 Hello, welcome to another video in the understanding thermodynamics series. My name is Adrian and today we are continuing our focus on substance properties and we are going to have a look at phase change and the different phase diagrams. In this video, we will look at phase change and the two phase systems. We will discuss the concept of equilibrium, the degrees of freedom of two phase systems. We will look at the phase diagrams of water specifically. And then lastly, we will also look at the three dimensional phase diagram of water. There are three two phase systems possible between the solid, liquid and gas phases of water. Ice and water is a solid liquid two phase system depicted in the first picture, which is a glass containing water and ice. A liquid gas interface results when water is boiling. We usually call the gaseous phase of water in a two phase system a vapor. Then lastly, when a snowflake forms, water vapor is transformed directly to a solid phase in what is called de-sublimation. Next, let's look at equilibrium. When we isolate a system from the environment and its properties does not change with time, we say the system is in equilibrium. Now consider the glass of liquid water and solid water or ice. When we add ice cubes to tap water in a glass, the temperatures of the ice and water are initially not the same and they are not in equilibrium. Some ice will melt and the temperature of water will drop after a while. However, if we prevent heat exchange with the environment, the amount of ice will remain constant and the temperature of the ice and water will be the same and remain constant at zero degrees Celsius. We can now say that they have reached a state of equilibrium. Usually, we consider three types of equilibrium. Thermal equilibrium is when the temperature of the phases are the same. The boiling water of the previous slide may be in thermal equilibrium, but not in mechanical equilibrium, which is the second equilibrium state, as there is no equality of opposing forces. Now, mechanical equilibrium is only reached once all the bubbles has risen to the top and there is no more bulk movement of the liquid and vapor phases. Then lastly, we get chemical equilibrium and that is reached when a chemical potential of the different phases are equal. With pure substances, phases do not undergo chemical reactions and chemical equilibrium always exists. Now, let's have a look at a phase diagram. In this graph, there are three different two phase systems which line the lines separating the different phases. We have the solid liquid interface, we have the liquid vapor interface, and then here at the bottom, we have the solid vapor interface. Now, let's consider an example of heating an ice cube, which is taken out of a freezer initially at subzero temperature. Now, I assume the ambient pressure is 100 kilopascals and the temperature is minus 10 degrees when we take the ice out. Now, on the phase diagram, this state is presented by the little circle. Initially, it's in the single phase, which is ice, which is a solid. And as the temperature rises, when we reach the solid liquid phase boundary at 100 kilopascals, the ice will start to melt and a two phase mixture will form. Now, upon further heating, a single phase liquid will result and as we continue heating it up until 99.63 degrees Celsius, the water will start to evaporate and the state is now indicated by the little square in the phase diagram. This is the equilibrium temperature of water at 100 kilopascals. Sure, it is starting to get hot in here or is it just me? Let me just have a drink of water first. If we increase the rate of heating, the rate of evaporation will increase while the temperatures stay the same. Only once all the water has evaporated, the temperature will start to rise and the state become that of superheated vapor. The little diamond shape is the state of water at 300 degrees Celsius in the superheated region. It is important to note that in two phase systems, temperature and pressure are no longer independent. If we increase the pressure on a liquid vapor system, as in a pressure cooker shown here, the boiling point of water will increase and the food inside the pressure cooker will be done quicker as the higher temperature speeds up the chemical reactions. The point on the graph where the three states meet is called the triple point and it is at 0.61 kilopascals and 0.01 degrees Celsius. At the triple point, free phases are in equilibrium and the degrees of freedom are zero. If we change either the temperature or the pressure, one or two phases will disappear. Lastly, we usually assume that the phase boundary between ice and liquid is vertical. This means that water at pressures higher than 0.61 kilopascal and temperatures lower than 0 degrees Celsius is solid ice. Now this figure represents water's phases on a temperature pressure diagram and we can also represent phase change on a temperature specific volume diagram. As mentioned already, if we heat up liquid water enough, it will start to evaporate. It will undergo a phase change. Now it's always nice to visually see the events that occur as a pure substance undergoes a phase change on a specific volume temperature diagram shown here. Now let's consider water at 101.325 kilopascal in a piston cylinder arrangement. Assume the combined effect of the cylinder and the ambient pressure around the cylinder results in a pressure of 101.325 kilopascal inside the piston cylinder setup and the piston is also frictionless and can therefore move up to accommodate any increasing volume and maintain a constant pressure inside. Now initially, the water inside the piston cylinder setup is at 20 degrees Celsius, a temperature lower than the boiling point at this pressure. Therefore, it is a single phase system. Its specific volume is 0.001 002 cubic meters per kilogram. Next, let's heat up the water while the pressure remains constant at 101.325 kilopascal. The volume increases slightly as the water is heated and the temperature rises. Now when we reach 100 degrees Celsius, the specific volume has increased to 0.001043 cubic meters per kilogram. A few water molecules have enough kinetic energy to break free from the liquid phase and the first small vapor bubble forms, which is shown there. The state is that of saturated liquid. On the pressure temperature phase diagram, which you've seen on the previous slide, the state is now on the phase boundary between the liquid and the vapor phases. As more heat is added, more vapor forms. All the heat that is added to the system is used to change the liquid into vapor and the temperature remains constant. As more heat is added to the system, the state of the water turns into a two-phase equilibrium mixture consisting of what is also known as saturated liquid water and saturated vapor water. And this can be visually shown here where we have vapor, which is light blue, and saturated water, which is dark blue. Now upon further heating, the state reaches the solid line boundary on the right. Only a very, very small liquid droplet remains with the majority of the water being converted to water vapor. We can also look at the same process on a pressure specific volume diagram. And the same holds true when we start again with water at 20 degrees Celsius and 100 kilopascals. The specific volume is 0.001, 002 cubic meters per kilogram and we heat the water and once it reaches the saturated liquid state at 99.61 degrees Celsius, the specific volume has changed to 0.001, 043 cubic meters per kilogram. We now continue heating the water and more vapor forms and the state moves horizontally to the right inside the dome. Inside the dome, the state is a two-phase equilibrium mixture consisting of saturated liquid water and saturated vapor water. Eventually all the water has evaporated and the state is saturated vapor. If we continue heating the state, it will move into the super heated region right to the saturated vapor line shown with this little diamond here. The relationship between the three phases of water forms a three-dimensional surface shown here. When you look from the right, you will see the pressure temperature phase diagram. We can trace the state of water at constant pressure heating at a pressure lower than the critical pressure. If we start off here, the water is in solid state or ice and we start heating it up, it will reach the equilibrium line between the solid and liquid water. After all the ice has melted, it will be subcooled water and as we heat it up more, it will reach the equilibrium line at 99.63 degrees Celsius. As we add more heat, we will enter the two-phase region where we have saturated water and saturated vapor. As we reach a purely saturated vapor line and heat it more, we will go into the super heated vapor region. When we look at it from the front, which is the pressure specific volume graph that we showed previously, we can trace another constant pressure scenario. As ice melts to water, your specific volume will decrease and then it will slowly increase as it's heated up. Once it reaches the saturated water line at 99.63 Celsius, if we heat it up more, the specific volume will increase until all the water is converted to vapor and it will increase further as the water moves to the super heated vapor region. So in summary, there are three possible two-phase systems. You get the solid liquid two-phase system, the liquid vapor two-phase system and the solid vapor two-phase system. Now for two-phase systems, temperature and pressure are no longer independent. At the triple point, all three phases are in equilibrium and there's no degrees of freedom at the triple point. And that's it. The course notes which these videos are based on is available on my website, adreonsblock.com. I'm also on Twitter. My Twitter handle is at ASVN90. If you have any questions, you're more than welcome to ask them and I will gladly answer them. Thank you for watching and I will see you in the next video. Bye.