Excess thermodynamic function internal energy

We have now seen that for real non-ideal solutions all the thermodynamic properties such as G, S, H, V and the internal energy U can differ significantly from the ideal values. This deviation from ideality can be conveniently expressed as a difference from the ideal quantities. The differences are called excess thermodynamic functions ... 

Further attempts have been made this last decade to obtain competitive results for ppex as compared to simulation data. Recently, Bomont proposed the approximation B X)(r) = a(T, p)B(r) [98], Once the correlation functions, the excess internal energy, the pressure, and the isothermal compressibility are calculated with respect to the first thermodynamic consistency condition, the parameter cl(T, p) is iterated until p0pex/0p satisfies the second thermodynamic consistency condition within 1% [Eq. (87)]. At the end of the iteration cycle... 

The integral equation theory consists in obtaining the pair correlation function g(r) by solving the set of equations formed by (1) the Omstein-Zernike equation (OZ) (21) and (2) a closure relation [76, 80] that involves the effective pair potential weff(r). Once the pair correlation function is obtained, some thermodynamic properties then may be calculated. When the three-body forces are explicitly taken into account, the excess internal energy and the virial pressure, previously defined by Eqs. (4) and (5) have to be, extended respectively [112, 119] so that... 

The enthalpy, internal energy and their excess quantities of the Lennard-Jones binary mixture have been determined using the PY approximation. The values obtained are in good agreement with the results of MC calculation. The enthalpy and isobaric heat capacity are calculated using the extended expression of the thermodynamic quantities in terms of pair correlation functions. 

We consider an interface between a nematic liquid crystal and a solid substrate (Fig. l).The interface of thickness has a structure with a composition different from both bulk phases (crystal/nematic) on its two sides and is characterized thermodynamically by the excess intensive variables such as the concentrations p of chemical species, the entropy s, the internal energy u, etc... . In the present case, where an anisotropic liquid meets an anisotropic solid at the interface, the internal energy u is not only a function of s and p but also depends on the direction of the nematic with respect to the anisotropic solid ... 

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