Variational thermodynamic derivation of the formula for pressure difference across a charged conducting liquid surface and its relation to the thermodynamics of electrical capacitance

1995 ◽  
Vol 450 (1938) ◽  
pp. 177-192 ◽  
Keyword(s):  
Free Energy ◽  
Pressure Difference ◽  
Liquid Surface ◽  
Field Energy ◽  
Conducting Liquid ◽  
Difference Formula ◽  
Direct Energy ◽  
Free Case ◽  
Definition Of ◽  
Work Done

The formula for pressure difference across a charged conducting liquid surface has conventionally been derived by adding a Maxwell stress term to the pressure-difference formula for the field-free case. As far as can be established, no derivation applying direct energy-based methods to the charged-surface case has ever been clearly formulated. This paper presents a first-principles variational derivation, starting from the laws of thermodynamics and modelled on Gibbs’s (1875) approach to the field-free case. The derivation applies to the static equilibrium situation. The method is to treat the charged liquid and its environment as a heterogeneous system in thermodynamic equilibrium, and consider the effects of a small virtual variation in the shape of the conducting-liquid surface. Expressions can be obtained for virtual changes in the free energies of relevant system components and for the virtual electrical work done on the system. By converting the space integral of the variation in electrostatic field energy to an integral over the surface of the liquid electrode, the usual pressure-difference formula is retrieved. It is also shown how the problem can be formulated, in various ways, as a free-energy problem in a situation involving electric stresses and capacitance. The most satisfactory approach involves the definition of an unfamiliar form of free energy, that can be seen as the electrical analogue of the Gibbs free energy and may have use in other contexts.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

The Development of Virtual Concurrent Engineering and its Application to Stamped Products

1992 ◽  
Author(s):  
J. Schmitz ◽  
S. Desa
Keyword(s):  
Product Development ◽  
Design Optimization ◽  
Concurrent Engineering ◽  
Extensive Study ◽  
Engineering Method ◽  
Engineering Product ◽  
Development Method ◽  
Computer Based ◽  
Definition Of ◽  
Work Done

Abstract It is well-known that so-called Concurrent Engineering is a desirable alternative to the largely sequential methods which tend to dominate most product development methods. However, the proper implementation of a concurrent engineering method is still relatively rare. In order to facilitate the development of a reliable concurrent engineering product development method, we start with a careful definition of concurrent engineering and, after an extensive study of all of product development, we propose three criteria which ideal concurrent engineering must satisfy. However, for labor, time, and overall cost considerations, ideal concurrent engineering is infeasible. Instead, we propose a computer-based environment which, by being constructed in accordance with the three criteria, attempts to approach ideal concurrent engineering. The result is the Virtual Concurrent Engineering method and computer implementation environment. This product development method and computer-based implementation system provide the detailed, structured information and data needed to optimally balance the product with respect to the main product development parameters (e.g., manufacturing costs, assembly, reliability). This important information includes re-design suggestions to improve the existing design. The designer can directly apply these re-design suggestions for design optimization, or he can use the results as input into a more complex design optimization or design parameterization function of his own. To demonstrate Virtual Concurrent Engineering, we use it to refine earlier work done by the authors in the Design for Producibility of stamped products. We discuss, in some detail, the results of applying Design for Producibility to complex stampings, including process plans and product producibility computations.

Surfaces, Interfaces, and Changing Shapes in Multilayered Films

MRS Bulletin ◽  
1999 ◽  
Vol 24 (2) ◽  
pp. 39-43 ◽  
Author(s):  
Daniel Josell ◽  
Frans Spaepen
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
External Pressure ◽  
Electronic Density ◽  
Spherical Drop ◽  
Crystal Anisotropy ◽  
Fundamental Quantity ◽  
The Difference ◽  
Image Position ◽  
Work Done

It is generally recognized that the capillary forces associated with internal and external interfaces affect both the shapes of liquid-vapor surfaces and wetting of a solid by a liquid. It is less commonly understood that the same phenomenology often applies equally well to solid-solid or solid-vapor interfaces.The fundamental quantity governing capillary phenomena is the excess free energy associated with a unit area of interface. The microscopic origin of this excess free energy is often intuitively simple to understand: the atoms at a free surface have “missing bonds”; a grain boundary contains “holes” and hence does not have the optimal electronic density; an incoherent interface contains dislocations that cost strain energy; and the ordering of a liquid near a solid-liquid interface causes a lowering of the entropy and hence an increase in the free energy. In what follows we shall show how this fundamental quantity determines the shape of increasingly complex bodies: spheres, wires, thin films, and multilayers composed of liquids or solids. Crystal anisotropy is not considered here; all interfaces and surfaces are assumed isotropic.Consideration of the equilibrium of a spherical drop of radius R with surface free energy γ shows that pressure inside the droplet is higher than outside. The difference is given by the well-known Laplace equation:This result can be obtained by equating work done against internal and external pressure during an infinitesimal change of radius with the work of creating a new surface.

Reply to Professor Simon’s comments

1952 ◽  
Vol 212 (1111) ◽  
pp. 477-477
Keyword(s):  
Free Energy ◽  
Potential Energy ◽  
Temperature Rise ◽  
Frictional Resistance ◽  
Mechanical Equivalent ◽  
Work Of Deformation ◽  
Work Done

The question raised by Professor Simon on the mechanism by which the work done against the frictional resistance is transformed into heat perhaps requires a more fundamental explanation than can be deduced from frictional experiments alone. I t is true that free energy is required for the formation of a new surface when the intermetallic junctions are ruptured, and this in itself does not produce an appreciable temperature rise. With plastic solids (as distinct from liquids), however, most of the work is required to deform the metal around the junctions. As Taylor & Quinney (1937) have shown at least 90% of the work of deformation is liberated as heat and less than 10 % remains as potential energy in the deformed metal, but if the metal is already heavily deformed the proportion of potential energy retained in the metal is negligibly small. Some of the early determinations of the mechanical equivalent of heat are of course based on the assumption that all the frictional work appears as heat. I would like to ask Dr A. J. W. Moore to comment further on this.

Indigenous Peoples in Africa

2017 ◽  
Author(s):  
Renee Sylvain
Keyword(s):  
United Nations ◽  
Indigenous Peoples ◽  
Indigenous Populations ◽  
State Governments ◽  
Legal Cases ◽  
The Status ◽  
International Activism ◽  
The United Nations ◽  
Definition Of ◽  
Work Done

Moringe ole Parkipuny addressed the United Nations Working Group on Indigenous Populations (UNWGIP) in 1989 and, for the first time, opened up discussion of the idea that certain groups of hunter-gathers and pastoralists in Africa merited the status of indigenous peoples. Local activists and international organizations took up the cause in the following decades. Several international conferences resulted in new forms of activism, the reformulation of local identities, and a growing body of scholarship addressing African indigeneity. As NGOs built solidarity among relatively scattered groups of pastoralists and hunter-gatherers, often skeptical state governments initially resisted what they saw as demands for recognition of status and claims to “special rights.” Disagreements between state interests and newly organized indigenous groups were expressed at the United Nations during the process of adopting the Declaration on the Rights of Indigenous Peoples (UNDRIP); but as the idea of indigeneity evolved through such discussions, African governments gradually came on board. International activism and work done by the African Commission on Human and Peoples’ Rights play significant roles in convincing African states to accept the concept of “indigenous peoples.” The issue of developing a definition of “indigenous peoples” appropriate for Africa remains unsettled and continues to present challenges. Mobilization among marginalized groups on the African continent itself, however, has presented NGOs, activists, states, and courts with the opportunity, through well-publicized struggles and several landmark legal cases, to refine the category to better fit with African contexts.

scholarly journals SURFACE EVOLVER SIMULATIONS OF DROPS ON MICROPOSTS

2012 ◽  
Vol 23 (08) ◽  
pp. 1240013 ◽  
Author(s):  
MATTHEW L. BLOW ◽  
JULIA M. YEOMANS
Keyword(s):  
Free Energy ◽  
Arbitrary Shape ◽  
Liquid Surface ◽  
Superhydrophobic Surfaces ◽  
Surface Evolver ◽  
Horizontal Section ◽  
Good Convergence ◽  
Cassie State ◽  
Wenzel State ◽  
Solid Liquid

An important feature in the design of superhydrophobic surfaces is their robustness against collapse from the Cassie–Baxter configuration to the Wenzel state. Upon such a transition a surface loses its properties of low adhesion and friction. We describe how to adapt the Surface Evolver algorithm to predict the parameters and mechanism of the collapse transition on posts of arbitrary shape. In particular, contributions to the free energy evaluated over the solid–liquid surface are reduced to line integrals to give good convergence. The algorithm is validated for straight, vertical and inclined, posts. Numerical results for curved posts with a horizontal section at their ends show that these are more efficient in stabilizing the Cassie state than straight posts, and identify whether the interface first depins from the post sides or the post tips.

scholarly journals Gravitational energy in the framework of embedding and splitting theories

2018 ◽  
Vol 27 (02) ◽  
pp. 1750188 ◽  
Author(s):  
D. A. Grad ◽  
R. V. Ilin ◽  
S. A. Paston ◽  
A. A. Sheykin
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gravitational Energy ◽  
Einstein Equations ◽  
Field Energy ◽  
Energy Localization ◽  
Embedding Theory ◽  
Isometric Embeddings ◽  
Definition Of ◽  
Noether Current

We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge–Teitelboim approach. For the embedding theory, we consider the coordinate translations on the surface as well as the coordinate translations in the flat bulk. In the latter case, the independent definition of gravitational energy–momentum tensor appears as a Noether current corresponding to global inner symmetry. In the field-theoretic form of this approach (splitting theory), we consider Noether procedure and the alternative method of energy–momentum tensor defining by varying the action of the theory with respect to flat bulk metric. As a result, we obtain energy definition in field-theoretic form of embedding theory which, among the other features, gives a nontrivial result for the solutions of embedding theory which are also solutions of Einstein equations. The question of energy localization is also discussed.

Offshore Secrecy Centers and the Necessary Role of States: Bucking the Trend

1995 ◽  
Vol 37 (4) ◽  
pp. 1-24 ◽  
Author(s):  
Anthony P. Maingot
Keyword(s):  
Political System ◽  
Theoretical Work ◽  
Dirty Hands ◽  
Public Office ◽  
Legal Definition ◽  
Inductive Theory ◽  
Definition Of ◽  
Work Done ◽  
The Relationship

Despite the growing interest in the theme of corruption, one cannot yet speak of a body of research and analysis sufficient to the creation of inductive theory. This is not to say that there has not been interesting empirical and theoretical work done. However, most of this work has dealt with variations to the legal definition of corruption as being the illegal use of public office for private gain or, as V. O. Key, Jr. put it, the uninstitutionalized influence of wealth in a political system. The relationship between “power” and corruption has been a subject of analytical speculation since Plato posed, and Machiavelli revived, the “dirty hands” dilemma.

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