Pressure-dependence of free energy

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... 

Kg/p = Vp — (4/3)V. This new parameter (sometimes thought of as the P-wave velocity of an equivalent fluid, for which G = 0) can be determined directly from static compression data V = Kg/p = (1 + Tay)(bP/bp)p. The bulk sound velocity possesses another desirable feature, in that it can also be constrained indirectly through chemical equilibrium experiments. Chemical equilibria describe free energy minima the pressure dependence of free energy is described by the molar volume, and the pressure dependence of volume (or density) is described by Kp and hence V. Thus, experimental determinations of equilibrium phase boundaries can... 

To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that comprise free energy, that is, enthalpy and entropy (recaii that G = H - TS). For an ideal gas, enthalpy is not pressure-dependent. However, entropy does depend on pressure because of its dependence on volume. Consider 1 moie of an ideai gas at a given temperature. At a volume of 10.0 L, the gas has many more positions avaiiable for its molecules than if its volume is 1.0 L. The positional entropy is greater in the iarger volume. In summary, at a given temperature for 1 mole of ideal gas... 

On the base of this approach thermodynamics of hydrogen absorbed outside and inside the (10,10) and the (20,20) single-wall carbon nanotubes with diameters 13.56 A and 27.13 A, respectively, was calculated. The dependencies of free energy F and thermodynamical potential H on applied pressure P and temperature T were calculated. The dependencies of content of hydrogen adsorbed on nanotubes m(P,T) surface on pressure and temperature were calculated from these data. For the first time the dependencies of m(P,T) with accounting of quantum effects and van der Waals forces were calculated. 

The pressure dependence of the reaction free energy is equivalent to the volume change resulting from one formula conversion ... 

It is well known that the energy profiles of Compton scattered X-rays in solids provide a lot of important information about the electronic structures [1], The application of the Compton scattering method to high pressure has attracted a lot of attention since the extremely intense X-rays was obtained from a synchrotron radiation (SR) source. Lithium with three electrons per atom (one conduction electron and two core electrons) is the most elementary metal available for both theoretical and experimental studies. Until now there have been a lot of works not only at ambient pressure but also at high pressure because its electronic state is approximated by free electron model (FEM) [2, 3]. In the present work we report the result of the measurement of the Compton profile of Li at high pressure and pressure dependence of the Fermi momentum by using SR. 

In that way, the thermodynamic approach with the use of conformational term of chemical potential of macromolecules permitted to obtain the expressions for osmotic pressure of semi-diluted and concentrated solutions in more general form than proposed ones in the methods of self-consistent field and scaling. It was shown, that only the osmotic pressure of semi-diluted solutions does not depend on free energy of the macromolecules conformation whereas the contribution of the last one into the osmotic pressure of semi-diluted and concentrated solutions is prelevant. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

In recent years we have undertaken a systematic investigation of the volumes and heat capacities of transfer of alkali halides and tetraalkylammonium bromides from water to mixed aqueous solvents (1-6). These properties are important because, when combined with enthalpies and free energies, they can be used to calculate the temperature and pressure dependences of various equilibrium properties of electrolytes in mixed solvents. Since the properties of electrolytes in mixed aqueous solvents are closely related to the corresponding properties of the nonelectrolyte in an electrolyte solution, infor-... 

The pressure dependence of the Gibbs free energy is needed to calculate G at conditions other than the standard state. From the definition of the free energy (Eq. 9.1) the total differential of G is... 

Equation 9.20 gives the pressure dependence of the Gibbs free energy of a pure substance. More generally, for a mixture one should consider the chemical potential /r, which is defined as the partial molar free energy of species k ... 

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