Density-temperature diagram: example

Figure 5.9. Examples of HIP diagrams (a) density/pressure mapT = 1473 K for alumina with a particle diameter of 2.5pm, (b) density/temperature map at Pappi. = 100 MN/m for alumina with a particle diameter of 2.5 pm and, (c) density/pressure map at T = 1473K for a superalloy with a particle diameter of 50 pm. ...

In the reduced p p) diagram in Fig. lb, the relevant range for SFE and SFC is shown as a shaded area. At temperatures and pressures just above their critical values, large density variations are induced by small pressure changes at constant temperatures. For example, the compressibility P, which is defined by... 

Polymer-Fluid Equilibria and the Glass Transition Most polymer systems fall in the Class HI or Class V phase diagrams, and the same system can often change from one class into the other as the polymer s molecular weight changes. Most polymers are insoluble in CO9 below 100°C, yet CO9 can be quite sohible in the polymer. For example, the sorption of CO9 into silicone rubber is highly dependent upon temperature and pressure, since these properties have a large influence on the density and activity of CO9. 

It has been proposed to define a reduced temperature Tr for a solution of a single electrolyte as the ratio of kgT to the work required to separate a contact +- ion pair, and the reduced density pr as the fraction of the space occupied by the ions. (M+ ) The principal feature on the Tr,pr corresponding states diagram is a coexistence curve for two phases, with an upper critical point as for the liquid-vapor equilibrium of a simple fluid, but with a markedly lower reduced temperature at the critical point than for a simple fluid (with the corresponding definition of the reduced temperature, i.e. the ratio of kjjT to the work required to separate a van der Waals pair.) In the case of a plasma, an ionic fluid without a solvent, the coexistence curve is for the liquid-vapor equilibrium, while for solutions it corresponds to two solution phases of different concentrations in equilibrium. Some non-aqueous solutions are known which do unmix to form two liquid phases of slightly different concentrations. While no examples in aqueous solution are known, the corresponding... 

We owe much to radioastronomy. It has taught us, for example, that the interstellar medium is the site of complex and varied chemistry, quite different to the chemistry we know and practise on Earth. Indeed conditions in space are very special low temperatures and densities are often accompanied by the effects of extreme radiation. All chemistry taking place in space depends on the cosmic abundances of the reagents. The commonest elements taking part in the combinatorial art of atoms are listed in Table 6.1, based on the abundance diagram. 

The density or its reciprocal, the specific volume, is a commonly used property for polymeric materials. The specific volume is often plotted as a function of pressure and temperature in what is known as a pvT diagram. A typical pvT diagram for an unfilled and filled amorphous polymer is shown, using polycarbonate as an example, in Figs. 2.10 and 2.11 The two slopes in the curves represent the specific volume of the melt and of the glassy amorphous polycarbonate, separated by the glass transition temperature. 

Transferability from the solid state to the liquid state is equally problematic. A truly transferable potential in this region of the phase diagram must reproduce not only the freezing point, but also the temperature of maximum density and the relative stability of the various phases of ice. This goal remains out of reach at present, and few existing models demonstrate acceptable transferability from solid to liquid phases.One feature of water that has been demonstrated by both an EE model study and an ab initio study °° is that the dipole moments of the liquid and the solid are different, so polarization is likely to be important for an accurate reproduction of both phases. In addition, while many nonpolarizable water models exhibit a computed temperature of maximum density for the liquid, the temperature is not near the experimental value of 277 Eor example, TIP4P and... 

Fig. 8 Phase diagram showing the triple point and the critical point. The supercritical zone exists at temperatures and pressures above the critical point. In the supercritical zone, the compound has the density and solvating power of a liquid, but the diffusivity and viscosity of a gas, and exists in a single homogeneous phase. Below the critical point, and along the liquid/gas coexistence line, a liquid and gas phase split can be observed visually. At the triple point, solid, liquid, and gas coexist. At temperatures and pressures below the triple point, solid can sublime directly to gas, for example, by freeze-drying.

Figure 13-18 Some interpretations of phase diagrams, (a) The phase diagram of water. Phase relationships at various points in this diagram are described in the text, (b) Two paths by which a gas can be liquefied. (1) Below the critical temperature. Compressing the sample at constant temperature is represented by the vertical line WZ. Where this line crosses the vapor pressure curve AC, the gas liquefies at that set of conditions, two distinct phases, gas and liquid, are present in equilibrium with each other. These two phases have different properties, for example, different densities. Raising the pressure further results in a completely liquid sample at point Z. (2) Above the critical temperature. Suppose that we instead first warm the gas at constant pressure from W to X, a temperature above its critical temperamre. Then, holding the temperamre constant, we increase the pressure to point Y. Along this path, the sample increases smoothly in density, with no sharp transition between phases. From Y, we then decrease the temperature to reach final point Z, where the sample is clearly a liquid.

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