1.
Thermodynamics
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Thermodynamics is a branch of science concerned with heat and temperature and their relation to energy and work. The behavior of these quantities is governed by the four laws of thermodynamics, the laws of thermodynamics are explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a variety of topics in science and engineering, especially physical chemistry, chemical engineering. The initial application of thermodynamics to mechanical heat engines was extended early on to the study of chemical compounds, Chemical thermodynamics studies the nature of the role of entropy in the process of chemical reactions and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged in the following decades, statistical thermodynamics, or statistical mechanics, concerned itself with statistical predictions of the collective motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a mathematical approach to the field in his axiomatic formulation of thermodynamics. A description of any thermodynamic system employs the four laws of thermodynamics that form an axiomatic basis, the first law specifies that energy can be exchanged between physical systems as heat and work. In thermodynamics, interactions between large ensembles of objects are studied and categorized, central to this are the concepts of the thermodynamic system and its surroundings. A system is composed of particles, whose average motions define its properties, properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes. With these tools, thermodynamics can be used to describe how systems respond to changes in their environment and this can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. This article is focused mainly on classical thermodynamics which primarily studies systems in thermodynamic equilibrium, non-equilibrium thermodynamics is often treated as an extension of the classical treatment, but statistical mechanics has brought many advances to that field. Guericke was driven to make a vacuum in order to disprove Aristotles long-held supposition that nature abhors a vacuum. Shortly after Guericke, the English physicist and chemist Robert Boyle had learned of Guerickes designs and, in 1656, in coordination with English scientist Robert Hooke, using this pump, Boyle and Hooke noticed a correlation between pressure, temperature, and volume. In time, Boyles Law was formulated, which states that pressure, later designs implemented a steam release valve that kept the machine from exploding. By watching the valve rhythmically move up and down, Papin conceived of the idea of a piston and he did not, however, follow through with his design. Nevertheless, in 1697, based on Papins designs, engineer Thomas Savery built the first engine, although these early engines were crude and inefficient, they attracted the attention of the leading scientists of the time. Black and Watt performed experiments together, but it was Watt who conceived the idea of the condenser which resulted in a large increase in steam engine efficiency. Drawing on all the work led Sadi Carnot, the father of thermodynamics, to publish Reflections on the Motive Power of Fire
2.
Carnot heat engine
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A Carnot heat engine is an engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824, the Carnot engine model was graphically expanded upon by Benoît Paul Émile Clapeyron in 1834 and mathematically elaborated upon by Rudolf Clausius in 1857 from which the concept of entropy emerged. Every thermodynamic system exists in a particular state, a thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, a heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed, in the adjacent diagram, from Carnots 1824 work, Reflections on the Motive Power of Fire, there are two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies to which we can give, or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of caloric. We will call the first the furnace and the second the refrigerator. ”Carnot then explains how we can obtain power, i. e. “work”. It also acts as a cooler and hence can also act as a Refrigerator, the previous image shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engines. The figure at right shows a diagram of a generic heat engine. In the diagram, the “working body”, an introduced by Clausius in 1850. Carnot had postulated that the body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury. The output work W here is the movement of the piston as it is used to turn a crank-arm, Carnot defined work as “weight lifted through a height”. The Carnot cycle when acting as a heat engine consists of the steps, Reversible isothermal expansion of the gas at the hot temperature. During this step the gas is allowed to expand and it work on the surroundings. The temperature of the gas does not change during the process, the gas expansion is propelled by absorption of heat energy Q1 and of entropy Δ S H = Q H / T H from the high temperature reservoir. For this step the piston and cylinder are assumed to be thermally insulated, the gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy. The gas expansion causes it to cool to the cold temperature, Reversible isothermal compression of the gas at the cold temperature, TC. Now the surroundings do work on the gas, causing an amount of heat energy Q2, once again the piston and cylinder are assumed to be thermally insulated
3.
Chemical thermodynamics
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Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. The structure of chemical thermodynamics is based on the first two laws of thermodynamics, starting from the first and second laws of thermodynamics, four equations called the fundamental equations of Gibbs can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the system can be derived using relatively simple mathematics. This outlines the framework of chemical thermodynamics. Gibbs’ collection of papers provided the first unified body of thermodynamic theorems from the principles developed by others, such as Clausius, the first was the 1923 textbook Thermodynamics and the Free Energy of Chemical Substances by Gilbert N. Lewis and Merle Randall. This book was responsible for supplanting the chemical affinity with the free energy in the English-speaking world. The second was the 1933 book Modern Thermodynamics by the methods of Willard Gibbs written by E. A. Guggenheim, the primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation. The 3 laws of thermodynamics, The energy of the universe is constant, breaking or making of chemical bonds involves energy or heat, which may be either absorbed or evolved from a chemical system. Energy that can be released because of a reaction between a set of substances is equal to the difference between the energy content of the products and the reactants. This change in energy is called the change in energy of a chemical reaction. The change in energy is a process which is equal to the heat change if it is measured under conditions of constant volume. Another useful term is the heat of combustion, which is the energy released due to a combustion reaction, food is similar to hydrocarbon fuel and carbohydrate fuels, and when it is oxidized, its caloric content is similar. In chemical thermodynamics the term used for the potential energy is chemical potential. Even for homogeneous bulk materials, the energy functions depend on the composition, as do all the extensive thermodynamic potentials. If the quantities, the number of species, are omitted from the formulae. For a bulk system they are the last remaining extensive variables, the expression for dG is especially useful at constant T and P, conditions which are easy to achieve experimentally and which approximates the condition in living creatures T, P = ∑ i μ i d N i. While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a process involved in changing the composition, e. g. a chemical reaction and we should find a notation which does not seem to imply that the amounts of the components can be changed independently
4.
Equilibrium thermodynamics
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Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance, Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its equilibrium state. In an equilibrium state the potentials, or driving forces, within the system, are in exact balance, an equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a reaction at constant temperature and pressure will reach equilibrium at a minimum of its components Gibbs free energy. In equilibrium thermodynamics, by contrast, the state of the system will be considered uniform throughout, defined macroscopically by such quantities as temperature, pressure, systems are studied in terms of change from one equilibrium state to another, such a change is called a thermodynamic process. Ruppeiner geometry is a type of information used to study thermodynamics. It claims that thermodynamic systems can be represented by Riemannian geometry, non-equilibrium thermodynamics Thermodynamics Adkins, C. J. Equilibrium Thermodynamics, 3rd Ed. & Boles, M. Thermodynamics – an Engineering Approach, 4th Ed, modern Thermodynamics – From Heat Engines to Dissipative Structures. New York, John Wiley & Sons
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Non-equilibrium thermodynamics
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Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium, non-equilibrium thermodynamics is a work in progress, not an established edifice. This article will try to sketch some approaches to it and some concepts important for it, some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many systems and processes will always remain far beyond the scope of non-equilibrium thermodynamic methods. This is because of the small size of atoms, as compared with macroscopic systems. The thermodynamic study of systems requires more general concepts than are dealt with by equilibrium thermodynamics. Another fundamental and very important difference is the difficulty or impossibility in defining entropy at an instant of time in terms for systems not in thermodynamic equilibrium. A profound difference separates equilibrium from non-equilibrium thermodynamics, equilibrium thermodynamics ignores the time-courses of physical processes. In contrast, non-equilibrium thermodynamics attempts to describe their time-courses in continuous detail, equilibrium thermodynamics restricts its considerations to processes that have initial and final states of thermodynamic equilibrium, the time-courses of processes are deliberately ignored. For example, in thermodynamics, a process is allowed to include even a violent explosion that cannot be described by non-equilibrium thermodynamics. Equilibrium thermodynamics does, however, for development, use the idealized concept of the quasi-static process. A quasi-static process is a conceptual smooth mathematical passage along a path of states of thermodynamic equilibrium. It is an exercise in differential geometry rather than a process that could occur in actuality, non-equilibrium thermodynamics, on the other hand, attempting to describe continuous time-courses, need its state variables to have a very close connection with those of equilibrium thermodynamics. This profoundly restricts the scope of thermodynamics, and places heavy demands on its conceptual framework. The suitable relationship that defines non-equilibrium thermodynamic state variables is as follows and it is necessary that measuring probes be small enough, and rapidly enough responding, to capture relevant non-uniformity. In reality, these requirements are demanding, and it may be difficult or practically, or even theoretically. This is part of why non-equilibrium thermodynamics is a work in progress, non-equilibrium thermodynamics is a work in progress, not an established edifice. This article will try to sketch some approaches to it and some concepts important for it, one problem of interest is the thermodynamic study of non-equilibrium steady states, in which entropy production and some flows are non-zero, but there is no time variation of physical variables
6.
Zeroth law of thermodynamics
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The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. Accordingly, thermal equilibrium between systems is a transitive relation, two systems are said to be in the relation of thermal equilibrium if they are linked by a wall permeable only to heat and they do not change over time. The physical meaning of the law was expressed by Maxwell in the words, for this reason, another statement of the law is All diathermal walls are equivalent. The law is important for the formulation of thermodynamics, which needs the assertion that the relation of thermal equilibrium is an equivalence relation. This information is needed for a definition of temperature that will agree with the physical existence of valid thermometers. A thermodynamic system is by definition in its own state of thermodynamic equilibrium. One precise statement of the law is that the relation of thermal equilibrium is an equivalence relation on pairs of thermodynamic systems. This means that a tag can be assigned to every system. This property is used to justify the use of temperature as a tagging system. This statement asserts that thermal equilibrium is a relation between thermodynamic systems. If we also define that every system is in thermal equilibrium with itself. Binary relations that are both reflexive and Euclidean are equivalence relations, one consequence of an equivalence relationship is that the equilibrium relationship is symmetric, If A is in thermal equilibrium with B, then B is in thermal equilibrium with A. Thus we may say that two systems are in equilibrium with each other, or that they are in mutual equilibrium. A reflexive, transitive relationship does not guarantee an equivalence relationship, in order for the above statement to be true, both reflexivity and symmetry must be implicitly assumed. It is the Euclidean relationships which apply directly to thermometry, an ideal thermometer is a thermometer which does not measurably change the state of the system it is measuring. The zeroth law provides no information regarding this final reading, the zeroth law establishes thermal equilibrium as an equivalence relationship. An equivalence relationship on a set divides that set into a collection of distinct subsets where any member of the set is a member of one, in the case of the zeroth law, these subsets consist of systems which are in mutual equilibrium. This partitioning allows any member of the subset to be tagged with a label identifying the subset to which it belongs
7.
First law of thermodynamics
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The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the energy of an isolated system is constant, energy can be transformed from one form to another. Equivalently, perpetual motion machines of the first kind are impossible, investigations into the nature of heat and work and their relationship began with the invention of the first engines used to extract water from mines. Improvements to such engines so as to increase their efficiency and power output came first from mechanics that worked with such machines, deeper investigations that placed those on a mathematical and physics basis came later. The first law of thermodynamics was developed empirically over about half a century, the first full statements of the law came in 1850 from Rudolf Clausius and from William Rankine, Rankines statement is less distinct relative to Clausius. A main aspect of the struggle was to deal with the previously proposed caloric theory of heat, in 1840, Germain Hess stated a conservation law for the so-called heat of reaction for chemical reactions. His law was recognized as a consequence of the first law of thermodynamics. The primitive notion of heat was taken as established, especially through calorimetry regarded as a subject in its own right. Jointly primitive with this notion of heat were the notions of empirical temperature and this framework also took as primitive the notion of transfer of energy as work. This framework did not presume a concept of energy in general, by one author, this framework has been called the thermodynamic approach. The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850, because of its definition in terms of increments, the value of the internal energy of a system is not uniquely defined. It is defined only up to an additive constant of integration. This non-uniqueness is in keeping with the mathematical nature of the internal energy. The internal energy is customarily stated relative to a conventionally chosen standard reference state of the system, the concept of internal energy is considered by Bailyn to be of enormous interest. Its quantity cannot be measured, but can only be inferred. Bailyn likens it to the states of an atom, that were revealed by Bohrs energy relation hν = En − En. In each case, a quantity is revealed by considering the difference of measured quantities. In 1907, George H. Bryan wrote about systems between which there is no transfer of matter, Definition, when energy flows from one system or part of a system to another otherwise than by the performance of mechanical work, the energy so transferred is called heat
8.
Second law of thermodynamics
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The second law of thermodynamics states that the total entropy of an isolated system can only increase over time. It can remain constant in ideal cases where the system is in a state or undergoing a reversible process. The increase in entropy accounts for the irreversibility of processes. Historically, the law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical thermodynamics, classical or quantum, explains the origin of the law. The second law has been expressed in many ways and its first formulation is credited to the French scientist Sadi Carnot in 1824, who showed that there is an upper limit to the efficiency of conversion of heat to work in a heat engine. The first law of thermodynamics provides the definition of internal energy, associated with all thermodynamic systems. The second law is concerned with the direction of natural processes and it asserts that a natural process runs only in one sense, and is not reversible. For example, heat flows spontaneously from hotter to colder bodies. Its modern definition is in terms of entropy, different notations are used for infinitesimal amounts of heat and infinitesimal amounts of entropy because entropy is a function of state, while heat, like work, is not. For an actually possible infinitesimal process without exchange of matter with the surroundings, the second law allows a distinguished temperature scale, which defines an absolute, thermodynamic temperature, independent of the properties of any particular reference thermometric body. These statements cast the law in general physical terms citing the impossibility of certain processes, the Clausius and the Kelvin statements have been shown to be equivalent. The historical origin of the law of thermodynamics was in Carnots principle. The Carnot engine is a device of special interest to engineers who are concerned with the efficiency of heat engines. Interpreted in the light of the first law, it is equivalent to the second law of thermodynamics. It states The efficiency of a quasi-static or reversible Carnot cycle depends only on the temperatures of the two reservoirs, and is the same, whatever the working substance. A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures, the German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. The statement by Clausius uses the concept of passage of heat, as is usual in thermodynamic discussions, this means net transfer of energy as heat, and does not refer to contributory transfers one way and the other
9.
Third law of thermodynamics
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Entropy is related to the number of accessible microstates, and for a system consisting of many particles, quantum mechanics indicates that there is only one unique state with minimum energy. The constant value is called the entropy of the system. Here a condensed system refers to liquids and solids, a classical formulation by Nernst is, It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations. It was proven in 2017 by Masanes and Oppenheim, the 3rd law was developed by the chemist Walther Nernst during the years 1906–12, and is therefore often referred to as Nernsts theorem or Nernsts postulate. The third law of thermodynamics states that the entropy of a system at zero is a well-defined constant. This is because a system at zero temperature exists in its ground state, in 1912 Nernst stated the law thus, It is impossible for any procedure to lead to the isotherm T =0 in a finite number of steps. An alternative version of the law of thermodynamics as stated by Gilbert N. This version states not only ΔS will reach zero at 0 K, some crystals form defects which causes a residual entropy. This residual entropy disappears when the barriers to transitioning to one ground state are overcome. With the development of mechanics, the third law of thermodynamics changed from a fundamental law to a derived law. The counting of states is from the state of absolute zero. In simple terms, the law states that the entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches zero. The alignment of a perfect crystal leaves no ambiguity as to the location and orientation of each part of the crystal, as the energy of the crystal is reduced, the vibrations of the individual atoms are reduced to nothing, and the crystal becomes the same everywhere. The third law provides a reference point for the determination of entropy at any other temperature. The entropy of a system, determined relative to this point, is then the absolute entropy of that system. Mathematically, the entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmanns constant kB = 6977137999999999999♠1. 38×10−23 J K−1. The entropy of a crystal lattice as defined by Nernsts theorem is zero provided that its ground state is unique. As a result, the initial value of zero is selected S0 =0 is used for convenience
10.
Thermodynamic system
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Usually, by default, a thermodynamic system is taken to be in its own internal state of thermodynamic equilibrium, as opposed to a non-equilibrium state. The thermodynamic system is enclosed by walls that separate it from its surroundings. The thermodynamic state of a system is its internal state as specified by its state variables. In addition to the variables, a thermodynamic account also requires a special kind of quantity called a state function. For example, if the variables are internal energy, volume and mole amounts. These quantities are inter-related by one or more functional relationships called equations of state, thermodynamics imposes restrictions on the possible equations of state and on the characteristic equation. The restrictions are imposed by the laws of thermodynamics, the only states considered in equilibrium thermodynamics are equilibrium states. In 1824 Sadi Carnot described a system as the working substance of any heat engine under study. The very existence of such systems may be considered a fundamental postulate of equilibrium thermodynamics. According to Bailyn, the commonly rehearsed statement of the law of thermodynamics is a consequence of this fundamental postulate. In equilibrium thermodynamics the state variables do not include fluxes because in a state of thermodynamic equilibrium all fluxes have zero values by postulation, non-equilibrium thermodynamics allows its state variables to include non-zero fluxes, that describe transfers of matter or energy or entropy between a system and its surroundings. Thermodynamic equilibrium is characterized by absence of flow of matter or energy, equilibrium thermodynamics, as a subject in physics, considers macroscopic bodies of matter and energy in states of internal thermodynamic equilibrium. It uses the concept of thermodynamic processes, by which bodies pass from one state to another by transfer of matter. The term thermodynamic system is used to refer to bodies of matter, the possible equilibria between bodies are determined by the physical properties of the walls that separate the bodies. Equilibrium thermodynamics in general does not measure time, equilibrium thermodynamics is a relatively simple and well settled subject. One reason for this is the existence of a well defined quantity called the entropy of a body. It is characterized by presence of flows of matter and energy, for this topic, very often the bodies considered have smooth spatial inhomogeneities, so that spatial gradients, for example a temperature gradient, are well enough defined. Thus the description of thermodynamic systems is a field theory
11.
Thermodynamic state
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Once such a set of values of thermodynamic variables has been specified for a system, the values of all thermodynamic properties of the system are uniquely determined. Usually, by default, a state is taken to be one of thermodynamic equilibrium. This means that the state is not merely the condition of the system at a specific time, Thermodynamics sets up an idealized formalism that can be summarized by a system of postulates of thermodynamics. A thermodynamic system is not simply a physical system, a thermodynamic system is a macroscopic object, the microscopic details of which are not explicitly considered in its thermodynamic description. The number of state variables required to specify the state depends on the system. Always the number is two or more, usually it is not more than some dozen, the choice is usually made on the basis of the walls and surroundings that are relevant for the thermodynamic processes that are to be considered for the system. For Planck, the characteristic of a thermodynamic state of a system that consists of a single phase. Such non-equilibrium identifying state variables indicate that some non-zero flow may be occurring within the system or between system and surroundings and they are uniquely determined by the thermodynamic state as it has been identified by the original state variables. For an idealized continuous or quasi-static process, this means that infinitesimal incremental changes in such variables are exact differentials, together, the incremental changes throughout the process, and the initial and final states, fully determine the idealized process. In the most commonly cited example, an ideal gas. Thus the thermodynamic state would range over a state space. The remaining variable, as well as other such as the internal energy. The state functions satisfy certain constraints, expressed in the laws of thermodynamics. Various thermodynamic diagrams have been developed to model the transitions between thermodynamic states, physical systems found in nature are practically always dynamic and complex, but in many cases, macroscopic physical systems are amenable to description based on proximity to ideal conditions. One such ideal condition is that of an equilibrium state. Such a state is an object of classical or equilibrium thermodynamics. Based on many observations, thermodynamics postulates that all systems that are isolated from the environment will evolve so as to approach unique stable equilibrium states. A few different types of equilibrium are listed below, thermal Equilibrium, When the temperature throughout a system is uniform, the system is in thermal equilibrium
12.
Equation of state
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In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describes the state of matter under a given set of physical conditions. It is an equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume. Equations of state are useful in describing the properties of fluids, mixtures of fluids, solids, the most prominent use of an equation of state is to correlate densities of gases and liquids to temperatures and pressures. One of the simplest equations of state for this purpose is the gas law. However, this becomes increasingly inaccurate at higher pressures and lower temperatures. Therefore, a number of more accurate equations of state have been developed for gases, at present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. Measurements of equation-of-state parameters, especially at pressures, can be made using lasers. In addition, there are equations of state describing solids. There are equations that model the interior of stars, including stars, dense matter. A related concept is the perfect fluid equation of state used in cosmology, in practical context, the equations of state are instrumental for PVT calculation in process engineering problems and especially in petroleum gas/liquid equilibrium calculations. A successful PVT model based on an equation of state can be helpful to determine the state of the flow regime. Boyles Law was perhaps the first expression of an equation of state, in 1662, the Irish physicist and chemist Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, then the volume of gas was measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the level in the short end of the tube and that in the long. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure, in mathematical form, this can be stated as, p V = c o n s t a n t. The above relationship has also attributed to Edme Mariotte and is sometimes referred to as Mariottes law. However, Mariottes work was not published until 1676, in 1787 the French physicist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to roughly the same extent over the same 80 kelvin interval. Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, daltons Law of partial pressure states that the pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone
13.
Ideal gas
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An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly elastic collision. The ideal gas concept is useful because it obeys the ideal gas law, an equation of state. One mole of a gas has a volume of 22.710947 litres at STP as defined by IUPAC since 1982. At normal conditions such as temperature and pressure, most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, the ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants, at high pressures, the volume of a real gas is often considerably greater than that of an ideal gas. At low temperatures, the pressure of a gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, the model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state, the deviation from the ideal gas behaviour can be described by a dimensionless quantity, the compressibility factor, Z. The ideal gas model has been explored in both the Newtonian dynamics and in quantum mechanics, the ideal gas model has also been used to model the behavior of electrons in a metal, and it is one of the most important models in statistical mechanics. There are three classes of ideal gas, the classical or Maxwell–Boltzmann ideal gas, the ideal quantum Bose gas, composed of bosons. The classical ideal gas can be separated into two types, The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas, the behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The ideal gas law is an extension of experimentally discovered gas laws, real fluids at low density and high temperature approximate the behavior of a classical ideal gas. This deviation is expressed as a compressibility factor, the classical thermodynamic properties of an ideal gas can be described by two equations of state. Multiplying the equations representing the three laws, V ∗ V ∗ V = k b a Gives, V ∗ V ∗ V =, under ideal conditions, V = R, that is, P V = n R T. The other equation of state of an ideal gas must express Joules law, in order to switch from macroscopic quantities to microscopic ones, we use n R = N k B where N is the number of gas particles kB is the Boltzmann constant. The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution, the assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas
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Real gas
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Real gases are non-hypothetical gases whose molecules occupy space and have interactions, consequently, they adhere to gas laws. The deviation from ideality can be described by the compressibility factor Z and it is almost always more accurate than the van der Waals equation, and often more accurate than some equations with more than two parameters. The equation is R T = or alternatively, p = R T V m − b − a T V m where a and b two empirical parameters that are not the parameters as in the van der Waals equation. The Virial equation derives from a treatment of statistical mechanics. P V m = R T or alternatively p V m = R T where A, B, C, A′, B′, Peng–Robinson equation of state has the interesting property being useful in modeling some liquids as well as real gases. Note that the γ constant is a derivative of constant α, englewood Cliffs, New Jersey 07632,1993. ISBN 0-13-275702-8 Stanley M. Walas, Phase Equilibria in Chemical Engineering, ISBN 0-409-95162-5 M. Aznar, and A. Silva Telles, A Data Bank of Parameters for the Attractive Coefficient of the Peng–Robinson Equation of State, Braz. Eng. vol.14 no.1 São Paulo Mar.1997, rao The corresponding-states principle and its practice, thermodynamic, transport and surface properties of fluids by Hong Wei Xiang http, //www. ccl. net/cca/documents/dyoung/topics-orig/eq_state. html
15.
State of matter
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In physics, a state of matter is one of the distinct forms that matter takes on. Four states of matter are observable in everyday life, solid, liquid, gas, some other states are believed to be possible but remain theoretical for now. For a complete list of all states of matter, see the list of states of matter. Historically, the distinction is based on qualitative differences in properties. Matter in the state maintains a fixed volume and shape, with component particles close together. Matter in the state maintains a fixed volume, but has a variable shape that adapts to fit its container. Its particles are close together but move freely. Matter in the state has both variable volume and shape, adapting both to fit its container. Its particles are close together nor fixed in place. Matter in the state has variable volume and shape, but as well as neutral atoms, it contains a significant number of ions and electrons. Plasma is the most common form of matter in the universe. The term phase is used as a synonym for state of matter. In a solid the particles are packed together. The forces between particles are strong so that the particles move freely but can only vibrate. As a result, a solid has a stable, definite shape, solids can only change their shape by force, as when broken or cut. In crystalline solids, the particles are packed in a regularly ordered, there are various different crystal structures, and the same substance can have more than one structure. For example, iron has a cubic structure at temperatures below 912 °C. Ice has fifteen known crystal structures, or fifteen solid phases, glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states, therefore they are described below as nonclassical states of matter
16.
Thermodynamic instruments
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A thermodynamic instrument is any device which facilitates the quantitative measurement of thermodynamic systems. In order for a parameter to be truly defined, a technique for its measurement must be specified. For example, the definition of temperature is what a thermometer reads. The question follows - what is a thermometer, there are two types of thermodynamic instruments, the meter and the reservoir. A thermodynamic meter is any device which measures any parameter of a thermodynamic system, a thermodynamic reservoir is a system which is so large that it does not appreciably alter its state parameters when brought into contact with the test system. Two general complementary tools are the meter and the reservoir and it is important that these two types of instruments are distinct. A meter does not perform its task accurately if it behaves like a reservoir of the variable it is trying to measure. If, for example, a thermometer, were to act as a reservoir it would alter the temperature of the system being measured. Ideal meters have no effect on the variables of the system they are measuring. A meter is a system which displays some aspect of its thermodynamic state to the observer. The nature of its contact with the system it is measuring can be controlled, the theoretical thermometer described below is just such a meter. In some cases, the parameter is actually defined in terms of an idealized measuring instrument. For example, the law of thermodynamics states that if two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other. This principle, as noted by James Maxwell in 1872, asserts that it is possible to measure temperature, an idealized thermometer is a sample of an ideal gas at constant pressure. From the ideal gas law, the volume of such a sample can be used as an indicator of temperature, although pressure is defined mechanically, a pressure-measuring device called a barometer may also be constructed from a sample of an ideal gas held at a constant temperature. A calorimeter is a device which is used to measure and define the energy of a system. Some common thermodynamic meters are, Thermometer - a device which measures temperature as described above Barometer - a device which measures pressure, an ideal gas barometer may be constructed by mechanically connecting an ideal gas to the system being measured, while thermally insulating it. The volume will then measure pressure, by the ideal gas equation P=NkT/V, calorimeter - a device which measures the heat energy added to a system
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Thermodynamic process
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Classical thermodynamics considers three main kinds of thermodynamic process, change in a system, cycles in a system, and flow processes. Defined by change in a system, a process is a passage of a thermodynamic system from an initial to a final state of thermodynamic equilibrium. The initial and final states are the elements of the process. The actual course of the process is not the primary concern and this is the customary default meaning of the term thermodynamic process. Such processes are useful for thermodynamic theory, defined by a cycle of transfers into and out of a system, a cyclic process is described by the quantities transferred in the several stages of the cycle, which recur unchangingly. The descriptions of the states of the system are not the primary concern. Cyclic processes were important conceptual devices in the days of thermodynamical investigation. Defined by flows through a system, a process is a steady state of flows into. The internal state of the contents is not the primary concern. The quantities of primary concern describe the states of the inflow and the materials, and, on the side, the transfers of heat, work. Flow processes are of interest in engineering, defined by change in a system, a thermodynamic process is a passage of a thermodynamic system from an initial to a final state of thermodynamic equilibrium. The initial and final states are the elements of the process. The actual course of the process is not the primary concern, a state of thermodynamic equilibrium endures unchangingly unless it is interrupted by a thermodynamic operation that initiates a thermodynamic process. Then it may be described by a process function that does depend on the path. Such idealized processes are useful in the theory of thermodynamics, defined by a cycle of transfers into and out of a system, a cyclic process is described by the quantities transferred in the several stages of the cycle. The descriptions of the states of the system may be of little or even no interest. A cycle is a sequence of a number of thermodynamic processes that indefinitely often repeatedly returns the system to its original state. For this, the states themselves are not necessarily described
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Isobaric process
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An isobaric process is a thermodynamic process in which the pressure stays constant, ΔP =0. The heat transferred to the system work, but also changes the internal energy of the system. This article uses the sign convention for work, where positive work is work done on the system. Using this convention, by the first law of thermodynamics, Q = Δ U − W where W is work, U is internal energy, and Q is heat. Pressure-volume work by the system is defined as, W = − ∫ p d V where Δ means change over the whole process. Since pressure is constant, this means that W = − p Δ V. Applying the ideal gas law, this becomes W = − n R Δ T assuming that the quantity of gas stays constant, e. g. there is no phase transition during a chemical reaction. According to the theorem, the change in internal energy is related to the temperature of the system by Δ U = n c V Δ T. Substituting the last two equations into the first equation produces, Q = n c V Δ T + n R Δ T = n Δ T = n c P Δ T, where cP is specific heat at a constant pressure. To find the specific heat capacity of the gas involved. The property γ is either called the index or the heat capacity ratio. Some published sources might use k instead of γ, molar isochoric specific heat, c V = R γ −1. Molar isobaric specific heat, c p = γ R γ −1, the values for γ are γ = 7/5 for diatomic gases like air and its major components, and γ = 5/3 for monatomic gases like the noble gases. If the process moves towards the right, then it is an expansion, if the process moves towards the left, then it is a compression. The motivation for the specific conventions of thermodynamics comes from early development of heat engines. When designing an engine, the goal is to have the system produce. The source of energy in an engine, is a heat input. If the volume compresses, then W <0 and that is, during isobaric compression the gas does negative work, or the environment does positive work