Pressure-temperature cross curves

In the normal mechanism the reaction runs simultaneously over the entire cross-section of the tube the curves presented in 11.5 illustrate the change in pressure, temperature and composition. We axe fully justified in using an approach in which we consider all quantities characterizing the state to be dependent only on the distance of the point from the shock wave front. In the case of the SM, in the mechanism which we have proposed here for rough tubes, in each intermediate cross-section part of the substance has not reacted at all (the core of the flow) and part of the substance has completely reacted (the peripheral layers) the states of the two parts— composition, temperature, specific volume—are sharply different. The only common element is the pressure, which is practically identical in a given cross-section in the two parts of the flow (in the compressed, but unreacted mixture and in the combustion products), but which changes as combustion progresses from one cross-section to another. 

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. 

The 8,-82-V triple point is one at which the reversible transformation of the crystalline polymorphs can take place. If both 8, and 82 are capable of existing in stable equilibrium with their vapor phase, then the relation is termed enantiotropy, and the two polymorphs are said to bear an enantiotropic relationship to each other. For such systems, the 8,-82-V triple point will be a stable and attainable value on the pressure-temperature phase diagram. A phase diagram of a hypothetical enantiotropic system is shown in Fig. 7. Each of the two polymorphs exhibits a 8-V sublimation curve, and they cross at the same temperature at which they meet the 8,-82 transition curve. The 82-V curve... 

Fig. 2.3. Absorbance as a function of optical density for selected shock tube investigations employing OH electronic absorption spectrometry. The unmarked curve represents the semi-empirical relationship derived in Reference 37, evaluated at a pressure (5 1 atm) and temperature (1520 K) typical of recombination experiments in an argon diluent. Tlie curves labelled 6 1, 3 1 and 1 3 were empirically determined over a selected range of recombination pressures and temperatures for mixtures dilute in argon with those particular initial H2/O2 ratios (Reference 32). The curve identified by HJ (Reference 24) was empirically determined in a 1 % Hg-l % 02-98 % Ar mixture at 1300 K for a selected range of pressures. The cross-hatched area represents the approximate range of absorbances and optical densities observed with an atomic bismuth line source (Reference 41). Also shown are the line HH derived from photographic spectroscopy using instrumental definition of absorption line centres on a continuum (Reference 48), and a solid circle (beyond the range of the abscissa) denoting the photoelectric absorbance reported in Reference 47 for a continuum source at an optical density of 750 x 10" moles liter cm.

T, X curve entirely analogous to the T, Vm, (or T, p) curve for a pure fluid. A constant-temperature cross-section yields a similar p, x coexistence curve. One can take these constant-pressure or -temperature sections including two-phase regions without complication because these variables are fields , variables that have the same values in the conjugate phases on opposite sides of the coexistence surface. In contrast a section at constant x would have no simple interpretation because the curve representing the intersection of the constant-jc plane with the coexistence surface represents points on tie-lines that do not lie in the plane and that terminate at a second phase with a different value of x. 

In Fig. lb, we see the same fluid in a pressure-volume representation. The region corresponding to the supercritical states in Fig. la is cross-hatched in Fig. lb. Fig. lb looks very dift erent from Fig. la. The reason is that volume, as well as density, enthalpy, energy and entropy, are very different variables compared to pressure or temperature. Pressure, temperature, and also chemical potential, called field variables, are equal in coexisting phases, but volume is not, nor are density, enthalpy etc., called density variables. So the single vapor pressure curve corresponds to a coexistence curve with two branches, one for... 

Figure 7. Experimental pressure-temperature phase diagram of AS2S3. Crosses show points and their uncertainties for the experimentally observed phase transitions. Solid line is an approximation of the melting curve, and dashed lines are approximations for the experimental kinetic curves of the solid-solid phase transitions. The points of viscosity measurements are shown hy solid circles and marked by measured values of viscosity (in Pa s units). Shaded region selects a boundary between the melting states with low and high conductivities.

Intermediate temperature polarization curves for two different PEM single cells equipped with the Nafion and Aquivion membranes under slightly pressurized conditions are reported in Fig. 2.23. Polarizations are carried out at 130 °C (3 bar abs. 100 % RH). A higher OCV is registered for the Aquivion-based MEA at this temperature than for the Nafion-based MEA. This behavior could be attributed principally to an increase of the hydrogen cross-over effect in... 

I wo pressure-temperature phase diagrams are shown for H2O (top) and CO2 (bottom). Phase transformations occur when phase boundaries (the red curves) on these plots are crossed as temperature and/or pressure is changed. For example, ice melts (transforms... 

Figure4.4 shows the possibly simplest of all phase diagrams in the t-v- and in the 1-p-plane. The solid line in the upper diagram is the same as the dashed line, i.e. the phase coexistence curve, in Fig. 4.1. The dotted line is the spinodal. The lower graph shows the phase boundary between gas and liquid in the pressure-temperature plane. Notice that here no coexistence region appears because the pressure is constant throughout this region (at constant t). The crosses are vapor pressure data for water taken from HCP.

Table 13.1). In the solid P(CH4) > P(CD4) but the curves cross below the melting point and the vapor pressure IE for the liquids is inverse (Pd > Ph). For water and methane Tc > Tc, but for water Pc > Pc and for methane Pc < Pc- As always, the primes designate the lighter isotopomer. At LV coexistence pliq(D20) < Pliq(H20) at all temperatures (remember the p s are molar, not mass, densities). For methane pliq(CD4) < pLiq(CH4) only at high temperature. At lower temperatures Pliq(CH4) < pliq(CD4). The critical density of H20 is greater than D20, but for methane pc(CH4) < pc(CD4). Isotope effects are large in the hydrogen and helium systems and pLIQ/ < pLiQ and P > P across the liquid range. Pc < Pc and pc < pc for both pairs. Vapor pressure and molar volume IE s are discussed in the context of the statistical theory of isotope effects in condensed phases in Chapters 5 and 12, respectively. The CS treatment in this chapter offers an alternative description.

Fig. 42. Partial pressure of mercury in atm along the three-phase curve for the liquid (Hg0 7Cd0 3)JTe1 y is shown as a solid curve. The uppermost line gives the vapor pressure of pure mercury. Each cross along the three-phase curve marks the pressure and temperature where is equal to the value given near that cross. The dashed lines are calculated results for the liquids (Hg0 7Cd0.3),Te, = 0.4,0.5,0.6, and 0.7, for temperatures above the liquidus temperature. The solid symbols are experimental values (Steininger, 1976). Solid circles are for = 0.50 diamonds are for = 0.40.

After a series of experiments has been performed as a function of temperature, we can obtain the relation between the composition, equilibrium oxygen pressure, and temperature as shown in Fig. 1.2 (the curves for different temperature never cross on the F,-composition plane). In this case, only phase (I) and (II) are assumed to be existent. Phase (I) is known as a... 

The solid line on Figure 12-1 represents the results if the pressure and temperature are in the two-phase region. The correct value of fig is obtained at the point where the solid curve crosses the 2xj = 1.0 line. If the summation results in a value less than 1.0 for a particular trial value of fig, increase the next trial value of ng. Conversely, if the summation is greater than 1.0, decrease the next trial value of ng. Fortunately, the curve in the vicinity of the correct value is relatively straight so that linear interpolation can be used once calculations have been made for two trial values. This should result in rapid convergence on the true value. 

The temperature at which boiling occurs when the external pressure is exactly 1 atm is called the normal boiling point of the liquid. On the plots in Figure 10.13a, the normal boiling points of the three liquids are reached when the curves cross the dashed line representing 760 mm Hg—for ether, 34.6°C (307.8 K) for ethanol, 78.3°C (351.5 K) and for water, 100.0°C (373.15 K). 

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