|
Hard Spheres
Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") repulsion that atoms and spherical molecules experience at very close distances. Hard spheres systems are studied by analytical means, by molecular dynamics simulations, and by the experimental study of certain colloidal model systems. Beside being a model of theoretical significance, the hard-sphere system is used as a basis in the formulation of several modern, predictive Equations of State for real fluids through the SAFT approach, and models for transport properties in gases through Chapman-Enskog Theory. Formal definition Hard spheres of diameter \sigma are particles with the following pairwise interaction potential: V(\mathbf_1, \mathbf_2) = \begin 0 & \text \quad , \mathbf_1-\mathbf_2, \geq \sigma \\ \infty & \text \qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ..., information theory and sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Fluid
Classical fluidsR. Balescu, ''Equilibrium and Nonequilibrium Statistical Mechanics'', (John Wiley, 1975) are systems of particles which retain a definite volume, and are at sufficiently high temperatures (compared to their Fermi energy) that quantum effects can be neglected. A system of hard spheres, interacting only by hard collisions (e.g., billiards, marbles), is a model classical fluid. Such a system is well described by the Percus–Yevik equation. Common liquids, e.g., liquid air, gasoline etc., are essentially mixtures of classical fluids. Electrolytes, molten salts, salts dissolved in water, are classical charged fluids. A classical fluid when cooled undergoes a freezing transition. On heating it undergoes an evaporation transition and becomes a classical gas that obeys Boltzmann statistics. A system of charged classical particles moving in a uniform positive neutralizing background is known as a one-component plasma (OCP). This is well described by the hyper-netted chain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Revised Enskog Theory
Revise or revised may refer to: Bibles * Revised Version of the King James Bible ** New Revised Standard Version of the King James Bible Government and law * Revised Penal Code of the Philippines * Revised Statutes of the United States Other uses * Revised Julian calendar * ''Revised New General Catalogue'', an astronomy catalog * Revised Romanization of Korean See also * Revisable-Form Text Document Content Architecture, or DCA for short, is a standard developed by IBM for text documents in the early 1980s. DCA was used on Mainframe computer, mainframe and IBM i systems and formed the basis of DisplayWrite's file format. DCA was late ... * Revision (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pair Potential
In physics, a pair potential is a function that describes the potential energy of two interacting objects solely as a function of the distance between them. Some interactions, like Coulomb's law in electrodynamics or Newton's law of universal gravitation in mechanics naturally have this form for simple spherical objects. For other types of more complex interactions or objects it is useful and common to approximate the interaction by a pair potential, for example interatomic potentials in physics and computational chemistry that use approximations like the Lennard-Jones and Morse potentials. Functional form The total energy of a system of N objects at positions \vec_i, that interact through pair potential v is given by E=\frac12\sum_^N\sum_^Nv\left(\left, \vec_i - \vec_j\\right)\ . Equivalently, this can be expressed as E=\sum_^N\sum_^Nv\left(\left, \vec_i - \vec_j\\right)\ . This expression uses the fact that interaction is symmetric between particles i and j. It also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Distribution Function
In statistical mechanics, the radial distribution function, (or pair correlation function) g(r) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is taken to be at the origin ''O'', and if \rho = N/V is the average number density of particles, then the local time-averaged density at a distance r from ''O'' is \rho g(r). This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below. In simplest terms it is a measure of the probability of finding a particle at a distance of r away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of r and r+dr away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and the blue particles are those whose centers are with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Potential
In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of Thermodynamic free energy, free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial Molar concentration, molar Gibbs free energy. At chemical equilibrium or in phase equilibrium, the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmholtz Free Energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature ( isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium. In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant ''pressure''. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure changes. It is also frequently used to define fundamental equations of state of pure substances. The concept of free energy was developed by Hermann von Helmholtz, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residual Property (physics)
In thermodynamics a residual property is defined as the difference between a real fluid property and an ideal gas property, both considered at the same density, temperature, and composition, typically expressed as X(T, V, n) = X^(T, V, n) + X^(T, V, n) where X is some thermodynamic property at given temperature, volume and mole numbers, X^ is value of the property for an ideal gas, and X^ is the residual property. The reference state is typically incorporated into the ideal gas contribution to the value, as X^(T, V, n) = X^(T, n) + \Delta_ X (T, V, n) where X^ is the value of X at the reference state (commonly pure, ideal gas species at 1 bar), and \Delta_ X is the departure of the property for an ideal gas at (T, V, n) from this reference state. Residual properties should not be confused with excess properties, which are defined as the deviation of a thermodynamic property from some reference system, that is typically not an ideal gas system. Whereas excess properties and ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molar Concentration
Molar concentration (also called molarity, amount concentration or substance concentration) is the number of moles of solute per liter of solution. Specifically, It is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/ dm3 (1000 mol/ m3) in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as + Definition Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Avogadro Constant
The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where the particles in question are any designated elementary entity, such as molecules, atoms, ions, ion pairs. The numerical value of this constant is known as the Avogadro number, commonly denoted . The Avogadro ''number'' is an exact number equal to the number of constituent particles in one mole of any substance (by definition of the mole), historically derived from the experimental determination of the number of atoms in 12 grams of carbon-12 (12C) before the 2019 revision of the SI. Both the constant and the number are named after the Italian physicist and chemist Amedeo Avogadro. The Avogadro constant is used as a proportionality factor in relating the ''amount of substance'' , in a sample of a substance , to the corresponding n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
