Pressure Dependence of p T

Fig. 36. Pressure dependence of p(T) for (La0.25Ndo.75)o.7Cao.3Mn03 with t = 0.952 < tc after Zhou et al. (1996). Lower inset shows p(T) at low temperatures upper insets show Tq and p(30 K), p(250 K) vs. pressure.

Gal] The pressure dependence of p(T ) Kondo effect in paramagnetic phase... 

Fig. 29. Pressure dependence of p(T) for (La 25Ndo 75)0 jCao sMnOs with t = 0.952 < tj after [143]...

Similar thermal and pressure dependence of aP T P) and /37 (T, P) is needed to complete the metric derivative matrix m that would enable complete characterization of l/"-type derivatives in Ms-... 

An alternative derivation of FFF 5 can be performed by starting with FFF 3 and moving the pressure dependence of y T, P, x ) into a Poynting factor. That Poynting factor will contain an integral over the partial molar excess volume. Then we would combine that Poynting factor with the one already appearing in FFF 3. 

Figure 30. (a) Temperature dependence of the spontaneous polarization of DOBAMBC at different pressures, (b) Pressure dependence of P, of D8 at T = 87.7°C. " (Reprinted with kind permission from the authors and the editor, Gordon and Breach Publishers, World Trade Center, 1(K)0 Lausanne 30, Switzerland.) (c) Pressure dependence of the tilt angle 0 at different temperatures in the Sm C phase of DOBAMBC [(a) and (c) reprinted with kind permission from the authors and the editor, Institute of Physics Publishing,]... 

It can be seen from Equation (7.70) that to calculate AG at any temperature and pressure we need to know values of AH and AS at standard conditions (P= 100 kPa, T = 298 K), the value of ACp as a function of temperature at the standard pressure, and the value of AEj- as a function of pressure at each temperature T. Thus, the temperature dependence of AC/> and the temperature and pressure dependence of AVj-are needed. If such data are available in the form of empirical equations, the required integrations can be carried out analytically. If the data are available in tabular form, graphical or numerical integration can be used. If the data are not available, an approximate result can be obtained by assuming ACp and AVp are constant... 

An interesting example of a one-component systems is SiOa, which can exist in five different crystalline forms or as a liquid or a vapor. As C = 1, the maximum number of phases that can coexist at equilibrium is three. Each phase occupies an area on the T P diagram the two-phase equilibria are represented by curves and the three-phase equilibria by points. Figure 13.1 (2, p. 123), which displays the equUi-brium relationships among the sohd forms of Si02, was obtained from calculations of the temperature and pressure dependence of AG (as described in Section 7.3) and from experimental determination of equUibrium temperature as a function of equilibrium pressure. 

A quantity (symbolized by AV or A V ) derived from the pressure dependence of a reaction rate constant Ay = -RT(dlnk/dF)j where R is the molar gas constant, T is the absolute temperature, k is the reaction rate constant, and P is pressure. For this equation, the rate constants of all non-first-order reactions are expressed in pressure-independent units (e.g., molarity) at a fixed temperature and pressure. 

Fig.1 The s T) responses of ST018 and ST016 at 1 bar over an extended range of T. Also shown is /e T). The insets show an expanded view of s T) at low T and the pressure dependence s (P) for the two crystals at 293 K [15]...

Figure 21. LCT computations for the reduced configurational entropy 5ic defined by Eq. (53) as a function of the reciprocal of the reduced pressure SP = P — Po /P (where P denotes the Vogel pressure) for high molar mass (M = 40001) F-S polymer fluid at fixed temperature T = 388 K. The inset illustrates the temperature dependence of P (symbols) and the line represents a fit to the data points, using P = a + bT with a = —378.6 MPa and b = 1.0825 MPa/K. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Chemical Physics 123, 111102 (2005). Copyright 2005 American Institute of Physics.)...

Cj) Caldirola Paterson Equation of State. Dunkle (Ref 10, p 183), stated that Cook (Ref 2c) found by working backward from experimental detonation rates to Corresponding values of covolume, that for all expls at very high pressures the Covolume is a function of the specific volume only. At these pressures all molecules have the same covolume per unit weight the dependence of a(T,v) on temperature is exceedingly small. The equation of state can be written pV = nRT +a(v)p... 

We have also seen that we can treat the vapor pressure like an equilibrium constant Km- Hence, the temperature dependence of p L can be described by the van t Hoff equation (Eq. 3-50) ... 

Adsorbed Phase Density. Taking into account that isosteres and saturated vapor pressure curves are linear for coordinates In p vs. T l, Bering and Dubinin s method (16) allowed us to derive p vs. T by Equation 6, along an isostere. Neglecting the dependence of p on q relative to that of p on T, according to a classical assumption, we obtained p = f(T) with adjustable parameters. 

Suzuki et al. reported cloud-point temperatures as a function of pressure and composition in mixtures of poly(ethyl acrylate) and poly(vinylidene fluoride) [9], Their data in terms of p(T) curves at constant composition show that miscibility in the same system may either improve or decline with rising pressure, depending on the blend s composition. Important consequences for blend-processing ensue. A planned two-phase extrusion may easily be jeopardized by the pressure building up in the extruder. Conversely, a homogeneous melt may be turned into a two-phase system when the pressure on the blend increases. 

Fig. 9. (a) Scaled resistivity p(T)/p (300 K) vs. T/Tq for YbFe4Sbi2> where Tq is the scaling temperature. Inset shows the pressure dependence of Tq. (b) Scaled resistivity of CeFe4Sbi2 vs. T/Tq. Inset shows pressure dependence of Tq. The room temperature resistivity of both compounds was about 0.8 m cm at ambient pressure (E.D. Bauer et al., 2000). 

To the degree that a single phase of one component has only two degrees of freedom, (dV/da)P T is zero. Even with highly accurate measurements, we expect this quantity and, from Eq. (11), the pressure dependence of the surface tension to be very small. 

Phonon vibration spectrum was determined from force constant k which was determined from dependence of the calculated molecule average energy on volume ( a3), i.e. from compressibility k d2Etot(a,T)lda2. The pressure in the system was determined conventionally as P(a,T) = -dF(a,T) / 8V One can determine the lattice constant a(T) for every value of (P,T) by numerical inversion of the dependence P a,T) => a(P,T) ... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

The isoplethes are approximately a linear function of pressure and Tred- The slope of constant composition lines depend on vapour pressure of a component in solution. With increased solubility of gas in PEG the incline of the isoplethes and vapour pressure increases. In the measurements of P-T diagram for a system PEG-CO2 a liquid solution of C02 in PEG is established even below the melting point of PEG at ambient pressure. This phenomenon is caused by a reduction of the liquefaction temperature of PEG in presence of pressurized C02. 

Figure 3.12 Qualitative temperature and pressure dependence of the Joule-Thomson coefficient Mjt(T P) for C02.

The pressure dependence of N(EF) has been measured recently through the pressure dependence of the 13C-NMR Knight shift in K3Q0 [94]. In Fig. 25, a plot of In T P) versus K(P) is presented. As shown by this plot, linear behavior is effectively observed, which intersects the y axis at flph = 600 K and = N(EF)V = 0.3 at ambient pressure [94]. Thus the value of Tc appears to be governed by N(EF) and the pressure data suggest that high-frequency intraball phonons are likely to be involved in the superconductivity of fullerenes [20,94]. 

Using the correct Pt-Pt distances R(T) or R(p) it is possible to determine the pressure dependence of the coefficient of thermal expansion ac(p). According to Eq. (11) the mean linear coefficient of thermal expansion (in K-1) is given by ... 

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