 Hello, welcome to another video in the understanding thermodynamics video series where today we are going to look at the two-phase region of water and quality. In this video we will look at specific volume, temperature and pressure in the two-phase region. We will define quality, we will look at how we can calculate quality and we will look at an example where we calculate the specific volume of two-phase vapor liquid mixtures. The saturation or equilibrium temperature of water at 100 kilopascals is 99.61 degrees Celsius and lies on the boundary line between the liquid and vapor phases which is shown by the square. However, the state at 100 kilopascals and 99.61 degrees Celsius can vary from a saturated liquid to a two-phase mixture to a saturated vapor. In order to quantify the quantity saturated liquid and the quantity saturated vapor, we make use of the concept of quality. For a saturated liquid vapor mixture, the quality which is denoted by x is the mass of vapor in a 1 kilogram liquid vapor mixture. The specific volume of the two-phase mixture is equal to the volume of the steam fraction plus the volume of the liquid fraction. The volume of the steam fraction is equal to the mass of the steam x multiplied by the specific volume of the saturated steam. The volume of the liquid fraction is equal to the mass of liquid 1 minus x multiplied by the specific volume of the saturated liquid. This gives us the equation as specific volume is equal to the quality x times the specific volume of a saturated vapor plus 1 minus x times the specific volume of a saturated liquid. Do take note that quality varies between zero and one and is only defined for two-phase mixtures. On the graph, the little square is saturated liquid water at 100 kilopascals and 99.61 degrees Celsius. Its quality is zero. Every state inside the dome is a two-phase mixture consisting of a saturated liquid and a saturated vapor. The quality in this region ranges between zero and one. The little circle denotes saturated vapor. Its quality is one. Outside the dome, the quality is not defined. Now let's do an example. The question asks that we calculate the volume of 2 kilograms of water at 100 kilopascals with a quality of 0.3. Now we know the total volume is equal to mass multiplied by the specific volume. And as the quality lies between zero and one, we know that for this question, the water is a two-phase saturated mixture. We therefore need to calculate the specific volume of a two-phase mixture, which is given by the equation shown. We find the values of the saturated liquid and the saturated vapor in the saturated water pressure table. And you can see at 100 kilopascals, we have the value for specific volume for saturated liquid and the specific volume for saturated vapor. And we get an answer of 0.5089 cubic meters per kilogram. Note the small contribution of the saturated liquid to the specific volume. As this is a two-phase saturated mixture, we know the temperature is equal to the saturation temperature at 100 kilopascals, which is 99.61 degrees Celsius. And that also shown in the table here. We can look at the two-phase saturated mixture on a temperature specific volume diagram as well. Now again, the small square shows a saturated liquid where the quality is zero. We have a two-phase state inside the dome where the quality is between zero and one. And then we have saturated vapors shown by the little circle where the quality is equal to one. And outside the dome, the quality is undefined. The next question asks us to calculate the quality of a two-phase saturated water at 80 degrees Celsius with a specific volume of 0.1 cubic meters per kilogram. We know we can calculate specific volume using this equation. And as we are told that this is a two-phase mixture, we can read the values of the saturated liquid water and the saturated vapor from the saturated water temperature table. So at 80 degrees, we have the two values that we need here. And we get an answer of 0.02907, which is between zero and one, which confirms that this is a two-phase mixture. And the pressure is therefore the saturation pressure of 47.416 kilopascal. And this can also be found in the table. So in summary, the quality is the mass fraction vapor in a two-phase liquid vapor mixture. Quality is always between zero and one. And at zero, it shows it's a saturated liquid. And at one, it shows it is a saturated vapor. Quality is only defined for the saturated state. We can also use this equation to calculate the specific volume of a two-phase liquid vapor mixture using quality. I hope you've enjoyed this video. The course notes, which these videos are based on, is on my website, rdransblog.com. I'm also on Twitter. My Twitter handle is at ASVA90, where you can ask me any question, and I will answer it gladly. Thank you very much for watching, and I will see you in the next video. Bye.