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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'' or ''H''. The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume (thermodynamics), 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 may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Equations
Thermodynamics is expressed by a mathematical framework of ''thermodynamic equations'' which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. Introduction One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous ''On the Motive Power of Fire'', he states: “We use here the expression ''motive power'' to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.” With the inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Work (Thermodynamics)
In thermodynamics, work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy. An exchange of energy is facilitated by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings, or vice versa. In the surroundings, this mechanical work can lift a weight, for example. The externally measured forces and external effects may be electromagnetic,Guggenheim, E.A. (1985). ''Thermodynamics. An Advanced Treatment for Chemists and Physicists'', seventh edition, North Holland, Amsterdam, .Jackson, J.D. (1975). ''Classical Electrodynamics'', second edition, John Wiley and Sons, New York, .Konopinski, E.J. (1981). ''Electromagnetic Fields and Relativistic Particles'', McGraw-Hill, New York, . gravitational,North, G.R., Erukhimova, T.L. (2009). ''Atmospheric Thermodynamics. Elementary Physics and Chemistry'', Cambridge University Press, Cambridge (UK), . or mechanical (such as pressure-v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, 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 quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann 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 distribu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (classical Thermodynamics)
In classical thermodynamics, entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-nineteenth century from the Greek word τρoπή (''transformation'') to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the system. Ludwig Boltzmann explained the entropy as a measure of the number of possible microscopic configurations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (statistical Thermodynamics)
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] |
Adiabatic Theorem
The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: :''A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum.'' In simpler terms, a quantum mechanical system subjected to gradually changing external conditions adapts its functional form, but when subjected to rapidly varying conditions there is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. Diabatic vs. adiabatic processes At some initial time t_0 a quantum-mechanical system has an energy given by the Hamiltonian \hat(t_0); the system is in an eigenstate of \hat(t_0) labelled \psi(x,t_0). Changing conditions modify the Hamiltonian in a continuous manner, resulting in a final Hamiltonian \hat(t_1) at some later time t_1. The system will e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introduction To Eigenstates
Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum will have some numerical value. The uncertainty principle also says that eliminating uncertainty about position maximises uncertainty about momentum, and eliminating uncertainty about momentum maximizes uncertainty about position. A probability distribution assigns probabilities to all possible values of position and momentum. Schrödinger's wave equation gives wavefunction solutions, the squares of which are probabilities of where the electron might be, just as Heisenberg's probability distribution does. In the everyday world, it is natural and intuitive to think of every object being in its own eigenstate. This is another way of saying that every object appears to have a definite position, a definite momentum, a definite measured value, and a definite time of occurrence. However, the uncertainty principle says that it i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microcanonical Ensemble
In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time. The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: ), the system's volume (symbol: ), as well as the total energy in the system (symbol: ). Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the ensemble. In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at . All other microstates are given a probability of zero. Since the probabilities must add up to 1, the ... [...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. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. 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 microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat
In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is also often used to refer to the thermal energy contained in a system as a component of its internal energy and that is reflected in the temperature of the system. For both uses of the term, heat is a form of energy. An example of formal vs. informal usage may be obtained from the right-hand photo, in which the metal bar is "conducting heat" from its hot end to its cold end, but if the metal bar is considered a thermodynamic system, then the energy flowing within the metal bar is called internal energy, not heat. The hot metal bar is also transferring heat to its surroundings, a correct statement for both the strict and loose meanings of ''heat''. Another example of informal usage is the term '' heat content'', used despite the fact that p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Forces
Generalized forces find use in Lagrangian mechanics, where they play a role conjugate to generalized coordinates. They are obtained from the applied forces, Fi, i=1,..., n, 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, δW, of the applied forces. The virtual work of the forces, Fi, acting on the particles Pi, i=1,..., n, is given by :\delta W = \sum_^n \mathbf _ \cdot \delta \mathbf r_i where δri is the virtual displacement of the particle Pi. Generalized coordinates Let the position vectors of each of the particles, ri, be a function of the generalized coordinates, qj, j=1,...,m. Then the virtual displacements δri are given by :\delta \mathbf_i = \sum_^m \frac \delta q_j,\quad i=1,\ldots, n, where δqj is the virtual d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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