Equilibrium temperature and pressure

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

The presence of impurities can cause a shift in the dissociation point. It implies that the equilibrium temperature and pressure of the carbonate decomposition reaction are shifted. The effect of silica is particularly illustrative in the case of limestone. If silica is present as an impurity, it lowers the decomposition point of limestone. The acid anhydride silica slags combines with the basic calcium oxide according to following ... 

A process in which the velocity of the combustion products is exactly sonic at the equilibrium temperature and pressure of the products (CJ condition), and the velocity of the front relative to the undisturbed medium ahead is supersonic. (The same considerations apply... 

Still further in his lecture Dunkle stated that the fifth equation is obtd by assuming that the deton velocity is the sum of the particle vel and the velocity of sound in the deton products at their equilibrium temperature and pressure ... 

We generally distinguish between two methods when the determination of the composition of the equilibrium phases is taking place. In the first method, known amounts of the pure substances are introduced into the cell, so that the overall composition of the mixture contained in the cell is known. The compositions of the co-existing equilibrium phases may be recalculated by an iterative procedure from the predetermined overall composition, and equilibrium temperature and pressure data It is necessary to know the pressure volume temperature (PVT) behaviour, for all the phases present at the experimental conditions, as a function of the composition in the form of a mathematical model (EOS) with a sufficient accuracy. This is very difficult to achieve when dealing with systems at high pressures. Here, the need arises for additional experimentally determined information. One possibility involves the determination of the bubble- or dew point, either optically or by studying the pressure volume relationships of the system. The main problem associated with this method is the preparation of the mixture of known composition in the cell. 

The metastability of the system prevents hydrate forming immediately at Point D (at the hydrate equilibrium temperature and pressure Figure 3.1b). Instead the system pressure continues to decrease linearly with temperature for a number of hours, without hydrate formation occurring (A to B is the induction period, cf. 1 in Figure 3.1a). At Point B, hydrates begin to form. The pressure drops rapidly to Point C (about 1.01 MPa or 10 atm in 0.5 h). B to C is the catastrophic growth period (cf. 2 in Figure 3.1a). 

With few exceptions (as indicated in the table), all structure H equilibria data were obtained with methane as the small component. Also because there were always four phases present (Lw-H-V-Lhc) with three components (including water) the Gibbs Phase Rule provides for only one composition of each phase which satisfies the equilibrium conditions. Consequently all data were taken without measurement of any phase composition, and only the equilibrium temperature and pressure of the four phases are reported. Due to the paucity of structure H data, included here are one binary including nitrogen and three structure H systems with inhibitor. Such systems clearly illustrate the need for more structure H data. 

Ginsburg and Soloviev (1998, pp. 150-151) state that the BSR is the most widely used indirect indication of gas hydrates. The most important evidence of the hydrate caused nature of the BSR is the coincidence of temperature and pressure calculated at it s depth with the equilibrium temperatures and pressure of gas hydrate stability. The association with the base of the hydrate stability zone is beyond question. ... 

Solubilities of meso-tetraphenylporphyrin (normal melting temperature 444°C) in pentane and in toluene have been measured at elevated temperatures and pressures. Three-phase, solid-liquid-gas equilibrium temperatures and pressures were also measured for these two binary mixtures at conditions near the critical point of the supercritical-fluid solvent. The solubility of the porphyrin in supercritical toluene is three orders of magnitude greater than that in supercritical pentane or in conventional liquid solvents at ambient temperatures and pressures. An analysis of the phase diagram for toluene-porphyrin mixtures shows that supercritical toluene is the preferred solvent for this porphyrin because (1) high solubilities are obtained at moderate pressures, and (2) the porphyrin can be easily recovered from solution by small reductions in pressure. 

Solid-11quid-gas (SLG) equilibrium temperatures and pressures were measured in a constant-volume view cell. A known amount of porphyrin was loaded into the cell, which was then attached to the solvent delivery system and heated to the desired operating temperature. Once thermal equilibrium was obtained, solvent was metered into the cell until the pressure within the cell reached the SLG pressure. Equilibrium was obtained when the pressure stablized and all three phases could be observed. This pressure and the corresponding temperature were recorded as one point on the SLG equilibrium line for the binary mixture. Additional points were obtained by setting a new temperature and repeating the procedure. 

Three-phase, SLG equilibrium temperatures and pressures for binary mixtures of pentane and toluene with TPP are given in Tables II and III, respectively. A lower critical endpoint (LCEP) was observed for pentane-TPP mixtures, and is also denoted in Table II. 

The cloud chemistry simulation chamber (5,6) provides a controlled environment to simulate the ascent of a humid parcel of polluted air in the atmosphere. The cloud forms as the pressure and temperature of the moist air decreases. By controlling the physical conditions influencing cloud growth (i.e. initial temperature, relative humidity, cooling rate), and the size, composition, and concentration of suspended particles, chemical transformation rates of gases and particles to dissolved ions in the cloud water can be measured. These rates can be compared with those derived from physical/chemical models (7,9) which involve variables such as liquid water content, solute concentration, the gas/liquid interface, mass transfer, chemical equilibrium, temperature, and pressure. 

Thermobarometry is the estimation of the equilibrium temperatures and pressures (depths) recorded by mineral chemical equilibria. 

The entropy change A 5 and tlie volume change A are tlie changes wliich occur when a unit amount of a pine chemical species is transferredfrom phase a to phase at tlie equilibrium temperature and pressure. Integration of Eq. (6.8) for this change yields tlie latent heat of phase transition ... 

When a crystalline solid is heated to the temperature at which it melts and passes into the liquid state, the solid/liquid system is univariant. Consequently, for a given pressure value, there will be a definite temperature (independent of the quantities of the two phases present) at which the equilibrium can exist. As with any univariant system, a curve representing the equilibrium temperature and pressure data can be plotted, and this is termed the melting point curve or fusion curve. Since both phases in a solid/liquid equilibrium are condensed (and difficult to compress), the effect of pressure on the melting point of a solid is relatively minor unless the applied pressures are quite large. 

We determine first the equilibrium temperatures and pressures for coexistence. Conde and Vega in their work [31] performed similar calculations using long NPT MD trajectories (up to 1 ps). They waited for complete crystallization or complete melting of the initial three-phase system at several fixed temperatures. We follow another approach looking directiy for the phase coexistence conditions. 

We conclude from these equations that when the system reaches equilibrium, temperature and pressure must be uniform throughout the system. That is, entropy, as defined above, leads to the correct equilibrium conditions of thermal and mechanical equilibrium. 

One of the first versions of such set up was a hydrothermal reactor with two chambers connected by a narrow aperture that can be closed by a valve at equilibrium temperature and pressure (Copeland et ah, 1953). This apparatus was used to study the compositions of liquid and vapor in two-phase equilibrium. In a vertical position of autoclave the sampling chamber, separated by a valve, could be filled by either liquid phase or vapor phase only, whereas main chamber contains both phases. A separation of the contents of these chambers by a valve permitted to keep the sample of liquid or vapor for analysis after cooling. 

In the equations above, T is the arithmetic average of cathode inlet and exit temperatures. Since the cathode does not have a reforming unit, the partial pressures are treated as arithmetic averages of inlet and exit gas partial pressures. In the anode, however, x denotes the reforming unit exit mole fraction, which is essentially the entrance to the anode. These are solved for by assuming that the water gas shift and reforming reactions are at equilibrium, corresponding to a pre-equilibrium temperature and pressure. The assumptions made for pre-equilibrium temperature and pressure are... 

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