 Hello! I thought I'd hit you with an intro to reading thermodynamic steam tables, recovering saturated liquid mixtures, saturated vapors, superheated gas, and temperature-specific volume diagrams. So here is a table. It is from thermodynamics and engineering approach. This is table A4. This is the saturated water table. And I want to talk about how to read this. And in order to do that, I really think it makes the most sense to just talk about temperature, pressure, and the specific volumes. Everything we're about to learn also applies to specific internal energy, specific enthalpy, and specific entropy, but we really don't need those now. So we can just kind of get rid of those. Also, notice that this is only going up to 200 degrees Celsius. And we're going to need the table on the second page. So this is the second page of that table. It goes all the way up to the critical point here at 373.95 degrees Celsius. But just like the previous one, we can get rid of internal energy, enthalpy, and entries. We don't need to use them for now to learn how to use the tables. So we'll just take those two tables side by side. This is that one from 0 to 200, and then from 2 to 5 to 370, 4 almost. That's our whole steam envelope. And this is what that looks like. I just posted a video on how to make this graph so that you can make it for yourself if you want. But here is the TV diagram for saturated water. And this graph comes exactly from these tables. They're just different ways of looking at it. In fact, this is V sub F. So this is the specific volume of water at each of those temperatures if all of it is liquid. And so that's this left side of the graph here, the left side of the diagram. These are the specific volumes in meters cube per kilogram of 100% saturated liquid water. So each of these points is the boiling point. But when it is all liquid, right before it starts to turn into gas, right before it starts to evaporate. And of course, we've talked before about how once you start dumping in energy, if you're looking this as a process, if you're dumping in energy here, it would just be going straight across. If the pressure was staying the same, it would just be changing phase and getting larger and larger in volume going across. And so it would go all the way across to this side, this side right here. This is the specific volume of those same temperatures, same boiling point, but now it's 100% saturated gas. So this is the line of 100% saturated gas. This is the line of 100% saturated liquid. This point right here is the critical point where the specific volume of the saturated liquid in the specific volume of the saturated vapor are the same. Notice that I'm switching between saturated gas and saturated vapor. They're the same in this case because we're talking about water. So if it's a saturated gas, we just call that vapor. So let's get rid of that stuff. This is the graph and the tables that we are working with. Just to make this easier to present, let's only look at from a zero to 200 degrees Celsius. So we'll only look at this first table just because I don't want the two tables on the page. So really that only covers us to about here. I'm only going to ask you questions that are down under this dotted line only because that fits on the first page. It's going to make it fit better. Let's look at some problems. So let's say you have six problems you're looking at. You're looking at this table and you're asked to complete this table with blank values. So let's just jump into it. First one. This is the first one off that table. It asks you if the temperature is 100 degrees Celsius and X is zero. What is the specific volume and what is the pressure? Now, from studying quality, you know that zero means that it is a mixture and it is completely saturated liquid because X means it has quality and quality means that it's a mixture and it's defined as the mass of the gas over the mass of the total mixture. If it is all saturated liquid, then there's zero mass of the gas. So therefore, X is zero. If we look at our tables, you'll see here that this is, sorry, excuse me, that this is 100 degrees Celsius right here. Here is the pressure, atmosphere pressure for 100 degrees Celsius. And then it's 100% saturated liquids, all saturated liquid. X is zero. So right there, that's our answer. It's X is zero. That is V sub F. And so this one ends up being pretty easy. The specific volume is 0.001043 meters cubed per kilogram. And the pressure is 101.42. Finding the pressure from the temperature is really easy if it has any quality. If it has any quality anywhere between zero and one, temperature and pressure are dependent variables. For instance, 40 degrees C is a boiling point only at a pressure of 7.3851 kilopascals. For us, atmospheric pressure 100 degrees C, those things are tied together. If it's a mixture, it is both those things. If it's something else, if it's superheated gas or a compressed liquid, then those are no longer dependent. Let's look at where that falls on the graph. Here it is. So there is our graph. Here is the V sub F line. Here is 100 degrees Celsius. You can look way down here. Here we are at 0.001043. Notice that this is a logarithmic scale because this jump is actually quite big, right? You go from let's pick a really extreme one where you're at 20 degrees C is a boiling point. So your pressure is only about 2.3 kilopascals. You go from a specific volume of 0.001 meters cube per kilogram way up to 57.762 meters cube per kilogram. So we have to have this on a log scale for it to work. That was number one. Super easy. Let's do another easy one. Number two. 100 degrees C again, but now X is 1. X being 1 means that this is a completely saturated gas, a completely saturated vapor. That's what X equals 1 means. X equals 1 means. And so we just do the same thing. We go down here. Here's 100 degrees C. Well, we know the pressure because it has a quality. It means it's a mixture. So it's just gonna be that pressure 101.42 kilopascals. Also one means V sub G. So our specific volume is just gonna be 1.672 meters cube per kilogram. Bam. Plug those in. Finish number two. Let's just look at where that is on the graph. Here it is way over at this side. Lager of the mix scale. So this is way larger specific volume than it was before. We went from here all the way over to here between one and two. Alright, that's it. Number two. Easy one. Let's do another one. Number three. This one. 100 degrees C. So you probably know the pressure because I'm telling you it has a quality. The difference is now the quality is in zero or one. So we find our 100 degrees C. We know our pressure because it has quality. But now the specific volume is gonna be somewhere between these two numbers. If you didn't have time to answer this question, you could just say, well, the specific volume is somewhere between 0.001043 and 1.672. I don't know if that's gonna help you with a professor or at work. But you know it's somewhere in between those two things because it has quality. So let's look at how we do that. At 100 degrees C, we saw that V sub F is 0.001043 meters cube per kilogram. V sub G is 1.672 meters cube per kilogram. And the problem tells us that X is 0.4. So we plug this into our equation. The specific volume is just equal to the specific volume of the liquid. Plus whatever the quality is times the distance from the specific volume of the gas to a specific volume of the liquid. And we can just plug in those numbers. Boom, boom, boom. And the final answer is 0.6694 meters cube per kilogram. Quick test to make sure that you did the pluses and minuses and all that stuff right. Just make sure that this number is indeed between these two numbers. If it's between there, that doesn't mean you're right for sure. But if it's not between those two, then you know that you're wrong. So now we've solved it. The specific volume is 0.6694 meters cube per kilogram. Plug those numbers in there. Oh, I had a few more decimals. That's, you probably don't know it out to that accuracy, but this still works for learning purposes. And so you might be asking, where does that fit on this? And there it is. It's way over here. The next question you might ask is like, okay, well sure. It's 100 degrees and it's somewhere between the left and the right. Great. But 0.4, doesn't it feel like 0.4 should be like kind of more to the left? This doesn't really look like 0.4 if it's about the distance between the two. But remember this is a log scale. So if we took it off of log and made it a linear scale and we kind of zoomed into that area, what you would see is that from way over here to here, that is about 0.4 of the way. So this is what it would look like on the linear scale. And then you would see that that 0.4 fits in there. That's just in case you were looking to build your intuition about what 0.4 would mean. You're going to come back. This is our answer right here, 0.6694 meters cube per kilogram and the pressure 101.42. All right. Let's look at number four. Number four, this one is 200 degrees C, but it's still only 100 kilopascals. We've been using 101.42 like atmospheric, but let's just round this to 100 kilopascals. But if it's 100 kilopascals, since 200 degrees C, you might already know that this table isn't going to work for you. It doesn't matter if you don't know. Just look at this table first. If we look at this table, we see that 100 kilopascals is right around here. It's between these two, but the temperature is way higher. If the temperature is higher for this boiling point pressure, then you know it must be superheated. A higher temperature for this same pressure, it must be superheated. What we need to do is say, okay, well, it doesn't fit into this. Let's go to the superheated table. Here is one page of the superheated table. We can zoom in. We can find the one that fits for 100 kilopascals. It's this one right here. 100 kilopascals is 0.1 megapascals. It's just this table right here. Let's zoom into this. Now we are looking at the table for superheated. Notice that you have a bunch more tables because pressure and temperature are now independent variables because it's superheated. Those two things are no longer bound together. We take our 100 kilopascals. We use this table. Then we find our 200 degrees C. There it is right there. We find that this is our specific volume. For 100 kilopascals, 200 degrees C, there's our specific volume right on there. It has no quality. It's superheated. There is no mixture. There is no quality. This is our final answer. A specific volume of 2.1724 meters cube per kilogram. If you have 200 degrees Celsius water at 100 kilopascals, you might ask, well, where is that on the graph that we're looking at on our TV diagram? Well, it lives right there. There's 200 degrees C. There's a specific volume of 2.1724. You can see that this region up here, this is all the superheated region. Everything under here is a mixture. Everything over here is a compressed aka subcooled liquid. Over here, superheated, that's where that point lays. That's number four. Let's hit number five. Number five says 100 degrees Celsius. We were dealing with 100 degrees Celsius earlier, but the pressure is much lower. Well, if water boils at 100 degrees Celsius when the atmospheric pressure is about 100 or 101 kilopascals and you have much lower pressure, then you know it also must be superheated. Lower pressure at what was the boiling point, but now the pressure is much lower. Boom. It is superheated. So we come back to this. We say, no, it can't be that. Must be on the superheated tables. Luckily, I picked values that are still on this first page because there's a bunch of pages of these. And now this one isn't going to work. This was our 100 kilopascals. We're at 50 kilopascals. That's that one right there. 0.05 megapascals. So we come to this table. Pressure and temperature are no longer tied together. So we find 100 degrees Celsius. There it is on this, the 50 kilopascal table. So there's our answer 3.4187 meters cube per kilogram. There is no quality because it's superheated. Plug that in. Boom. We're done with number five, but let's look at where it is on the TV diagram. There it is. Here we are at 100 degrees Celsius, but because the pressure is lower, even though you don't see that on this graph, you do see that its specific volume is out here at 3.4187. So it means it's in the superheated region, which of course we knew when we were solving the problem. All right. Let's look at one last one. Let's look at one where instead, you're given a specific volume and a temperature, but you don't know if it has a quality and you don't know its pressure. So what you're going to do is you're going to find 100. You can use your intuition first. This one, I'm not going to be able to use my intuition, but sometimes I like to look at these and be like, okay, is this superheated? This is a pretty high temperature, but this is a kind of reasonable specific volume. So I just don't know if this is superheated or not. If I don't know, I'm always going to start on my saturated table. So I come down here to 190 degrees Celsius and I look for 0.15 and sure enough, 0.15 does fit between v sub f and v sub g. If it fits between those two things, then it must be a mixture. If this specific volume was 0.16, then I would have known to look on the superheated table because 1.16 is a greater specific volume than 0.15636. But 0.15 fits right in between the two. If it was below 0.001141, it would be sub cooled, but nope, it's right in the middle. So that means I know it's a mixture, I know its pressure must be 1,255.2 kilopascals. And at 190, v sub f is 0.001141 meters cube per kilogram, v sub g, 0.1536 meters cube per kilogram. And we're given that the specific volume is 0.15. So I plug this into the equation we used earlier for finding specific volume, but instead I solve for x. So x is just the specific volume you have minus the specific volume of the liquid at those conditions divided by the difference between the specific volume of the gas and the specific volume of the liquid at those temperatures. Your tables might actually give you something called v sub fg, and that is that subtraction. Plug in those numbers. We get that x equals 0.95902, or just 0.959. And plug those in, right up into your table. We knew that it was 1,255.2 kilopascals because it was a mixture, and it's 0.959 is its quality. There it is. Oh, it looks like it's on that line, but it's not. It's just really close. It is a little bit to the left. So there's still a tiny bit more liquid to evaporate before it can break free into the superheated region. All right, that is all six of those problems. These are the two tables that we were working with, or it's really just one table broken to two. These were the v sub f's on the left. These were the v sub g's on the right. This is the critical point. That's where v sub f equals v sub g. Everything under here is some type of mixture. Everything over here is a superheated gas. Everything up here is a sub-cooled liquid. I hope you enjoyed it.