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Non-equilibrium Thermodynamics
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Many systems and processes can, however, be considered to be in equilibrium locally, thus allowing description by currently known equilibrium thermodynamics. Nevertheless, some natural systems and processes remain beyond the scope of equilibrium thermodynamic methods due to the exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantity, physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the thermodynamic efficiency, efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot, Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form \mathrmV = \rho(u_1,u_2,u_3)\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3 where the u_i are the coordinates, so that the volume of any set B can be computed by \operatorname(B) = \int_B \rho(u_1,u_2,u_3)\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3. For example, in spherical coordinates \mathrmV = u_1^2\sin u_2\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3, and so \rho = u_1^2\sin u_2. The notion of a volume element is not limited to three dimensions: in two dimensions it is often known as the area element, and in this setting it is useful for doing surface integrals. Under changes of coordinates, the volume element changes by the absolute value of the Jacobian determinant of the coordinate transformation (by the change of variables formula). This fact allows volume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating Johnson–Nyquist noise, thermal noise in resistors. The Boltzmann constant has Dimensional analysis, dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "Physical constant, defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly joules per kelvin, with the effect of defining the SI unit ke ... [...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] |
Gibbs Free Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–volume work, pressure–volume work, that may be performed by a closed system, thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as G(p,T) = U + pV - TS = H - TS where: * U is the internal energy of the system * H is the enthalpy of the system * S is the entropy of the system * T is the temperature of the system * V is the volume of the system * p is the pressure of the system (which must be equal to that of the surroundings for mechanical equilibrium). The Gibbs free energy change (, measured in joules in International System of Units, SI) is the ''maximum'' amount of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legendre Transformation
In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, is an involutive transformation on real-valued functions that are convex on a real variable. Specifically, if a real-valued multivariable function is convex on one of its independent real variables, then the Legendre transform with respect to this variable is applicable to the function. In physical problems, the Legendre transform is used to convert functions of one quantity (such as position, pressure, or temperature) into functions of the conjugate quantity (momentum, volume, and entropy, respectively). In this way, it is commonly used in classical mechanics to derive the Hamiltonian formalism out of the Lagrangian formalism (or vice versa) and in thermodynamics to derive the thermodynamic potentials, as well as in the solution of differential equations of several variables. For sufficiently smooth functions on ... [...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] |
Extensive Quantity
Physical or chemical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. The terms "intensive and extensive quantities" were introduced into physics by German mathematician Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. According to International Union of Pure and Applied Chemistry (IUPAC), an intensive property or intensive quantity is one whose magnitude is independent of the size of the system. An intensive property is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, an extensive property or extensive quantity is one whose magnitude is additive for subsystems. Examples include mass, volume and Gi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Fluids
Complex fluids are mixtures that have a coexistence between two phases: solid–liquid ( suspensions or solutions of macromolecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions). They exhibit unusual mechanical responses to applied stress or strain due to the geometrical constraints that the phase coexistence imposes. The mechanical response includes transitions between solid-like and fluid-like behavior as well as fluctuations. Their mechanical properties can be attributed to characteristics such as high disorder, caging, and clustering on multiple length scales. Example Shaving cream is an example of a complex fluid. Without stress, the foam appears to be a solid: it does not flow and can support (very) light loads. However, when adequate stress is applied, shaving cream flows easily like a fluid. On the level of individual bubbles, the flow is due to rearrangements of small collections of bubbles. On this scale, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radiation. The first laser was built in 1960 by Theodore Maiman at Hughes Research Laboratories, based on theoretical work by Charles H. Townes and Arthur Leonard Schawlow and the optical amplifier patented by Gordon Gould. A laser differs from other sources of light in that it emits light that is coherence (physics), ''coherent''. Spatial coherence allows a laser to be focused to a tight spot, enabling uses such as optical communication, laser cutting, and Photolithography#Light sources, lithography. It also allows a laser beam to stay narrow over great distances (collimated light, collimation), used in laser pointers, lidar, and free-space optical communication. Lasers can also have high temporal coherence, which permits them to emit light ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Couette Flow
In fluid dynamics, Couette flow is the flow of a viscosity, viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The relative motion of the surfaces imposes a shear stress on the fluid and induces flow. Depending on the definition of the term, there may also be an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like the Earth's mantle and Atmosphere of Earth, atmosphere, and flow in lightly loaded Fluid bearing, journal bearings. It is also employed in Viscometer, viscometry and to demonstrate approximations of Time reversibility, reversibility. It is named after Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century. Isaac Newton first defined the problem of Couette flow in Proposition 51 of his Philosophiæ Naturalis Principia Mathematica, ''Philosophiæ Naturalis Principia Mathematica'', and expanded upon the ideas i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constitutive Equation
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or loads to strains or deformations. Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. Howe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
