Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.

Open-Circuit Voltage Comes from Non-Equilibrium Thermodynamics

Originally derived by Walther Nernst more than a century ago, the Nernst equation for the open-circuit voltage is a cornerstone in the analysis of electrochemical systems. Unfortunately, the assumptions behind its derivation are often overlooked in the literature, leading to incorrect forms of the equation when applied to complex systems (for example, those with ion-exchange membranes or involving mixed potentials). Such flaws can be avoided by applying a correct thermodynamic derivation independently of the form in which the electrochemical reactions are written. The proper derivation of the Nernst equation becomes important, for instance, in modeling of vanadium redox flow batteries or zinc-air batteries. The rigorous path towards the Nernst equation derivation starts in non-equilibrium thermodynamics.

Geometrical Construction of Auxiliary Axes in an Ellingham Diagram

To facilitate the assessment of the oxide stability in H2-H2O or CO-CO2 atmospheres, auxiliary axes are constructed in the Ellingham diagram. Based on A. Ghosh’s approach, the geometrical interpretation of the diagram is proposed for the reaction 2X + O2 = 2Y, where X and Y could be originated from H2 and H2O or CO and CO2. Two cases are considered when oxygen partial pressures are lower and higher than one bar. By a geometrical method, it is proved that with an appropriate set-up of values relating to the auxiliary axes, the axes representing the ratio between the equilibrium partial pressure of hydrogen and that of water vapour, as well as the ratio between the equilibrium partial pressure of carbon monoxide and that of carbon dioxide, can be constructed. The geometrical method on the construction of axes using thermodynamic derivation is explained in the paper.

Thermodynamic derivation of a non-linear poroelastic model describing hemodynamicsmechanics interplay in the lamina cribrosa

In this paper we formulate a poroelastic model starting from a model of species diffusion in an elastic material. The model is applied to study the mechanics of the lamina cribrosa (LC) in the eye. The LC is a porous tissue at the head of the optic nerve. Deformation of this tissue and impairment of blood flow induced by tissue deformation are considered to be related to the pathogenesis of glaucoma.The governing equations are derived from general thermomechanical principles. We carefully revise the role of the energy-stress Eshelby tensor, mutuated from the framework of tissue growth, in describing the hemo-mechanical behaviour of the tissue.The model accounts for non-linear deformations of the solid matrix and deformation-induced changes in porosity and permeability. The model provides a qualitative better undertanding of the phatophysiology and pathogenesis of glaucoma in terms of coupling between tissue deformation and the resulting impaired hemodynamics inside the LC.