 Hello, my name is Adrian and welcome to another video of understanding thermodynamics, where today we are going to look at real gases and the phases of water. Now, in this video, we are going to discuss what is a phase. We're going to look at the different phases of water, what is the relationship between pressure, specific volume and temperature for real gases such as steam. I'm going to show you how to do linear interpolation to find the different properties of steam and what is the relationship between pressure, specific volume and temperature when it comes to liquids and solid phases. And then lastly, we're going to have a look at exactly what is meant by incompressibility. So what is a phase? The term phase refers to a quantity of matter that is homogeneous throughout in both chemical composition and physical structure. Now, homogeneity in physical structures mean that the matter is all solid or all liquid or all gas. An oil-water mixture consists of two liquid phases, the water phase and the oil phase, and they are both liquids, but their chemical compositions differ. Therefore, there are two different liquid phases and the mixture is not homogeneous. Now, there are four naturally occurring states, solids, liquids, gases and plasma. For the purposes of this course, we will not consider plasma. Let's look at the different phases of water. Now, we can distinguish three phases from water, which we've mentioned previously, which is solid, liquid and gas. Now, at 100 kilopascals and minus 5 degrees Celsius, water will be a single phase solid. And when we heat up the solid ice, the ice will turn into liquid water at zero degrees. And at 100 kilopascals between zero and almost 100 degrees Celsius, water will be a single phase liquid. And for temperatures higher than 99.63 degrees Celsius, water will be a gas or what we call superheated steam. Now, we call it superheated steam to distinguish it from the two phase equilibrium mixture of liquid water and steam, which is called saturated liquid or saturated steam. And we will discuss the equilibrium state of the saturated liquid and saturated steam in a later video. Now, away from the line separating these three phases, the single phase solid, liquid and gas phases of water also has two degrees of freedom. In order to fix this state, we therefore need to specify the value of two independent variables. And in this graph, it is temperature and pressure. In general, we do not consider steam as an ideal gas. Therefore, we cannot use the ideal gas law to determine properties such as specific volume. Now, the relationship between pressure and temperature and specific volume is found in tables in what we call steam tables. And these steam tables can be found in thermodynamic textbooks or on the internet. Now, this slide shows an excerpt from a steam table in a textbook. Now, note in the steam tables, water refers to the chemical H2O rather than being an indication of phase. We therefore talk of solid water, liquid water and vapor water. In this case, superheated vapor water is in the heading of the table. The state of water on the phase separation line in the previous slide is indicated by the three letters sat. And it's the saturated state with liquid water and vapor water, which is part of a two phase system. And we will consider two phase systems in a later video. The third column U is internal energy and H is enthalpy. They are also properties, but we will get to them later. From the table, we can read the specific volume for superheated vapor water at 5000 kilopascals and different temperatures. So there's different temperatures along the side here. Now at 400 degrees Celsius, specific volume is 0.05781 cubic meters per kilogram. Now, there may be cases where you don't necessarily have the exact temperature at 400 or 450, but somewhere in between. And thus you will need to interpolate between these two values to get your specific volume. Let's do an example of one of these cases now. So for this case, the pressure of steam is 5000 kilopascal and its specific volume is 0.054 cubic meters per kilogram. And the question asks you to determine the temperature. Now, if you look at the table, specifically the specific volume column, you can see that the value given for specific volume of 0.054 cubic meters per kilogram falls between these two values here, meaning that the temperature that the question asks for is between 350 and 400 degrees Celsius, and we need to use interpolation to get the exact value. We can use the principle of uniform triangles to do our interpolation. We assume a straight line between the two known data points. Distance A divided by distance B is equal to distance C divided by distance D. The answer will thus be 400 minus A, and we get a final value of 367.8 degrees Celsius, where the specific volume of the steam will be 0.054 cubic meters per kilogram. You're welcome to pause this video and see if you get the same answer as me using this interpolation technique. Now, let's look at liquids and solids of water. Let's consider a liquid water at 20 degrees Celsius, and the specific volume of liquid water is a function of temperature and pressure. And this can also be found in the steam tables, as mentioned before. Now, to distinguish single-phase water from saturated water, which is part of two-phase water mixture, we use the words compressed or subcooled liquid water. Now, for these two cases, pressure has almost no effect on the specific volume of liquid water. Now, for a case where we increase the pressure 10-fold from 500 kilopascals to 5000 kilopascals, the change in specific volume is negligible. We can therefore assume that liquid water is incompressible. And we can also assume the same for solids. Right, so in summary, a phase is homogeneous in chemical composition and physical structure. Water can exist in three phases, like we said solids, liquids, and gas, which is usually superheated water vapor, and pressure, specific volume, and temperature has got a relationship which you can find in the steam tables for real gases, where the ideal gas law does not apply. And for values that is not shown in the steam tables, we can use interpolation to calculate those values. Liquids and solids are assumed to be incompressible. Thank you very much for watching. Course notes on which these videos are based on is available on my website, audreonsblog.com. I'm also on Twitter with the Twitter handle at ASVN 90. If you want to connect with me and ask any questions, I am more than happy to answer them. I will see you in the next video. Bye.