Phase diagram of a pure substance

Fig. 2-4, Typical phase diagram of a pure substance with two lines of isobaric temperature change 123below critical pressure, 45 above critical pressure.

A supercritical fluid is a substance above its critical temperature and pressure. Figure 3.4 shows a phase diagram of a pure substance, where curve... 

Figure 3.4. Phase diagram of a pure substance. (Reproduced from Ref. 24, with permission from Kluwer Academic Publishers.)...

QUESTIONS 9-11 REFER TO THE PHASE DIAGRAM OF A PURE SUBSTANCE, SHOWN BELOW ... 

Fig. 3-2. P/V/T phase diagram of a pure substance (pure solvent) showing domains in which it exists as solid, liquid, gas (vapour), and/or sc-fluid (CP = critical point TP = triple point p = mass density). The inserted isotherms T2 (T2 > Tc) and Tj, T3 Tc) illustrate the pressure-dependent density p of sc-fluids, which can be adjusted from that of a gas to that of a Hquid. The influence of pressure on density is greatest near the critical point, as shown by the greater slope of isotherm T2 compared to that of T3, which is further away from Tc- Isotherm Ti demonstrates the discontinuity in the density at subcritical conditions due to the phase change. This figure is taken from reference [220].

A phase diagram of a pure substance is a plot of one system variable against another that shows the conditions at which the substance exists as a solid, a liquid, and a gas. The most common of these diagrams plots pressure on the vertical axis versus temperature on the horizontal axis. The boundaries between the single-phase regions represent the pressures and temperatures at which two phases may coexist. The phase diagrams of water and carbon dioxide are shown in Figure 6.1-1. 

Figure 3.4 Phase diagram of a pure substance. As the temperature increases the solid can change from one structure to another (pol3miorphism), and transform directly to the vapour (sublimation). Normally a solid passes initially to a liquid (melting) and then to a vapour (boiling)...

Figure 1. Schematic cuts of the phase diagram of a pure substance, showing the stable, metastable, and unstable regions (a) a low-temperature isotherm with a metastable liquid branch reaching negative pressure, (b) temperature-density cut, and (c) pressure-temperature cut.

Figure 14.13 The pressure temperature phase diagram of a pure substance, emphasizing the supercritical fluid region. The critical point is the highest pressure and temperature at which a pure substance can exist in a vapor iquid equilibrium.

Figure 2.2 Pressure-temperature phase diagram of a pure substance (schematic). Point cp is the critical point, and point tp is the triple point. Each area is labeled with the physical state that is stable under the pressure-temperature conditions that fall within the area. A solid curve (coexistence curve) separating two areas is the locus of pressure-temperature conditions that allow the phases of these areas to coexist at equilibrium. Path ABCD illustrates continuity of states.

Fig. 7-1. Phase diagram of a pure substance. Dotted lines are the solid-liquid and gas-liquid equilibrium curves. Solid line is the eluent cycle of PS-SFC. Further explanations see text.

Figure 13.1 Schematic phase diagram of a pure substance.

Phase Diagram for a Pure Substance — Use of Phase Diagrams — Vapor Pressure of a Pure Substance Pressure-Volume Diagram for a Pure Substance -Density-Temperature Diagram for a Pure Substance Two-Component Mixtures 61... 

Figure 2.12 Pressure-temperature diagram of the phase transitions of a pure substance, illustrating the critical region the circle represents the critical point and the triangle the triple point. Source adapted from Scurto [110],...

The phase behavior of a pure substance may be depicted schematically on a pressure-temperature diagram as shown in Figure 1.1. The curve OC, the vapor pressure curve, separates the vapor and liquid phases. At any point on this curve, the two phases can coexist at equilibrium, both phases having the same temperature and pressure. Phase transition takes place as the curve is crossed along any path. Figure 1.1 shows two possible paths at constant pressure (path AB) and at constant temperature (path DE). At the critical point, C, the properties of the two phases are indistinguishable and no phase transition takes place. In the entire region above the critical temperature or above the critical pressure, only one phase can exist. 

Fig. 4 Enthalpy of carbon tetrachloride as a function of temperature at 1 atm A plot of the enthalpy of a system as a function of its temperature provides a concise view of its thermal behavior. The slope of the line is given by Cp. The enthalpy diagram of a pure substance such as water shows that this plot is not uniform, but is interrupted by sharp breaks at which the value of Cp is apparently infinite, meaning that the substance can absorb or lose heat without undergoing any change in temperature at all. This, of course, is exactly what happens when a substance undergoes a phase change you already know that the temperature of the water boiling in a kettle can never exceed 100°C until all the liquid has evaporated, at which point the temperature (of the steam) resumes its increase as more heat flows into the system.

The transformation of a pure compound from a liquid to a gaseous state and vice versa corresponds to a phase change that can be induced over a limited domain by pressure or temperature. For example, a pure substance in the gaseous state cannot be liquefied above a given temperature, called the critical temperature Tq, irrespective of the pressure applied to it. The minimum pressure required to liquefy a gas at its critical temperature is called the critical pressure Pq (Figure 6.1). These points are the defining boundaries on a phase diagram for a pure substance. The curve, which limits the gas and liquid domains, stops at the critical point... 

Figure 4.8 Phase diagram for a pure substance composed of hard spheres. The fluid-phase Z was computed from the Carnahan-Starling equation (4.5.4) the solid-phase Z was taken from the computer simulation data of Alder et al. [14]. The broken horizontal line at Zt = 6.124 connects fluid (T = 0.494) and solid (t = 0.545) phases that can coexist in equilibrium, as computed by Hoover and Ree [12].

Figure 1 Generalized phase diagram for a pure substance showing the locations of the supercritical and near-critical regions.

The solid-liquid phase equilibrium of a pure substance is described in the state diagram (see Fig. 1-15) by the melting pressure curve p T). This curve is formed by the connection of state points, where the liquid and solid phase coexist at phase equilibrium. For crystallization processes which start from the melting point, a knowledge of this curve is important. 

For a pure substance, the phase diagram is simply a graph of temperature versus pressure. For mixtures, the phase diagram also includes variables that describe the composition of the substance. To illustrate the information contained in a phase diagram, we will examine the phase diagrams of two pure substances water and carbon dioxide. 

When two phases of a single substance are at equilibrium, the pressure is a function only of the temperature. A phase diagram for a pure substance contains three curves representing this dependence for the solid-liquid, solid-gas, and liquid-gas equilibria. These three curves meet at a point called the triple point. The liquid-vapor coexistence curve terminates at the critical point. Above the critical temperature, no gas-liquid phase transition occurs and there is only one fluid phase. The law of corresponding states was introduced, according to which all substances obey the same equation of state in terms of reduced variables... 

Fig. 2. PT diagram for a pure substance that expands on melting (not to scale). For a substance that contracts on melting, eg, water, the fusion curve. A, has a negative slope point / is a triple state point c is the gas—Hquid critical state (—) are phase boundaries representing states of two-phase equiUbrium ...

Vapor—Liquid Systems. The vapor-liquid region of a pure substance is contained within the phase or saturation envelope on a P-V diagram (see Figure 2-80), A vapor, whether it exists alone or in a mixture of gases, is said to be saturated if its partial pressure (P.) equals its equilibrium vapor pressure (P, ) at the system temperature T. This temperature is called the saturation temperature or dew point T ... 

Quality of a Wet Vapor, in the vapor-liquid region of a pure substance, the composition of a two-phase system (at given T and P) varies from pure saturated liquid at the bubble jjoint M to pure saturated vapor at the dew point N along the line MQN on the P- V diagram (Figure 2-80). For a wet vapor represented by an intermediate... 

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