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J. W. Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American mechanical engineer and scientist who made fundamental theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis. In 1863, Yale University awarded Gibbs the firs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Haven, Connecticut
New Haven is a city of the U.S. state of Connecticut. It is located on New Haven Harbor on the northern shore of Long Island Sound. With a population of 135,081 as determined by the 2020 United States census, 2020 U.S. census, New Haven is List of municipalities in Connecticut, the third largest city in Connecticut after Bridgeport, Connecticut, Bridgeport and Stamford, Connecticut, Stamford, the largest city in the South Central Connecticut Planning Region, Connecticut, South Central Connecticut Planning Region, and the principal municipality of Greater New Haven metropolitan area, which had a total population of 864,835 in 2020. New Haven was one of the first Planned community, planned cities in the U.S. A year after its founding by English Puritans in 1638, eight streets were laid out in a four-by-four Grid plan, grid, creating the "Nine Square Plan". The central common block is New Haven Green, the New Haven Green, a square at the center of Downtown New Haven. The Green is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exergy
Exergy, often referred to as "available energy" or "useful work potential", is a fundamental concept in the field of thermodynamics and engineering. It plays a crucial role in understanding and quantifying the quality of energy within a system and its potential to perform useful work. Exergy analysis has widespread applications in various fields, including energy engineering, environmental science, and industrial processes. From a scientific and engineering perspective, second-law-based exergy analysis is valuable because it provides a number of benefits over energy analysis alone. These benefits include the basis for determining energy quality (or exergy content), enhancing the understanding of fundamental physical phenomena, and improving design, performance evaluation and optimization efforts. In thermodynamics, the exergy of a System (thermodynamics), system is the maximum useful work (thermodynamics), work that can be produced as the system is brought into Thermodynamic equili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massieu Function
In thermodynamics, the Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol ( Psi), is defined by the following relation: : \Psi = \Psi \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, where for every system with degree of freedom one may choose variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) , to define a coordinate system, where and are extensive and intensive variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system. The -th variable, , is then called the Massieu function.Inden, Gerhard. (2008). �Introduction to Thermodynamics��, ''Materials Issues for Generation IV Systems'', pgs. 73–112. Springer The Massieu function was introduced in the 1869 paper "On the Characteristic Functions of Various Fluids" by French engineer François Massieu (1832-1896). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Rheology
Surface rheology is a description of the rheological properties of a free surface. When perfectly pure, the interface between fluids usually displays only surface tension. The stress within a fluid interface can be affected by the adsorption of surfactants in several ways: * Change in the surface concentration of surfactants when the in-plane flow tends to alter the surface area of the interface (Gibbs' elasticity). * Adsorption/desorption of the surfactants to/from the interface. Importance of surface rheology The mechanical properties (rheology) of dispersed media such as liquid foams and emulsions An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Althoug ... is strongly affected by surface rheology. Indeed, when they consist of two (or more) fluid phases, deforming the material impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Distribution
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution Translated by J.B. Sykes and M.J. Kearsley. See section 28) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: :p_i \propto \exp\left(- \frac \right) where is the probability of the system being in state , is the exponential function, is the energy of that state, and a constant of the distribution is the product of the Boltzmann constant and thermodynamic temperature . The symbol \propto denotes proportionality (see for the proportionality constant). The term ''system'' here has a wide meaning; it can range from a collection of 'sufficient number' of atoms or a single atom to a macroscopic system such as a natural gas storage tank. Therefore, the Boltzmann distribution can be used to sol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Algorithm
FILE:Josiah Willard Gibbs -from MMS-.jpg, 200px, Josiah Willard Gibbs In statistical mechanics, the Gibbs algorithm, introduced by J. Willard Gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstate (statistical mechanics), microstates of a thermodynamic system by minimizing the average log probability : \langle\ln p_i\rangle = \sum_i p_i \ln p_i \, subject to the probability distribution satisfying a set of constraints (usually expectation values) corresponding to the known macroscopic quantities. in 1948, Claude E. Shannon, Claude Shannon interpreted the negative of this quantity, which he called entropy_(Information_theory), information entropy, as a measure of the uncertainty in a probability distribution. In 1957, E.T. Jaynes realized that this quantity could be interpreted as missing information about anything, and generalized the Gibbs algorithm to non-equilibrium systems with the principle of maximum entropy and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Entropy
The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microscopic states that constitute thermodynamic systems. Boltzmann's principle Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states (''microstates'') of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the ''macrostate'' of the system. A useful illustration is the example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, '' Vector Analysis'', though earlier mathematicians such as Isaac Newton pioneered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Stress
Surface stress was first defined by Josiah Willard Gibbs (1839–1903) as the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface science, surface. Depending upon the convention used, the area is either the original, unstretched one which represents a constant number of atoms, or sometimes is the final area; these are atomistic versus continuum definitions. Some care is needed to ensure that the definition used is also consistent with the elastic strain energy, and misinterpretations and disagreements have occurred in the literature. A similar term called "surface free energy", the excess Thermodynamic free energy, free energy per unit area needed to create a new surface, is sometimes confused with "surface stress". Although surface stress and surface free energy of liquid–gas or liquid–liquid Interface (chemistry), interface are the same, they are very different in solid–gas or solid–solid interface. Both terms represent an ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Ensemble (mathematical Physics)
In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The concept of an ensemble was introduced by J. Willard Gibbs in 1902. A thermodynamic ensemble is a specific variety of statistical ensemble that, among other properties, is in statistical equilibrium (defined below), and is used to derive the properties of thermodynamic systems from the laws of classical or quantum mechanics. Physical considerations The ensemble formalises the notion that an experimenter repeating an experiment again and again under the same macroscopic conditions, but unable to control the microscopic details, may expect to observe a ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Separation
Phase separation is the creation of two distinct Phase (matter), phases from a single homogeneous mixture. The most common type of phase separation is between two immiscible liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium. Colloids are formed by phase separation, though not all phase separations forms colloids - for example oil and water can form separated layers under gravity rather than remaining as microscopic droplets in suspension. A common form of spontaneous phase separation is termed spinodal decomposition; it is described by the Cahn–Hilliard equation. Regions of a phase diagram in which phase separation occurs are called miscibility gaps. There are two boundary curves of note: the binodal, binodal coexistence curve and the spinodal, spinodal curve. On one side of the binodal, mixtures are absolutely stable. In between the binodal and the spinodal, mixtures may be metastable: staying mixed (or unmixed) absent some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Optics
In physics, physical optics, or wave optics, is the branch of optics that studies Interference (wave propagation), interference, diffraction, Polarization (waves), polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory (optics), coherence theory. Principle ''Physical optics'' is also the name of an approximation commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray (optics), ray optics and not that it is an exact physical theory. This approximation consists of using ray optics to estimate the field on a surface and then integral, integrating that field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
