Details of the Tv Diagram |
On the previous page, we showed how several different isobars could be placed on the Tv diagram for a pure substance. On this page we will discuss the various curves, regions and points on this diagram. In the text below, click on the hyperlink of a particular aspect to see how it appears on the Temperature-Volume (Tv) diagram shown to the right. On the previous page we showed how the locus of saturated liquid and vapor points could be connected to form a two phase region. For any point inside this region, there will be both liquid and vapor phases present. The two phase region is bounded by the saturated liquid curve on one side and the saturated vapor curve on the other. Notice that these two curves meet at a point that corresponds to where one (and only one) of the isobars becomes horizontal at a single point. This point is called the critical point and it corresponds to the highest temperature and highest pressure for which a vapor and liquid can coexist. The temperature at this point is called the critical temperature Tc and the isobar that passes through this point (the only isobar that is horizontal at a single point) is called the critical pressure Pc. The specific volume at this point is called the critical volume vc. All pure substances have Tv phase diagrams that look like the one to the right. However, the scales are much different. For instance, water has a critical temperature and pressure of 647 K and 218 atm but helium's critical temperature is 5 K (only 5 degrees above absolute zero !) and its critical pressure is only about 2 atm. On the other hand, the critical temperature of mercury is above 1800 K. Several isobars, in addition to the critical isobar, are shown on the Tv diagram. Subcritical isobars are isobars for which the pressure is less than the critical pressure. They cut through the two phase region and move from vapor to liquid by a phase transition inside the two phase region. Supercritical isobars are isobars for which pressure is greater than the critical pressure. In an experiment that proceeds along a supercritical isobar, it is possible to move from a state that most would call a gas to one that most would agree was a liquid without ever observing a phase transition. In other words, the change in density from high to low would be gradual and continuous. In fact, because it is possible to move from liquid-like behavior to gas-like behavior without an abrupt transition, it is difficult to pin down exactly where the liquid region is and where the gas region is. We will give one set of definitions here but keep in mind that some of the breaks between one region and another are defined arbitrarily since no abrupt change in material behavior occurs along them. The single phase liquid region, also known as the subcooled liquid region is to the left of the two phase region. It is sometimes considered to end at the critical temperature as shown. To see why this region is referred to as subcooled liquid, consider one of the subcritical isobars shown in the drawing at the right. Note that if a state is located on this isobar and is in the single phase liquid region, it will be at a temperature lower than its boiling temperature at that same pressure. For this reason, it is called subcooled. The single phase vapor region, also known as the superheated vapor region, is to the right of the two phase region. This region often is (arbitrarily) considered to end at the critical isobar. To understand the logic of calling this region superheated vapor, consider again one of the subcritical isobars. Note that a state located on this isobar and in the single phase vapor region will be at a temperature higher than the boiling temperature at that same pressure. Hence, it is called superheated. You may have noticed that there is a region on the diagram that we have not yet discussed. The supercritical fluid region is so called because states in this region are above both the critical temperature and critical pressure. Material in this region has properties somewhat intermediate between what most people would call a gas and what most would call a liquid. Sometimes this is called the dense gas region and other times the expanded liquid region. The word fluid covers both gases and liquids so perhaps supercritical fluid is the best way to describe this region. That pretty much covers all the important points about the Tv diagram. Before moving on though, it should be mentioned that while the constant pressure process was a convenient one to use to generate the Tv diagram, other types of processes are certainly possible and may be traced out on the Tv diagram. Consider, for instance, the case where a fixed mass of a pure substance is placed in a rigid vessel and heated. Since the vessel is rigid, total volume V is constant. Since mass is also constant, the specific volume v would be constant as well. What path would this follow on the Tv diagram? Click here to see. Shown to the right are three different constant v processes, each originating at a temperature T inside the two-phase region and each heated until the system becomes a single phase. Notice however, that process A starts in the two-phase region and ends up as liquid while C starts as two-phase and ends as vapor. Imagine a vessel partly filled with liquid and the remainder vapor with a clearly visible meniscus between the two. In process A, we would observe the meniscus rise to the top of the vessel until the contents became all liquid. In process C, we would see the meniscus fall until the contents became all vapor. Which happens (A or C) simply depends on where in the two phase region the process originates. For process A, the system is mostly liquid to begin with and for process C the system is initially mostly vapor. It is interesting to ask what would happen if we started with a mixture of liquid and vapor at temperature T that had the same overall specific volume as the critical point (process B). As the material in the container was heated, we would see very little change in the position of the meniscus until we got close to the top of the dome. Then we would not see the meniscus rise to the top or fall to the bottom. Rather we would see it become wavy and slowly fade from site as the critical point was passed through. If you ever have a chance to see a film of this phenomena, grab it. Phenomena around critical points are often counter-intuitive and always dramatic. Before leaving this demonstration of the constant volume process, note that each of the three processes shown would cross a number of isobars as the temperature increased. So in these processes, volume is constant but both temperature and pressure change. Now that we have identified all of the important aspects about the Tv diagram we are ready to take the next step. We have been showing several different lines of constant pressure (isobars) on the diagram. Each of these lines represents a different pressure. We could imagine plotting pressure as a third axis where each isobar would represent a different level on the new (pressure) axis. Such a graph would represent a three dimensional PvT surface as shown to the right. The red lines in this diagram represent isobars. We have used the word isobar to represent a line of constant pressure. Frequently, we will be interested in lines of constant temperature as well. A line which represents a constant temperature process is called an isotherm. You could obtain isotherms from the PvT surface to the right by slicing the surface at planes of constant temperature. Click here to see the PvT surface with several isotherms shown in blue. To this point we have not said anything about solids - only liquids and vapors. We will discuss the complete PVT surface (with the solid region included) on the next page. Important Points:
Next page Previous page Contents page Exit tutorial
|