diagram in terms of common phase changes so those are all things that I would expect you to be familiar with so if I told you what do you have a vapor that's undergoing a condensation process you'd know that explicitly its going to take you through the vapor dome so start you outside the vapor dome and put you back into the liquid region okay well not back into but put you into the liquid region. Okay so now we have these great diagrams for our for our use and again there really meant to give us a, a pictorial understanding of the states. So we can see that if I know pressure and volume I should be able to uniquely define temperature if I know. temperature and pressure I should be able to uniquely define specific [UNKNOWN]. So, we can move between these different variables, these different thermodynamic properties with ease. Okay. Having said that, now I want you to assay, okay let's go back to that P V diagram. because we did a bunch of examples where we used P V diagrams, but there weren't any saturation domes or vapor domes on them. And we didn't look at isotherms and isobars, and things like that. But they were there, they're implicit. Okay? So, take our example that we considered earlier about how we had the two step process where we were compressing and then expanding air. Okay, what we're going to find is that well, for us to condense air into a liquid takes a lot. You can do it, and I'm sure many of you are familiar with liquid Nitrogen, liquid Oxygen and liquid air. Okay, you have to really compress the heck out of it, and you have to drop the temperatures quite a bit. So, they're typically cryogenic systems. So that means, in that system that we considered before, here is our little example. We said we were going to, remember, we, do the polytropic compression process from one to two, and then we did an expansion, constant pressure expansion process from two to three. That vapor dome is on that figure, it's just way down here. Note, not to scale. Okay? And, again I'll try and use my different colors here to emphasize this, there were lines of constant temperature on there as well, or we didn't draw them on there I should say, but they would look something like this. Okay. So they would have curvature that would be different curvature than the, so these are my isotherms. [SOUND] And they would have different curvature than the polytropic process. Okay. So just need to remember that these state diagrams are valid for every substance. Every substance can be defined, every simple substance, every pure substance can be defined in terms of the state diagram. So we talked about isotherms and isobars already, I'm just going to flip. so I just wanted to emphasize again, two more things and I promise we'll get off the subject of these phase diagrams because they tend to be pretty dry. Oh, no pun intended. so let's go back to the pv diagram that we had talked about before. And again, typically we only consider phase change between liquids and gasses because we need to be able to have our fluids moving and we don't move solids so well, although we can. and so we typically cheat and we just put the saturation region as a simple dome. Okay, so this is my saturation region. And again, I'll label it as liquid. And here's my vapor. Okay. And then we know my lines of, constant temperature. In the dome, the lines of constant temperature have to be straight lines because again we know that the pressure and temperature are dependent within the saturation region. So this is the saturation dome. Vapor dome, all sorts of names. Saturation regions, vapor dome, etc., etc. So I told you before that if we have a saturated liquid or a a saturated vapor that uniquely defines the state, assuming we know one other independent intensive variable. So if I know temperature and I tell you it's a saturated vapor. Then let's say its this temperature TA or T1 we'll call it here, that defines if its a saturated vapor at T1 that uniquely defines the point shown on this graph okay so now I want to introduce that term quality. Quality in thermodynamics has a very specific meaning, and it is in fact a thermodynamic property. In addition too, I hope you do high quality work. So, quality is only defined within the saturation region. So quality is defined as the mass of vapor relative to the mass of liquid plus mass of vapor present in the system. And it's given, I, I misspoke earlier, there is an x in thermodynamics and that x is the quality. So the x defines, is the variable notation that we use to define quality. You can see that it should be dimensionless, because we have mass divided by mass, so it's actually dimensionless like this. And you can see that it's a fraction, where if you have a fully saturated vapor, where all of your mixture, and by mixture I mean phase mixture. Is in the vapor phase, then your quality is equal to one. And if all of your mixture is in the liquid phase, then that's a quality of zero. So x=1 is saturated vapor. Then X equal to zero is a saturated liquid and so these lines these isotherms which are also isobars within the saturation region are defining this line up to the critical critical point. That defines the line where the quality is equal to 0. That's the saturated the saturated liquid line. And then this line here on this side is the saturated vapor line. Where x is equal to 1. saturated liquid, okay. So, if I were to go at some arbitrary location between these two endpoints, and say, okay, well that's a quality of 30% or 0.3 You would again, if you have the quality and the pressure or the quality and the temperature, you fully define the state. Okay, so again we want to emphasize, quality is only defined within that dome. [NOISE] [SOUND] Okay. so again that's, we'll keep coming back to these examples of these phase diagrams and how to put states on, and how to put our processes on them. But again, I want you to be thinking in terms of the phase diagrams, the units, the sign convention are all cumulative. They're all built. And work together to help you understand the system and for you to be able to conduct your analysis accurately, with good intuitive understanding. I did want to close with one question for you. And that's a question of if you were to what I want you to do is to sketch what constant pressure condensation looks like on this PV diagram, assuming you start with an unsaturated vapor and end with a condensed liquid. Okay, so lots of words so I wanted to write that down so you can understand, and they're all meant to cue to to very specific places. So, what you - again, draw on a PV diagram condensation from, and I'll, again I'm going to use this as a teaching moment. This region here to the right of the saturation line. This is referred to as the superheated region. [SOUND] And that has a very specific meaning in that it's superheated to a temperature higher than the saturation temperature. Okay. So, that's vapor is at a temperature greater than T saturation. Okay, and if you have a subcooled liquid. So this again. So this area is a superheated region. And a superheated vapor is, a superheated vapor, oops now I said it twice. Vapor. A superheated vapor is, is a vapor at a temperature greater than T Sat. A subcooled, so in this region we're going to define subcooled liquids, So, that's the super-heated vapor region, this is the sub-cooled liquid region, and a sub-cooled liquid Is at a temperature cooler than the saturated liquid temperature. So is at a temperature, is at a temp lower than the saturation temperature. Of that pressure or that condition. So in other words you have to be for a sub-cooled liquid, you're essentially to the left of the saturated liquid line. For super heated vapor you're to the right of the saturated vapor line. Okay? That's it. One, alright that looks like a one. Alright, so again let's get back to our question. Draw on a PV diagram, so first of all, always practice good habits. So draw your PV diagram, label the axis, put the dome on there and write, and put on there your isotherms. Okay, few examples. Typically I like three isotherms. Okay. So, draw your PV diagram, put the dome on your diagram, put the 3 isothermes on your diagram, understand which temperature is higher then the other, so, again, these are lines of increasing temperature here and on that diagram I you to draw a condensation from a superheated vapor to a sub-cooled liquid, okay? So your superheated vapor is state 1, your sub-cooled liquid is state 2. Sketch that on your P-V diagram, and we'll talk about that next time. Thank you.
