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Josiah Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive 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 invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period). In 1863, Yale awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Haven, Connecticut
New Haven is a city in the U.S. state of Connecticut. It is located on New Haven Harbor on the northern shore of Long Island Sound in New Haven County, Connecticut and is part of the New York City metropolitan area. With a population of 134,023 as determined by the 2020 U.S. census, New Haven is the third largest city in Connecticut after Bridgeport and Stamford and the principal municipality of Greater New Haven, which had a total 2020 population of 864,835. New Haven was one of the first 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, creating the "Nine Square Plan". The central common block is the New Haven Green, a square at the center of Downtown New Haven. The Green is now a National Historic Landmark, and the "Nine Square Plan" is recognized by the American Planning Association as a National Planning Landmark. New Haven is the home of Yale University, New Haven's biggest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exergy
In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its environment. Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant (1904–1972) by using the Greek '' ex'' and ''ergon'' meaning "from work", but the concept had been earlier developed by J Willard Gibbs (the namesake of Gibbs free energy) in 1873. Energy is neither created nor destroyed during a process. Energy changes from one form to another (''see First Law of Thermodynamics''). In contrast, exergy is always destroyed when a process is irreversible, for example loss of heat to t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massieu Function
In thermodynamics, Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol \Psi (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 ''r'' one may choose r variables, e.g. \big( X_1, \dots, X_i, Y_, \dots Y_r \big) \, , to define a coordinate system, where ''X'' and ''Y'' 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 (''r'' + 1)-th variable, \Psi , 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Rheology
{{more references, date=November 2011 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. But when surfactants are adsorbed on the interface, because they lower the surface tension, the stress within the interface is affected by the flow for several reasons. * 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 is strongly affected by surface rheology. Indeed, when they consist of two (or more) fluid phases, deforming the material implies deforming the constitutive phases ( bubbles, drops) and thus their interfaces Interface or interfacing may refer to: Academic journals * '' ... [...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 e^ where is the probability of the system being in state , 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 very 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 solve a very wide variety of problems. The distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Algorithm
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 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 Shannon interpreted the negative of this quantity, which he called 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 maximum entropy thermodynamics. Physicists call the result of applying the Gibbs algorithm the Gibbs distribution for th ... [...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 a large ensembles of microstates 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 of a sam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-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 quaternion analysis 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''. In the conventional form using cross products, vector calculus does not generalize to higher dime ... [...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. A suggestion is surface stress define as association with the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface instead of up definition. A similar term called "surface free energy", which represents the excess free energy per unit area needed to create a new surface, is easily confused with "surface stress". Although surface stress and surface free energy of liquid–gas or liquid–liquid interface are the same, they are very different in solid–gas or solid–solid interface, which will be discussed in details later. Since both terms represent a force per unit length, they have been referred to as "surface tension", which contributes further to the confusion in the literature. Thermodynamics of surface stress Definition of surface free energy is seemly th ... [...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 phases from a single homogeneous mixture. The most common type of phase separation is between two immiscible liquids, such as oil and water. 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. Phase separation in cold gases A mixture of two helium isotopes ( helium-3 and helium-4) in a certain range of temperatures and concentrations separates into parts. The initial mix of the two isotopes spontaneously separates into ^He-rich and ^3He-rich regions. Phase separation also exists in ultracold gas systems. It has been shown experimentally in a two-component ultracold Fermi gas case. The phase separation can compete with other phenomena as vortex lattice formation or an exotic Fulde-Ferrell-Larkin-Ovchinnikov phase. See also * Biomolecular condensate * ... [...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, diffraction, 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. 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 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 integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
