P-V-T diagram

Predict the p-V-T behavior of a pure component or a mixture given the p-V-T diagram, and identify a specified state as residing in the solid, liquid, or vapor single-phase region or the solid plus liquid, solid plus vapor, or liquid plus vapor two-phase region. 

The dilatometry at different pressures leads to a full p-V-T phase diagram. Linear macromolecules in the liquid state can reach equilibrium and have then been successfully described by a single p-V-T diagram. The semicrystalline and glassy... 

A schematic, three-dimensional, one-component, p-V-T diagram is reproduced in Fig. 4.20. Its surface represents all possible equilibrium states of the system. The gas area, especially at high temperature and volume, is well described by the ideal gas law, at lower temperatures, the van der Waals equation is applicable as seen in Fig. 2.99. 

The polymer density p is a function of pressure, temperature, and cooling rate. Specific volume V is the reciprocal of density, V = 1/p. The general P, V, T diagram of an amorphous polymer is shown in Fig. 6.24. 

A general P, V, T diagram of a semi-crystalline polymer is shown in Fig. 6.25. 

While the cooling phase lasts until the mold opens, the time at which the cavity pressure again reaches atmospheric pressure is of great importance. At this moment, the plastic is released from the sensor front, and the shrinkage of the molded part starts. This time is not only significant for explaining the p-V-T-diagram but is also used in practical situations. 

The p-V-T diagram of linear macromolecules has only been successfully described for the liquid state. The semicrystalline and glassy states present considerable difficulties because of their nonequilibrium nature. Figure 6.7 shows a typical graph for liquid polypropylene. Empirically the data can be fitted to the empirical Tait equation [Eq. (1) of Fig. 6.7]. Both constants in this equation, vJiT) and B(7), are exponential functions of temperature. 

Plots of the properties of various substances as well as tables and charts are extremely useful in solving engineering thermodynamic problems. Two-dimensional representations of processes on P-V, T-S, or H-S diagrams are especially useful in analyzing cyclical processes. The use of the P-V diagram was illustrated earlier. A typical T-S diagram for a Rankine vapor power cycle is depicted in Figure 2-36. 

Figure 2-78. Typical phase diagram for a pure substance showing P-V-T surface and its projections [60],...

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].

Figure 1 (a) Pressure-Temperature (P-T) and (b) Pressure-Volume (Density) (P-V) phase diagrams for pure... 

High-pressure/high-temperature studies (SC, PD) for determination of P-V-T equations of state. These results lead to an understanding of thermoelastic properties, of exsolution phenomena and of phase diagrams. 

The foremost thermodynamic property associated with any phase boundary is the location of its surface in the p-V-T phase diagram. Most laboratory experiments of glass formation are carried out in a particular V-T plane, usually for atmospheric pressure, and the temperature dependence of volume through the transition is determined. If the glass transition is indeed dictated by the repulsive part of the potential, we expect, at least for simple steeply repulsive systems, that it will occur at the same molecular-reduced volume for many real and model systems and that this will be largely insensitive to the strength of the attractive component of the pair potential relative to kT. 

When molar volume data are not available for at least one high pressure value, as for liquid oxygen, the assumption of the linearity of the p T isochores may be used in order to make reasonable estimates. In this case the entire p-F-T diagram can be described by a series of straight lines determined each by the V value at saturated vapor pressure and by the slope yV. At high pressure the assumed linearity is not valid the error on />, however, remains smaller than 1 % and the accuracy on is then of the same order of magnitude. 

The Fig. 1 phase diagram is for orientation and the regions indicated have been selected for thermodynamic computations p]. Thermodynamic functions may be calculated for the ideal-gas state from spectroscopic data [ ]. Density dependence of the functions on isotherms then may be computed from P-U-T data and used to establish values over that part of the P-V-T surface which is below and to the right of the coexistence region of Fig. 1. However, additional, detailed properties are required, to establish related values for compressed liquid states. These are described below. 

R. Boehler, M. Nicol, and M. L. Johnson, Internally heated diamond anvil cell Phase diagram and P-V-T of iron, in High Pressure Research in Mineral Physics, Geophys. Monogr. Ser., M. H. Manghnani and Y. Syono (Eds), AGU, Washington, DC, 1987, pp. 173-176. 

A schematic diagram showing the P-V-T path followed by a typical point within an amorphous polymer injection moulding. Lines a, b, c represent isobars of increasing pressure. 

If the relationship between the pressure P, the molar volume v, the absolute temperature T and, additionally, the ideal gas specific heat capacity Cp of a pure substance are known, all thermodynamic properties of this substance can be calculated. The typical PvT behavior is shown in Figure 2.1 in a three-dimensional diagram. All thermodynamically stable states are represented by the surface. Depending on the values of the state variables P, v, T the substance exists as a solid (S), liquid (L), or a vapor phase (V) or as a combination of two or three phases. They can be characterized as follows. 

Fig. 2.2 The van dta- Waals-lype phase diagram in T-P (Jefi) and P-V (right) axes. C is the critical point TP is the triple point of the eoexistence between solid, liquid, and vapor (TP is a line in the P-V phase diagram). Solid lines are the phase boundaries, whereas the dashed lines are isotherms at different temperatures (a. below Tc, P slightly below Tc, and y above Tf). The liquid-gas, solid-liquid, and solid-vapor coexistence regions are also shown (After Flowers and Mendoza 1970)...

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

Figure 1.9 Schematic diagram of autoclave for p-V-T-x measurements (Ravich, M.I. and Borovaya, F.E. (1964a) Zh. Neorgan. Khimii, 9, pp. 952-974. With permission from MAIL / Nauka Interperiodica).

We shall consider in detail some versions of p-V-T-x curve methods using schemes of typical isothermal and isobaric sections (Figure 1.10) of phase diagrams for binary systems. 

Figure 6 Schematic diagram of Burnett s apparatus for p, V, T measurement...

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