Welcome back. So last time we were talking about the 2D phase diagrams and specifically we introduced isobars and isotherms and what does a saturation region look like on those diagrams. And so we were looking at a pressure volume, specific volume diagram. And our question was, draw the process on a P-v diagram of condensation where you're moving from a superheated vapor to a subcooled liquid. So, let's get that set up. So, here's our P-v diagram. And we know I'll draw a saturation region on here. And first thing we want to do is always draw the isotherms on that P-v diagram. Okay. So now we're oriented, so the question was, draw condensation. So hopefully we remembered that this is gas phase over here, the vapor phase region. This is a saturation region or the dome. And here's the liquid region and I've cheated now and I'm not including the solid phase region because again we're not going to use solid materials on phase diagram. So the question was draw the condensation process. So we know that we're going to move from a gas to a liquid and the trickier part here isn't all that tricky. but the trickier part of this is to recognize I haven't told you what the process was. So, a lot of people will intuitively say okay, well, we know we need to start in superheat region. I told you that. It's a superheated vapor. So, we're going to start somewhere out here on the right side of that diagram. And then we're going to end in the sub cooled region, and again intuitively what a lot of people will do is just like in our example. We were talking about in the last segment, is you would draw a process that's a constant pressure process. But it doesn't have to be a constant pressure process, right? I could have a process that goes from this state to this state in a straight line. I could have a process that goes from this state to this state in some sort of clever complex function. So again, connecting 'em we can define the end points. That's straightforward. because we've already been told it's a super-heated vapor and we know it's going into the sub-cooled liquid region. The trickier part is I haven't gave you enough information for you to say what the process looks like. So that's kind of my trickier part. And hopefully you saw that, that as you drew the end points you're like, Hey, hm, how do I connect these, what's the process that connects them? I could even have a process for example that connects the same two endpoints but takes two different pathways. Ok, so that gets us thinking about, hmm, sometimes these are very obvious the types of diagrams that we want to draw, and sometimes we want to think a little bit more about them. Now this is the pressure volume phase diagram. And we also looked at, very briefly, the temperature-volume diagram. And I wanted to draw that on here too. And again, we're going to do the same thing, in that we're not going to show the solid phase region, we're just going to go ahead and show the, saturation region. And just like we had before, this is going to be the superheat region. So this is the superheat. Again all different ways of saying the same thing. So this is super heated gas or super heated vapor, whatever you want to call it. So here's my super heat region and here's my liquid region again. But now on this diagram what I want to show you are isobars. Now in the saturation region we made a big point of this and the last few segments of saying temperature and pressure are not independent during phase change. So in this saturation region within the dome, we know that the constant pressure lines are in fact straight lines. Right? For, on this TV axis, on this temperature specific volume axis. Now what we want to think about is hey, out here in the superheat region. What do the isobars do? And they can pretty much only do one of two things. They can either move up or they can move down. So let's think about if we were sitting at a fixed volume, again a fixed specific volume or fixed total volume. As we increase temperature, what's going to happen to the pressure in the system? So imagine if you had a closed vessel. That, where you had a constant mass, so imagine like if you had a can of air. And somehow you were, so that volume, the mass within the volume is fixed, the volume itself is fixed, it's a rigid container. As the temperature increases, what would happen to the pressure in the can? And hopefully that kind of mental exercise, that mental experiment, would say hey, that pressure should increase. So our isobars look like this. So these are isobars. Here we have our two pressure lines, here. And again, because of that thought exercise, we know that this is the high-pressure line and that's the low-pressure line. So in this direction, we see increasing pressure. So in that direction we see increasing pressure. And over here, for similar arguments, we know that that's T high and that's T low. Okay, so every time you draw a state diagram, for a process. And were going to do that, in a few segments from now were going to make more and more complex examples. You want to be able to draw those processes on the state diagrams. And you need to be able to orient yourself with respect to the saturation region and with respect to isobars if you're on a temperature density diagram. If you're on a pressure density or a pressure specific dia, volume diagram you want to orient yourself for isotherms. Okay. So we need to know how the isobars and how the isotherms vary, for each of our diagrams. So that's something you need to really focus on, and it's an outcome of this course of thermodynamics. Is understanding how the states interact with each other. How temperature, pressure, density, all interact. ok, so let's follow up with that. We talked about the P-v-T or the pressure specific volume or density temperature surfaces, the 3D diagram. Then we broke those down into 2D diagrams and those were graphical forms. That's kind of cumbersome, we're past the day in age of looking up things on graphs. So most of the time, what we would use are tabulated values for these properties. So if you have the curve, like I show on the previous couple of sketches, you can always tabulate those values. And they're available in extensive tables all over the place. And the more modern area, what we have, era, I should say, online calculators. So you should be fluent with understanding any of these. You should be able to read numbers off a graph. You should be able to look things up off of a table and you should be able to use the online calculators, okay? Any, most of the time, the main stream fluids, ha, bad pun, are available in all forms. So those fluids are water, which will be referred to as steam, and steam, I hate using that phrase, but it's very traditional. We're using that word to describe the water tables, because steam, I think intuitively, implies a vapor phase or maybe a two phase system. But steam is really the reference that we use for all phases of water, we call them the steam tables. Air, nitrogen there are a number of different refrigerants. And those are the most common working fluids. A really good question to ask yourself, and I think we've already answered it once before, is, why are water and air the most common working fluids? They're the most common working fluids because they're the least expensive, they're non toxic, and they're readily available. So water and air are our two primaries and then after that we have more specific fluids that we'll use for applications like refrigeration, cooling. some other kind of more, nitrogen is used, or excuse me, ammonia is used quite a bit. And we'll do some examples with ammonia. And we'll see why they have attractive properties that are sometimes better suited for our applications than water or air are. Okay. So when we go to tabulated forms of data, those tables are, are chunked up based on what phase they're divided. Those tables are divided into what phase we're concerned with. So saturation tables, as you see here Contain only the saturated liquid and saturated gas data. So, what they do, they're kind of interesting, is that so let's go back to our PV diagram here. Is that all the information we need, here's my PV diagram, here's my critical point. Remember that this line here is the line of saturated liquid. So, this is the saturated liquid line. And this line here is the saturated vapor line. Okay, and we remember, we rem, if you recall. We said, hey, if you're within, let's like say, a constant pressure region or if you're on a constant pressure process. It moves between a saturated vapor and a saturated liquid That within the P-v diagram we know of course that this is going to be constant temperature line. And where you are along this line is uniquely defined by the quality. That was the extra variable we introduced last time. And recall that quality is simply a fraction that tells us how much vapor is present relative to the total mass in the system, so it's. Which in the case of a phase change between a liquid and a gas is simply the sum of the mass in the liquid phase and the sum of the mass in the vapor phase. So, if we have a fully saturated vapor, we know that the quality is equal to one. And, if we have a fully saturated liquid, we know the quality is equal to zero. So that means if I need any state information within the dome, all I need are the saturated liquid data, the saturated vapor data, and the quality. So the saturation tables only include the information along these lines. They don't fill in the details in the middle. We're expected to do that using the quality. Okay. So let's follow up on that. Okay. So for the specific volume, we know that if we have a system. And I'm going to use the subscript total to denote the amount of specific volume that's in the vapor phase plus the amount that's in the liquid phase. So we know that, that's going to be equal to, the sum of those two components. So that's going to be, if we take the definition of the total volume. Okay, the specific volume by definition is the total volume normalized by the total mass in the system. And that's going to consist of, the liquid volume. Divided by the total mass, plus the vapor phase, the volume of the vapor phase materials, divided by the total mass. But we know that the volume of the liquid is simply the mass of the liquid times the volume of the liquid. And again tradition, I don't like this notation, but we will follow tradition. The mass of the liquid is defined as V subscript F, and I think it's because fluid but remember I said fluid really includes anything that's a gas phase or liquid. by tradition, when you use the subscript vf in thermodynamics. It's referring to these, liquid, the saturated liquid conditions. Okay? So this would be the line that describes vf. This would be the line that describes vg. And again, that's gas phase. So that one, that one kind of makes sense to us. so we can write this expression with the total volume is equal to the mass of liquid times the saturated liquid specific volume. And similarly the volume of the vapour is equal to the mass of the vapor times vg, the specific volume of the gas. We take these expressions, plug them back into this expression here. And what we find is that V total is equal to the mass of the liquid, divided by M total, times Vf, plus the mass of the vapor, divided by M total, times Vg. So, something looks pretty familiar in these expressions. We look at these rations, here. We come back and look at the definition of the quality. And we say, hey, look, that's simply telling us that the total volume in the system is simply 1 minus the quality times the saturated fluid. Or saturated liquid, specific volume, plus the quality times the saturated gas specific volume. Mkay. So for any system that exists within the saturation region. I simply look up the saturated liquid specific volume or the saturated liquid properties and then I look up the saturated vapor properties. And I use the quality to tell me what the property what the actual value of the property is within the saturation region. Okay? So that's how the saturation, data are referenced. And if you see steam tables or saturation tables. That's how you're going to use the saturation tables. So, we do have a crutch, in that we're going to use the online calculator. But you won't always have online calculators. And you do need to be able to. Evaluate these expressions. So, we will have some little. I will give you excerpts of steam tables, and you will be able. You will need to be able to use those steam tables in order to determine the system properties. Okay. So don't become completely dependent on the online calculators.