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Relations Between Heat Capacities
In thermodynamics, the heat capacity at constant volume, C_, and the heat capacity at constant pressure, C_, are extensive properties that have the magnitude of energy divided by temperature. Relations The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): :C_ - C_= V T\frac\, :\frac=\frac\, Here \alpha is the thermal expansion coefficient: :\alpha=\frac\left(\frac\right)_\, \beta_ is the isothermal compressibility (the inverse of the bulk modulus): :\beta_=-\frac\left(\frac\right)_\, and \beta_ is the isentropic compressibility: :\beta_=-\frac\left(\frac\right)_\, A corresponding expression for the difference in specific heat capacities (intensive properties) at constant volume and constant pressure is: : c_p - c_v = \frac where ρ is the density of the substance under the applicable conditions. The corresponding expression for the ratio of specific heat capacities remains the same since the thermodynamic sys ... [...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] |
Thermodynamic System
A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. Thermodynamic systems can be passive and active according to internal processes. According to internal processes, passive systems and active systems are distinguished: passive, in which there is a redistribution of available energy, active, in which one type of energy is converted into another. Depending on its interaction with the environment, a thermodynamic system may be an isolated system, a Closed system#In thermodynamics, closed system, or an Open system (systems theory), open system. An isolated system does not exchange matter or energy with its surroundings. A closed system may exchange heat, experience forces, and exert forces, but does not exchange matter. An open system can interact with its surroundings by exchanging both matter and energy. The physical condition of a thermodynamic system at a given time is described by its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gas Constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per ''particle''. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substance. The Boltzmann constant a ... [...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] |
Ideal Gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions. Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Of Second Derivatives
In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) is the fact that exchanging the order of partial derivatives of a multivariate function :f\left(x_1,\, x_2,\, \ldots,\, x_n\right) does not change the result if some continuity conditions are satisfied (see below); that is, the second-order partial derivatives satisfy the identities :\frac \left( \frac \right) \ = \ \frac \left( \frac \right). In other words, the matrix of the second-order partial derivatives, known as the Hessian matrix, is a symmetric matrix. Sufficient conditions for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations, it is called the Schwarz integrability condition. Formal expressions of symmetry In symbols, the symmetry may be expressed as: :\frac \left( \frac \right) \ = \ \frac \left( \frac \right) \qquad\text\qquad \frac \ = ... [...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] |
Maxwell Relation
file:Thermodynamic map.svg, 400px, Flow chart showing the paths between the Maxwell relations. P is pressure, T temperature, V volume, S entropy, \alpha coefficient of thermal expansion, \kappa compressibility, C_V heat capacity at constant volume, C_P heat capacity at constant pressure. Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell. Equations The structure of Maxwell relations is a statement of equality among the second derivatives for continuous functions. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant ( Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential and x_i and x_j are two different natural variables for that potential, we have ... [...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] |
Quasistatic Process
In thermodynamics, a quasi-static process, also known as a quasi-equilibrium process (from Latin ''quasi'', meaning ‘as if’), is a thermodynamic process that happens slowly enough for the system to remain in internal physical (but not necessarily chemical) thermodynamic equilibrium. An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. Such an idealized process is a succession of physical equilibrium states, characterized by infinite slowness.Rajput, R.K. (2010). ''A Textbook of Engineering Thermodynamics'', 4th edition, Laxmi Publications (P) Ltd, New Delhi, pages 21, 45, 58. Only in a quasi-static thermodynamic process can we exactly define intensive quantities (such as pressure, temperature, specific volume, specific entropy) of the system at any instant during the whole process; otherwise, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Capacity Ratio
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). It is sometimes also known as the '' isentropic expansion factor'' and is denoted by (gamma) for an ideal gasγ first appeared in an article by the French mathematician, engineer, and physicist Siméon Denis Poisson: * On p. 332, Poisson defines γ merely as a small deviation from equilibrium which causes small variations of the equilibrium value of the density ρ. In Poisson's article of 1823 – * γ was expressed as a function of density D (p. 8) or of pressure P (p. 9). Meanwhile, in 1816 the French mathematician and physicist Pierre-Simon Laplace had found that the speed of sound depends on the ratio of the specific heats. * However, he didn't denote the ratio as γ. In 1825, Laplace stated that the speed of sound i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its '' thermal mass''. Definition Basic definition The heat capacity of an object, denoted by C, is the limit C = \lim_\frac, where \Delta Q is the amount of heat that must be added to the object (of mass ''M'') in order to raise its temperature by \Delta T. The value of this parameter usually varies considerably depending o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
