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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] |
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] |
Centimetre–gram–second System Of Units
The centimetre–gram–second system of units (CGS or cgs) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism. The CGS system has been largely supplanted by the MKS system based on the metre, kilogram, and second, which was in turn extended and replaced by the International System of Units (SI). In many fields of science and engineering, SI is the only system of units in use, but CGS is still prevalent in certain subfields. In measurements of purely mechanical systems (involving units of length, mass, force, energy, pressure, and so on), the differences between CGS and SI are straightforward: the unit-conversion factors are all powers of 10 as and . For example, the CGS unit of force is the dyne, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Function (statistical Mechanics)
In physics, a partition function describes the statistics, statistical properties of a system in thermodynamic equilibrium. Partition functions are function (mathematics), functions of the thermodynamic state function, state variables, such as the temperature and volume. Most of the aggregate thermodynamics, thermodynamic variables of the system, such as the energy, total energy, Thermodynamic free energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular Thermodynamic free energy, free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the Environment (systems), environment at fixed temperature, volume, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical Ensemble
In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the heat bath, so that the states of the system will differ in total energy. The principal thermodynamic variable of the canonical ensemble, determining the probability distribution of states, is the absolute temperature (symbol: ). The ensemble typically also depends on mechanical variables such as the number of particles in the system (symbol: ) and the system's volume (symbol: ), each of which influence the nature of the system's internal states. An ensemble with these three parameters, which are assumed constant for the ensemble to be considered canonical, is sometimes called the ensemble. The canonical ensemble assigns a probability to each distinct microstate given by the following exponential: :P = e^, where is the total energy of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Forces
In analytical mechanics (particularly Lagrangian mechanics), generalized forces are conjugate to generalized coordinates. They are obtained from the applied forces , acting on a system that has its configuration defined in terms of generalized coordinates. In the formulation of virtual work, each generalized force is the coefficient of the variation of a generalized coordinate. Virtual work Generalized forces can be obtained from the computation of the virtual work, , of the applied forces. The virtual work of the forces, , acting on the particles , is given by \delta W = \sum_^n \mathbf F_i \cdot \delta \mathbf r_i where is the virtual displacement of the particle . Generalized coordinates Let the position vectors of each of the particles, , be a function of the generalized coordinates, . Then the virtual displacements are given by \delta \mathbf_i = \sum_^m \frac \delta q_j,\quad i=1,\ldots, n, where is the virtual displacement of the generalized coordinate . Th ... [...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] |
Fundamental Thermodynamic Relation
In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentially equations of state, and using the fundamental equations, experimental data can be used to determine sought-after quantities like ''G'' (Gibbs free energy) or ''H'' (enthalpy). The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way. \mathrmU= T\,\mathrmS - P\,\mathrmV\, Here, ''U'' is internal energy, ''T'' is absolute temperature, ''S'' is entropy, ''P'' is pressure, and ''V'' is volume. This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functions Of State
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example. In this law, one state variable (e.g., pressure, volume, temperature, or the amount of substance in a gaseous equilibrium system) is a function of other state variables so is regarded as a state function. A state ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Process (thermodynamics)
In thermodynamics, a reversible process is a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature. Throughout an entire reversible process, the system is in thermodynamic equilibrium, both physical and chemical, and ''nearly'' in pressure and temperature equilibrium with its surroundings. This prevents unbalanced forces and acceleration of moving system boundaries, which in turn avoids friction and other dissipation. To maintain equilibrium, reversible processes are extremely slow ( ''quasistatic''). The process must occur slowly enough that after some small change in a thermodynamic parameter, the physical processes in the system have enough time for the other parameters to self-adjust to match the new, changed parameter value. For example, if a container of water has sat in a room long enough to match the steady temperature of the surrounding air, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Law Of Thermodynamics
The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into Work (thermodynamics), work in a cyclic process."Young, H. D; Freedman, R. A. (2004). ''University Physics'', 11th edition. Pearson. p. 764. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Law Of Thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. For a thermodynamic process affecting a thermodynamic system without transfer of matter, the law distinguishes two principal forms of energy transfer, heat and thermodynamic work. The law also defines the internal energy of a system, an extensive property for taking account of the balance of heat transfer, thermodynamic work, and matter transfer, into and out of the system. Energy cannot be created or destroyed, but it can be transformed from one form to another. In an externally isolated system, with internal changes, the sum of all forms of energy is constant. An equivalent statement is that perpetual motion machines of the first kind are impossible; work done by a system on its surroundings requires that the system's internal energy be consumed, so that the amount of internal energy lost by that work must be resupplied as heat by an external e ... [...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] |
