Entropy pressure dependence

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

The simplicity and accuracy of such models for the hydration of small molecule solutes has been surprising, as well as extensively scrutinized (Pratt, 2002). In the context of biophysical applications, these models can be viewed as providing a basis for considering specific physical mechanisms that contribute to hydrophobicity in more complex systems. For example, a natural explanation of entropy convergence in the temperature dependence of hydrophobic hydration and the heat denaturation of proteins emerges from this model (Garde et al., 1996), as well as a mechanistic description of the pressure dependence of hydrophobic... 

The configurational entropy model describes transport properties which are in agreement with VTF and WLF equations. It can, however, predict correctly the pressure dependences, for example, where the free volume models cannot. The advantages of this model over free volume interpretations of the VTF equation are numerous but it lacks the simplicity of the latter, and, bearing in mind that neither takes account of microscopic motion mechanisms, there are many arguments for using the simpler approach. 

The site entropy is thus a sensible candidate for describing fluid relaxation outside the immediate vicinity of the glass transition. In a more precise language, is actually an entropy density, and the maximum in Sc T) derives from an interplay between changes in the entropy and fluid density as the temperature is varied. Explicit calculations demonstrate that the maximum in Sc T) disappears in the limit of an incompressible fluid, which is physically achieved in the limit of infinite pressure. The pressure dependence of Sc T) is described in Section X, where it is found that the maximum in Sc T) becomes progressively shallower and 7a becomes larger with increasing pressure. 

In addition to the equation of state, it will be necessary to describe other thermodynamic properties of the fluid. These include specific heat, enthalpy, entropy, and free energy. For ideal gases the thermodynamic properties usually depend on temperature and mixture composition, with very little pressure dependence. Most descriptions of fluid behavior also depend on transport properties, including viscosity, thermal conductivity, and diffusion coefficients. These properties generally depend on temperature, pressure, and mixture composition. 

For the upper point F corresponding to the given velocity of the spot, in contrast, we obtain strong increase in the pressure, temperature and entropy which depends only on the velocity, but is practically independent of the power of the light ray itself. 

Furthermore, the idealised pressure dependence of the entropy yields no change in the cell voltage caused by the system pressure. The reversible cell voltage resulting from the oxidation of hydrogen and carbon monoxide decreases with a higher system temperature and increases with a higher system pressure. 

Here the temperature and volume are dependent variables and are functions of the entropy, pressure, and mole numbers of the components. From... 

This signifies that the temperature dependence of the volume of activation should be equal to the pressure dependence of the entropy of activation. There are few cases where there is sufficient range of experimental data available to test this relationship. Satisfactory correlations have been noted in some cases.169... 

The entropy change depends on the pressure change. This equation tells us that as the pressure is raised the entropy of a gas decreases i.e., molecules in the gas become more ordered. 

When a system undergoes a process at a constant pressure, does the entropy change depend on the temperature ... 

Equations (25)-(28) are known as the Maxwell relations. We will find the latter two equations to be particularly useful. They give the surprising result that the volume and pressure dependence of entropy are determined by equations of state, from which the temperature derivatives of P and V can be calculated. 

MPa, and 81.5% only at 4.8 MPa [16], In absorption process, the reaction of magnesium with hydrogen is a nucleation and growth mechanism where the nucle-ation rate is pressure dependent. They estimated the enthalpy and corresponding entropy of MgH2 formation as -70.0 kJ/mol and -126 J/mol K, respectively. 

The enthalpy of an ideal gas is independent of pressure, but the entropy DOES depend on P ... 

On the right hand side of Eq. 3.42, the second term is the thermal part and the third term is the pressure-dependent part of the molar entropy. The entropy of a pure substance thus consists of the thermal part and the pressure-dependent part. Under ordinary conditions, however, the latter is so small compared with the former that we may regard the entropy as independent of pressure for condensed substances particularly (vid. Eqs. 7.29 and 7.30). For gaseous substances a slight change in entropy results from a change in pressure, s(T, p) -s (T, p0)- Rln p I p°) where p° is a reference pressure, as will be shown in section 3.8. 

The kinetic effect on (1/72—1/7)) is proportional to (Amagnetic field as shown in Fig. 7.23. From the temperature and pressure dependence, the kinetic parameters presented in Table 7.13 were obtained. The two activation parameters, namely the entropy and the volumes of activation, are negative and also are of the same magnitude for all the lanthanide ions. These activation parameters imply a common water exchange mechanism for all the lanthanides studied and possibly an associative activation path of exchange. The activation volume, AV of —6.0 cm3 mol-1 probably reflects the difference between a large negative contribution due to the transfer of a water molecule electrostricted in the second coordination sphere to the first coordination sphere and a positive contribution due to the difference in partial molar volumes of N + 1 coordinated transition state and N coordinated aquo lanthanide ion. It should be noted that the latter difference (in partial molar volumes of Fn(H20)w+i and Fn(H20)jv is due to the increase in Fn-O bond distance (Fig. 7.16). 

The association of radicals of intermediate complexity may be expected to show pressure dependence under proper conditions. Their lifetime, subject to correction for large entropy changes in the energized state and the contribution of excited states, may be predicted from Eq. (XI.3.4). The pressure range for showing third-order behavior is then predictable from Table XI.2, subject to further correction for the efficiency of deactivation. 

The influence of temperature can be studied, and the activation parameters (e g. the activation enthalpies and entropies) can be calculated. If necessary, the high-pressure stopped-flow technique can be used to study the pressure dependence of reactions, and the corresponding volumes of activation may be calculated. 

To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that constitute free energy—that is, enthalpy and entropy (recall that G = H - TS). For an ideal... 

Ghosh T, Garca AE, Garde S. Enthalpy and entropy contributions to the pressure dependence of hydrophobic interactions. J. Chem. Phys. 2002 116 2480-2486. 

Entropy of activation (continued) sign of, 256 Entropy unit, 242 Enzyme catalysis, 102 Enzyme-substrate complex, 102 Equilibrium, 60, 97, 99, 105, 125, 136 condition for, 205 displacement from, 62, 78 in transition state theory, 201, 205 Equilibrium assumption, 96 Equilibrium constant, 61. 138 complexation, 152 dissociation, 402 ionization, 402 kinetic determination of, 279 partition functions in, 204 pressure dependence of, 144 temperature dependence of, 143, 257 transition state, 207 Equivalence, kinetic, 123 Error analysis, 40 Error propagation, 40 Ester hydrolysis, 4 Euler s method, 106 Excess acidity method, 451 Exchange... 

D" AF (c) have been derived from dissociation pressure dependence upon temperature (van t Hoff relation) the standard entropy for salts D+AF (j.) have been evaluated. Table I contains data from these investigations, which are also pertinent to Figure 2. Standard entropies (7), for a wide variety of these and other salts (all of which are close-packed solids), show a linear dependence on volume, as illustrated in Figure 2. As may be seen, the linear relationship does satisfy the expectation that S° should become zero at zero volume. The standard entropy for a close-packed salt D+AF is therefore assumed, from this experience, to be determined by its FUV, the numerical relationship being ... 

---