Temperature-versus-pressure phase diagram system

F is at most two because the minimum value for p is one. Thus, the temperature and pressure can be varied independently for a one-component, one-phase system and the system can be represented as an area on a temperature versus pressure diagram. 

At a given pressure and temperature, the total Gibbs free energy of mixing of a one-phase polymer-solvent system of composition 2 should be necessarily minimum, otherwise the system will separate into two phases of different composition, as it is represented in a typical AG versus cp phase diagram of a binary solution (Fig. 25.3). The volume fractions at the minima (dAGIdcp = 0), cp, and (p will vary with temperature (binodal) up to critical conditions (T and (p ) where cp = tp" (Fig. 25.3b). 

Fig. 8.2 Illustration of basic phase diagrams of gas, liquid and solid of the single component system separately according to temperature versus pressure (/ ) and temperature versus density (right)...

FIG. 4.4 The surface conditions of different places in the solar system plotted on a phase diagram of temperature versus pressure. Note how the Earth sits in the liquid water region and Titan sits in the liquid methane region, but other places fall outside these regions and do not maintain surface oceans. 

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

Figure A2.5.5. Phase diagrams for two-eomponent systems with deviations from ideal behaviour (temperature T versus mole fraetion v at eonstant pressure). Liquid-gas phase diagrams with maximum (a) and minimum (b) boiling mixtures (azeotropes), (e) Liquid-liquid phase separation, with a eoexistenee eurve and a eritieal point.

Figure 5.12 is the pressure versus temperature phase diagram for the methane+ water system. Note that excess water is present so that, as hydrates form, all gas is incorporated into the hydrate phase. The phase equilibria of methane hydrates is well predicted as can be seen by a comparison of the prediction and data in Figure 5.12 note that the predicted hydrate formation pressure for methane hydrates at 277.6 K is 40.6 bar. 

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 2.2. The phase diagram of the hard-sphere system as a plot of reduced temperature (inverse reduced pressure) versus reduced density based on the results of Hoover and Ree [24].

Figure 2-34. Calculated ternary CVD phase diagram for the Y-Ba-Cu-C-O-H system at a temperature of 877 °C, a total pressure of 760Torr, and an oxygen partial pressure of 750Torr. The contours represent iso-yields of the tetragonal 123 phase with the numerical legends given as molar percentages 123 versus other phases. (From Vahlas and Besmann [213].)...

Although any of the designs mentioned above will provide the location of phase boundaries (versus temperature and pressure), it is also important to know the compositions of the two phases in equilibrium. Note that while tie lines (lines connecting phases in equilibrium on T-x or p-x diagrams) are horizontal for simple binary mixtures, this is not true for phase separation in multicomponent systems (most notably polymer-fluid systems where the polymer sample contains chains of various lengths). Consequently, ports which allow withdrawal of samples following phase separation and equilibration are an important feature of view cells. Such ports also allow for the measurement of partition coefficients of solutes between, for example, aqueous and CO2 phases. 

A phase diagram is a graph of pressure versus temperature that shows the conditions under which the phases of a substance exist. A phase diagram also reveals how the states of a system change with changing temperature or pressure. 

We deduce by the same reasoning as above that =n-r-. This will be, for example, the case of a divariant system if / = 2. If the system involves two independent components, the transformation will occm within the same solid phase. There will be two variables to fix, for example, temperature and pressure. In a P versus T diagram, there will be as many equilibrimn curves as there are compositions x, (Figure 3.1b). 

Since in all the above-mentioned systems the phase transition occurs with the presence of the vapor phase, the problem of finding the melting/freezing point reduces to the determination of the triple point for each of the cases considered. The general approach to treating this problem is based on the Clausius-Clapeyron relations, describing the solid-vapor and liquid-vapor lines of equilibrium on the phase diagrams in the pressure versus temperature coordinates ... 

Fig. 1. Predicted reaction pressure versus temperature curves for the systems MCI-XCI4, where M is an alkaline earth metal and X is one of the reactive metals Ti, Zr, or Hf. The analysis is only applicable to a binary system of this type which is described by a simple eutectic-type phase diagram and in the absence of solid solubility.

Figure 8.2a shows a Pxy phase diagram for a binary mixture of a and h that follows Raoult s law. The liquid- and gas-phase mole fractions of species a are plotted versus total pressure while the temperature of the system is held constant. The liquid mole fraction versus pressure line (labeled T-Xa) is called the bubble-point curve. It gets this name because if we start at high pressure and decrease the system pressure at constant temperature, this curve marks the pressure at which the first bubble of vapor forms. That bubble s composition can be found where the tie line denoted in the figure intersects the Fya curve. Similarly, the vapor mole fraction versus pressure curve line (labeled P-y is termed the dew-point curve because this marks when the first drop of liquid forms when a superheated vapor mixture is isothermally compressed. 

Fig. 1.29 An oxygen pressure versus temperature diagram for the CrO2 phase region in the Cr-O system. ...

Shown is the free energy of mixing versus composition diagram of the A-B binary system at the temperature 7 and the pressure P. The diagram shows two terminal phases, a and P, and one intermediate phase y. If the overall composition of the system is given by the point X shown in the diagram, find the stable equilibrium phase(s) at 7 and P. 

In this discussion the terms vapor and gas have been used interchangeably but sometimes a distinction is made. The term vapor is sometimes applied to the less dense phase when it coexists with the more dense liquid phase or when its pressure and temperature are such that the point which represents this system on the pressure-temperature diagram is in the area immediately below the vapor pressure versus temperature line. The term gas is sometimes applied to systems which are represented by points far below the vapor pressure versus temperature line. Obviously this distinction is only relative. 

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