Systemic modelling of soil water thermodynamics under natural conditions of air temperature and pressure

Following the recent theorization of the systemic approach of natural organizations such as soils, we give in this article the systemic definition of three fundamental variables of thermodynamics: temperature as the internal energy of molecules constituting a fluid phase “ ; entropy ( ), as the ratio of two organization variables of the phase that are: the occupational volume of molecules and their own volume in the phase of volume ; and the internal molecular chemical potential as the ratio of the temperature of a molecule to its mass . This allowed the following conceptual advances that could not be done using the two principles of thermodynamics: i) establishing the definitional equations of the 3 equivalent forms of the Gibbs free energy of the system, ii) establishing that the general equilibrium criterion of the system is the internal molecular potential rather than the temperature , iii) removing the confusion between internal and external pressures of the system that did not allow to distinguish the two types of energy of a molecule: internal and external , then iv) correcting accordingly the differential equations of thermodynamic potentials as well as the Gibbs-Duhem equation. Application to the soil water air system is given followed by some comments about this new vision of thermodynamic equilibrium modeling

Some remarks to the derivation of the “generalized Lippmann equation”

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

The Consequences of Extensivity

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the consequences of extensivity. The Euler equation can be derived from extensivity, and the Gibbs–Duhem equation can be derived from the Euler equation. The Gibbs–Duhem equation shows that changes in the chemical potential are not arbitrary, but are determined by changes in the temperature and pressure for. That in turn simplifies the reconstruction of the fundamental equation from the equations of state. The Euler equation also allows the various thermodynamic potentials to be rewritten in terms of other functions.

Comparative Examination of Nonequilibrium Thermodynamic Models of Thermodiffusion in Liquids

We analyze existing models for material transport in non-isothermal non-electrolyte liquid mixtures that utilize non-equilibrium thermodynamics. Many different sets of equations for material have been derived that, while based on the same fundamental expression of entropy production, utilize different terms of the temperature- and concentration-induced gradients in the chemical potential to express the material flux. We reason that only by establishing a system of transport equations that satisfies the following three requirements can we obtain a valid thermodynamic model of thermodiffusion based on entropy production, and understand the underlying physical mechanism: (1) Maintenance of mechanical equilibrium in a closed steady-state system, expressed by a form of the Gibbs–Duhem equation that accounts for all the relevant gradients in concentration, temperature, and pressure and respective thermodynamic forces; (2) thermodiffusion (thermophoresis) is zero in pure unbounded liquids (i.e., in the absence of wall effects); (3) invariance in the derived concentrations of components in a mixture, regardless of which concentration or material flux is considered to be the dependent versus independent variable in an overdetermined system of material transport equations. The analysis shows that thermodiffusion in liquids is based on the entropic mechanism.

Chemical potential, Gibbs–Duhem equation and quantum gases

Thermodynamic relations like the Gibbs–Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs–Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.