Pure substances are substances whose composition is fixed throughout a process. They can be composed of multiple elements, for example water is composed of hydrogen and oxygen, and even multiple phases, water and water vapor, for example heating water in a piston-cylinder system. If you add heat to piston-cylinder system, the temperature rises, which moves the piston up; basically the volume increases. Notice that the pressure is not changing because the atmospheric pressure is still what’s on the outside. From 1 to 2, the pressure is the same, meaning that this is an isobaric process. Now let’s say that we have water at 20 degrees Celsius If heat is added to the system we can make it go up to 100°C, and the volume would barely change. The density of water does change with temperature, which means that the volume changes (since we have the same mass; the mass is not going anywhere), but not by a lot compared to what’s coming next. From this state, we can keep adding heat, and SOME of the water, not all of it, will become vapor, but both the vapor and the liquid water will be at 100°C. At this state, we have liquid vapor. Btw, the density of water is about 2000 times more than that of vapor , so depending on the fraction of water that became vapor, this volume can expand dramatically ! We add more heat until we boil all the water and we have vapor only (roughly a 2000 times increase in volume), and it’s all still at the same temperature of 100°C. And finally, we add more heat, resulting in the same vapor, only at higher temperature, let’s say 250°C. We call these compressed liquid, saturated liquid , saturated liquid vapor mixture, saturated vapor , and super-heated vapor. In thermodynamics, we’ll constantly use Property Diagrams to show the states of our systems, and the processes they undergo to go from one state to the next. One of the most common ones is Temperature vs. Specific Volume. If we plot these 5 states in a T-v diagram, we’d see 20°C on the y-axis and roughly 1 cubic centimeter per gram on the x-axis for state 1, then up, SLIGHTLY moving right as the density decreases when water goes from 20 to 100°C to state 2, then without going up or down, moves right, meaning the specific volume increases dramatically, while water becomes vapor, passing through 3 to state 4, and finally go up to 250°C while also increasing the systems specific volume, moving right. Remember that all of these changes, due to the fact that we’re using a piston-cylinder system, occur at the same pressure. With this example, we can look at two definitions: the saturation temperature, Tsat, is the temperature at which phase change occurs at constant pressure. On the other hand, we have the saturation pressure, Psat, which is the pressure at which phase change occurs at a constant temperature. This one’s harder to grasp, and we’ll talk a lot more about it in a later lecture, but for now, just picture that if we have water at a constant temperature, let’s say 95°C, and we lower the pressure from 1 atm to let’s say .8 atm, we would be making that liquid water become water vapor. This is exactly what happens when you’re on a high-altitude location. You’re up in the mountains, let’s say, Denver, Mexico City, Bogotá… and you’re trying to boil water. Would you have to bring up the temperature to 100°C for it to boil? No. In these cities, and depending on the altitude , and therefore the atmospheric pressure there , the boiling temperature can be way lower, like for example 90°C in Bogota, Colombia. And the same is true for high pressure. A pressure cooker is nothing more than a pot that can have a pressure higher than that of the outside, atmospheric pressure. So if your pressure cooker is set to 15 psi , (and btw, that’s gauge pressure), which means that the absolute pressure is roughly 30 psi , water can still be liquid at 121 °C, which of course, results in food cooking much quicker (the entire purpose of using a pressure cooker). So going back to our T-v diagram, if pressure is not 1 atm but lower or higher, what changes? Well, we know that at lower pressure values (high elevation cities, for example), the boiling temperature is also lower, and this affects the temperatures lower and higher than the boiling temperature. And the opposite is true for higher pressure values. In a pressure cooker, the temperature needed to boil water is higher, and again, this affects volumes below and above boiling temperature. If we join all saturated liquid points on the left, and all saturated vapor points on the right, we obtain the saturation dome. Everything inside the dome is saturated liquid vapor, everything to the left of the dome is compressed liquid, and everything to the right of the dome is superheated vapor. The top of the dome is called the critical point, where anything above it is a supercritical fluid: a fluid that has properties of both liquids and gases, but none of that will be of interest in a Thermo 1 course. The data for every single state of water is found in textbook tables, where properties are tabulated for different values of Pressure, Temperature, specific volume, specific internal energy, enthalpy (h), and specific entropy (s). We’ll get to what those last two mean in a later lecture, link below if you’re interested in that now. We call these property tables, and you can find tables like these for substances other than water, for example, refrigerants or coolants, ammonia, and propane. The specific table you use will depend on the region your substance is located: you have two options for saturated liquid vapor: one table for compressed liquid, one table for superheated vapor, and two for saturated liquid vapor: one if you’re looking up pressure first, and another one if you’re looking up temperature first. With these tables, if we have any two of these properties, as long as they are INDEPENDENT, we can find the remaining values from this list, for that specific substance. For example, if we have temperature and specific volume of water specifically, we can find the pressure, the specific internal energy, enthalpy, and entropy. Now, independent properties are any combination of these that are NOT pressure and temperature. We’ll learn more about why that is later. To briefly explain it here, think about this: if we know the pressure and the temperature, can we ALWAYS find the specific volume of our substance? The answer is no: for a given pressure (meaning any one of these lines) and a given temperature, it might be that the substance is in the saturated liquid-vapor region, and therefore the specific volume can be anything that lies on that horizontal line. Sometimes, it might be enough, but sometimes it isn’t, so that’s why we call the combination of pressure and temperature a not-independent-properties combination. Now, what if your exact number for temperature is not in the table? What if the table shows property values for 30 and 35°C, but your temperature is 32.8°C. Well, what we normally do in Thermodynamics, is interpolate. And a BIG, BIG part of Thermo problems is tabulating these values. HOWEVER, and listen closely to this, even though this is the typical approach in any Thermo course, any school, any textbook, and it is indeed usually enough for solving Thermo designs, this oversimplified, linear interpolation is NOT precise. If you’ve already taken a course like numerical analysis before, you know that there are MULTIPLE ways of getting much more accurate values when interpolating . In general, you can still use the property tables for steam and coolants in your thermo textbook, and we will be going over simple linear interpolation in the next lecture, link below, specifically for explaining how we do interpolation for these values. But an easier and much quicker alternative to find properties is to use online tools or software like EES, where you enter two property values, like internal energy and temperature, and you get all the other properties as output, no time wasted on interpolating, and lower inaccuracies than linear interpolation. Now , specific volume, internal energy, enthalpy, and entropy can have subscripts. These can be f—for saturated liquid— g—for saturated vapor—, or fg—for the difference between the two. For example, v_g is the specific volume for a saturated vapor. V_f is the specific volume for a saturated liquid, and if you ever get v_fg, it just means the difference between the two, which is sometimes useful if you are trying to find the change in specific volume (although more useful for energy, enthalpy, and entropy) for a substance that went from saturated liquid to saturated vapor. Since there’s 4 main tables, if you’re going to use the tables to find the properties that you’re looking for, you first need to identify the state or region of your substance: saturated, compressed, or superheated. Let’s try identifying that with a simple example that covers everything we learned today, and if you want to see more complex examples on this same topic, make sure to check out the example links in the description below. Let’s say we are drawing a T-v diagram for water, and we want to find the coordinates for these six points, for three pressure situations for water: 100 kPa, 300kPa, and 618.23 kPa. Since these points are the saturated liquid and saturated vapor values for water, out of the four options I mentioned earlier, it makes sense to look up the tables for saturated water. For the first two values of pressure, we’ll use the saturated-pressure table (this means the table for saturated liquid vapor, where pressure is the first column). For 100 kPa, we see that the saturation temperature is 99.61°C, and that the saturated liquid has a specific volume, vf, of 0.001043 m3/kg, and that the saturated vapor has a specific volume, vg, of 1.6941 m3/kg. Looking at 300 kPa, we see a T_sat of 133.52°C, vf = 0.001073 m3/kg, and vg = 0.60582 m3/kg. Now, technically, if the third state we want to look for is also given by its pressure, we would use the same table. And since the value is not a whole number, we’d have to interpolate. But more often than not, these values are given because they correspond to a whole number for the other property, in this case temperature. If we go to the saturated table for temperature, we see that a pressure of 618.23 kPa corresponds to a temperature of 160°C. This is the same as looking up a pressure of 618.23 in the pressure table and finding that the Tsat is 160°C. The specific volumes would be 0.001102 and 0.30680 m3/kg. And that’s it. If for example we know that pressure is 100 kPa and that the temperature is 133.52°C, what region and table would we use? Well, since for 100 kPa, the saturation temperature is 99.61°C, being at 133.52 means that we are in the superheated vapor region. In this case we’d use the superheated table. What about P = 300 kPa and 133.52°C? Well, since Tsat is exactly 133.52 for a pressure of 300 kPa, then we’re in the saturated region and would therefore use either of the saturated tables (temperature or pressure). What if we know our specific volume is 2 m3/kg and the pressure is 300 kPa? In this case, since the specific volume is higher than that for saturated vapor, vg, we know we’re in the superheated region. At 160°C and a specific volume of 0.2 m3/kg? Easy; the saturated region. And finally, what can we say about the pressure if the temperature is 160 and the specific volume is 0.6 m3/kg? Is the pressure lower or higher than when the specific volume was 0.2 m3/kg? Well, we’d know that the pressure is lower, since we’re moving to the right and E is therefore on a constant pressure curve that is lower than before. If you wanna check out more complex examples for this topic, or the other lectures of the Thermo course, make sure to check out the links in the description below. You’ll find lecture from other courses, there, as well. Thanks for watching!