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.
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

3.
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

4.
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

5.
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

6.
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

7.
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

8.
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

9.
History of thermodynamics
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The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. The development of thermodynamics both drove and was driven by atomic theory and it also, albeit in a subtle manner, motivated new directions in probability and statistics, see, for example, the timeline of thermodynamics. The ancients viewed heat as related to fire. In 3000 BC, the ancient Egyptians viewed heat as related to origin mythologies, the Empedoclean element of fire is perhaps the principal ancestor of later concepts such as phlogin and caloric. Around 500 BC, the Greek philosopher Heraclitus became famous as the flux and fire philosopher for his proverbial utterance, Heraclitus argued that the three principal elements in nature were fire, earth, and water. Atomism is a part of todays relationship between thermodynamics and statistical mechanics. Ancient thinkers such as Leucippus and Democritus, and later the Epicureans, by advancing atomism, until experimental proof of atoms was later provided in the 20th century, the atomic theory was driven largely by philosophical considerations and scientific intuition. This view was supported by the arguments of Aristotle, but was criticized by Leucippus, from antiquity to the Middle Ages various arguments were put forward to prove or disapprove the existence of a vacuum and several attempts were made to construct a vacuum but all proved unsuccessful. This may have influenced by an earlier device which could expand and contract the air constructed by Philo of Byzantium. Around 1600, the English philosopher and scientist Francis Bacon surmised, Heat itself, its essence and quiddity is motion, in 1643, Galileo Galilei, while generally accepting the sucking explanation of horror vacui proposed by Aristotle, believed that natures vacuum-abhorrence is limited. Pumps operating in mines had proven that nature would only fill a vacuum with water up to a height of ~30 feet. Knowing this curious fact, Galileo encouraged his former pupil Evangelista Torricelli to investigate these supposed limitations, Torricelli did not believe that vacuum-abhorrence in the sense of Aristotles sucking perspective, was responsible for raising the water. Rather, he reasoned, it was the result of the pressure exerted on the liquid by the surrounding air, to prove this theory, he filled a long glass tube with mercury and upended it into a dish also containing mercury. Only a portion of the emptied, ~30 inches of the liquid remained. As the mercury emptied, and a vacuum was created at the top of the tube. The gravitational force on the heavy element Mercury prevented it from filling the vacuum, the theory of phlogiston arose in the 17th century, late in the period of alchemy. Its replacement by caloric theory in the 18th century is one of the markers of the transition from alchemy to chemistry. Phlogiston was a substance that was presumed to be liberated from combustible substances during burning

10.
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

11.
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

12.
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

13.
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

14.
Isochoric process
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The isochoric process here should be a quasi-static process. An isochoric thermodynamic process is characterized by constant volume, i. e. ΔV =0, the process does no pressure-volume work, since such work is defined by Δ W = P Δ V, where P is pressure. The sign convention is such that work is performed by the system on the environment. If the process is not quasi-static, the work can perhaps be done in a volume constant thermodynamic process, where cv is the specific heat capacity at constant volume, T1 is the initial temperature and T2 is the final temperature. We conclude with, Δ Q = m c v Δ T On a pressure volume diagram and its thermodynamic conjugate, an isobaric process would appear as a straight horizontal line. If an ideal gas is used in a process. Take for example a gas heated in a container, the pressure and temperature of the gas will increase. The ideal Otto cycle is an example of a process when it is assumed that the burning of the gasoline-air mixture in an internal combustion engine car is instantaneous. There is an increase in the temperature and the pressure of the gas inside the cylinder while the remains the same. The noun isochor and the adjective isochoric are derived from the Greek words ἴσος meaning equal, isobaric process Adiabatic process Cyclic process Isothermal process Polytropic process http, //lorien. ncl. ac. uk/ming/webnotes/Therm1/revers/isocho. htm

15.
Isothermal process
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An isothermal process is a change of a system, in which the temperature remains constant, ΔT =0. In contrast, a process is where a system exchanges no heat with its surroundings. In other words, in a process, the value ΔT =0 and therefore ΔU =0 but Q ≠0, while in an adiabatic process. Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including highly structured machines, some parts of the cycles of some heat engines are carried out isothermally. In the thermodynamic analysis of reactions, it is usual to first analyze what happens under isothermal conditions. Phase changes, such as melting or evaporation, are also isothermal processes when, as is usually the case, isothermal processes are often used and a starting point in analyzing more complex, non-isothermal processes. Isothermal processes are of special interest for ideal gases and this is a consequence of Joules second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. Thus, in a process the internal energy of an ideal gas is constant. This is a result of the fact that in a gas there are no intermolecular forces. Note that this is only for ideal gases, the internal energy depends on pressure as well as on temperature for liquids, solids. In the isothermal compression of a gas there is work is done on the system to decrease the volume, doing work on the gas increases the internal energy and will tend to increase the temperature. To maintain the constant temperature energy must leave the system as heat, if the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change. For details of the calculations, see calculation of work, for an adiabatic process, in which no heat flows into or out of the gas because its container is well insulated, Q =0. If there is no work done, i. e. a free expansion. For an ideal gas, this means that the process is also isothermal, thus, specifying that a process is isothermal is not sufficient to specify a unique process. For the special case of a gas to which Boyles law applies, the value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant. In other words, the gas law pV = nRT applies. This means that p = n R T V = constant V holds, the family of curves generated by this equation is shown in the graph in Figure 1

16.
Adiabatic process
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In thermodynamics, an adiabatic process is one that occurs without transfer of heat or matter between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred only as work, the adiabatic process provides a rigorous conceptual basis for the theory used to expound the first law of thermodynamics, and as such it is a key concept in thermodynamics. The adiabatic flame temperature is the temperature that would be achieved by a if the process of combustion took place in the absence of heat loss to the surroundings. A process that does not involve the transfer of heat or matter into or out of a system, so that Q =0, is called an adiabatic process, the assumption that a process is adiabatic is a frequently made simplifying assumption. Even though the cylinders are not insulated and are quite conductive, the same can be said to be true for the expansion process of such a system. The assumption of adiabatic isolation of a system is a useful one, the behaviour of actual machines deviates from these idealizations, but the assumption of such perfect behaviour provide a useful first approximation of how the real world works. According to Laplace, when sound travels in a gas, there is no loss of heat in the medium and the propagation of sound is adiabatic. For this adiabatic process, the modulus of elasticity E = γP where γ is the ratio of specific heats at constant pressure and at constant volume, such a process is called an isentropic process and is said to be reversible. Fictively, if the process is reversed, the energy added as work can be recovered entirely as work done by the system, if the walls of a system are not adiabatic, and energy is transferred in as heat, entropy is transferred into the system with the heat. Such a process is neither adiabatic nor isentropic, having Q >0, naturally occurring adiabatic processes are irreversible. The transfer of energy as work into an isolated system can be imagined as being of two idealized extreme kinds. In one such kind, there is no entropy produced within the system, in nature, this ideal kind occurs only approximately, because it demands an infinitely slow process and no sources of dissipation. The other extreme kind of work is work, for which energy is added as work solely through friction or viscous dissipation within the system. The second law of thermodynamics observes that a process, of transfer of energy as work, always consists at least of isochoric work. Every natural process, adiabatic or not, is irreversible, with ΔS >0, the adiabatic compression of a gas causes a rise in temperature of the gas. Adiabatic expansion against pressure, or a spring, causes a drop in temperature, in contrast, free expansion is an isothermal process for an ideal gas. Adiabatic heating occurs when the pressure of a gas is increased from work done on it by its surroundings and this finds practical application in diesel engines which rely on the lack of quick heat dissipation during their compression stroke to elevate the fuel vapor temperature sufficiently to ignite it. Adiabatic heating occurs in the Earths atmosphere when an air mass descends, for example, in a wind, Foehn wind

17.
Isenthalpic process
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An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy, H, or specific enthalpy, h. The throttling process is an example of an isenthalpic process. Consider the lifting of a valve or safety valve on a pressure vessel. The specific enthalpy of the fluid inside the vessel is the same as the specific enthalpy of the fluid as it escapes from the valve. With a knowledge of the enthalpy of the fluid. Sonntag, Fundamentals of Classical Thermodynamics, John Wiley & Sons, Inc

18.
Isentropic process
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Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. The word isentropic is occasionally, though not customarily, interpreted in another way and this is contrary to its original and customarily used definition. The second law of thermodynamics states that, T d S ≥ δ Q where δ Q is the amount of energy the system gains by heating, T is the temperature of the system, and d S is the change in entropy. The equal sign refers to a process, which is an imagined idealized theoretical limit. For an isentropic process, which by definition is reversible, there is no transfer of energy as heat because the process is adiabatic, for reversible processes, an isentropic transformation is carried out by thermally insulating the system from its surroundings. The entropy of a given mass does not change during a process that is internally reversible, a process during which the entropy remains constant is called an isentropic process, written △ s =0 or s 1 = s 2. Some isentropic thermodynamic devices include, pumps, gas compressors, turbines, nozzles, real world cycles have inherent losses due to inefficient compressors and turbines. The real world system are not truly isentropic but are rather idealized as isentropic for calculation purposes, in fluid dynamics, an isentropic flow is a fluid flow that is both adiabatic and reversible. That is, no heat is added to the flow, for an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline. Note that energy can be exchanged with the flow in an isentropic transformation, an example of such an exchange would be an isentropic expansion or compression that entails work done on or by the flow. For an isentropic flow, entropy density can vary between different streamlines, if the entropy density is the same everywhere, then the flow is said to be homentropic. All reversible adiabatic processes are isentropic, for any transformation of an ideal gas, it is always true that d U = n C v d T, and d H = n C p d T. Using the general results derived above for d U and d H, then d U = n C v d T = − p d V, and d H = n C p d T = V d p. So for a gas, the heat capacity ratio can be written as. Hence on integrating the above equation, assuming a perfect gas, we get p V γ = constant i. e. H. S. J. and Sonntag, fundamentals of Classical Thermodynamics, John Wiley & Sons, Inc. Library of Congress Catalog Card Number, 65-19470

19.
Polytropic process
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A polytropic process is a thermodynamic process that obeys the relation, p v n = C where p is the pressure, v is specific volume, n is the polytropic index, and C is a constant. The polytropic process equation can describe multiple expansion and compression processes which include heat transfer, in addition, when the ideal gas law applies, n =1 is an isothermic process, n = γ is an adiabatic process. Consider an ideal gas in a system undergoing a slow process with negligible changes in kinetic. Assuming K remain constant during the transformation, as d f f = d this relation can be integrated as d =0 ⟶ p v K + γ = C where C is a constant. Thus, the process is polytropic, with the coefficient n = K + γ and this derivation can be expanded to include polytropic processes in open systems, including instances where the kinetic energy is significant. It can also be expanded to include polytropic processes. For certain values of the index, the process will be synonymous with other common processes. Some examples of the effects of varying index values are given in the table, when the index n is between any two of the former values, it means that the polytropic curve will cut through the curves of the two bounding indices. For an ideal gas,1 < γ <2, since by Mayers relation γ = c p c v = c v + R c v =1 + R c v = c p c p − R. A solution to the Lane–Emden equation using a fluid is known as a polytrope

20.
Introduction to entropy
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Entropy is an important concept in the branch of science known as thermodynamics. The idea of irreversibility is central to the understanding of entropy, everyone has an intuitive understanding of irreversibility. If one watches a movie of everyday life running forward and in reverse, the intuitive meaning of expressions such as you cant unscramble an egg, or you cant take the cream out of the coffee is that these are irreversible processes. No matter how long you wait, the cream wont jump out of the coffee into the creamer, all real physical processes involving systems in everyday life, with many atoms or molecules, are irreversible. For an irreversible process in a system, the thermodynamic state variable known as entropy is always increasing. The reason that the movie in reverse is so easily recognized is because it shows processes for which entropy is decreasing, in everyday life, there may be processes in which the increase of entropy is practically unobservable, almost zero. In these cases, a movie of the run in reverse will not seem unlikely. In thermodynamics, one says that this process is practically reversible, the statement of the fact that the entropy of an isolated system never decreases is known as the second law of thermodynamics. Classical thermodynamics is a theory which describes a system in terms of the thermodynamic variables of the system or its parts. Some thermodynamic variables are familiar, temperature, pressure, volume, entropy is a thermodynamic variable which is less familiar and not as easily understood. A system is any region of space containing matter and energy, A cup of coffee, a glass of icewater, an automobile, thermodynamic variables do not give a complete picture of the system. Thermodynamics deals with matter in a sense, it would be valid even if the atomic theory of matter were wrong. This is an important quality, because it means that based on thermodynamics is unlikely to require alteration as new facts about atomic structure. The essence of thermodynamics is embodied in the four laws of thermodynamics, unfortunately, thermodynamics provides little insight into what is happening at a microscopic level. Statistical mechanics is a theory which explains thermodynamics in microscopic terms. It explains thermodynamics in terms of the possible detailed microscopic situations the system may be in when the variables of the system are known. These are known as microstates while the description of the system in thermodynamic terms specifies the macrostate of the system, many different microstates can yield the same macrostate. It is important to understand that statistical mechanics does not define temperature, pressure, entropy and they are already defined by thermodynamics

21.
Entropy
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In statistical thermodynamics, entropy is a measure of the number of microscopic configurations Ω that a thermodynamic system can have when in a state as specified by some macroscopic variables. Formally, S = k B ln Ω, for example, gas in a container with known volume, pressure, and temperature could have an enormous number of possible configurations of the collection of individual gas molecules. Each instantaneous configuration of the gas may be regarded as random, Entropy may be understood as a measure of disorder within a macroscopic system. The second law of thermodynamics states that an isolated systems entropy never decreases, such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environments entropy increases by at least that amount, since entropy is a function of the state of the system, a change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible, however, irreversible processes increase the combined entropy of the system and its environment. The above definition is called the macroscopic definition of entropy because it can be used without regard to any microscopic description of the contents of a system. The concept of entropy has found to be generally useful and has several other formulations. Entropy was discovered when it was noticed to be a quantity that behaves as a function of state and it has the dimension of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units. But the entropy of a substance is usually given as an intensive property—either entropy per unit mass or entropy per unit amount of substance. In statistical mechanics this reflects that the state of a system is generally non-degenerate. Understanding the role of entropy in various processes requires an understanding of how. It is often said that entropy is an expression of the disorder, or randomness of a system, the second law is now often seen as an expression of the fundamental postulate of statistical mechanics through the modern definition of entropy. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy and he made the analogy with that of how water falls in a water wheel. This was an insight into the second law of thermodynamics. g. Clausius described entropy as the transformation-content, i. e. dissipative energy use and this was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, henceforth, the essential problem in statistical thermodynamics, i. e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems. Carathéodory linked entropy with a definition of irreversibility, in terms of trajectories

22.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used

23.
Thermodynamic temperature
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Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is defined by the law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the constituents of matter have minimal motion. In the quantum-mechanical description, matter at absolute zero is in its ground state, the International System of Units specifies a particular scale for thermodynamic temperature. It uses the Kelvin scale for measurement and selects the point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically, the Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a means of estimating the thermodynamic temperature to a very high degree of accuracy. Internal energy is called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a degree of freedom. At equilibrium, each degree of freedom will have on average the energy, k B T /2 where k B is the Boltzmann constant. Temperature is a measure of the random submicroscopic motions and vibrations of the constituents of matter. These motions comprise the internal energy of a substance, more specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the average kinetic energy per classical degree of freedom of its constituent particles. Translational motions are almost always in the classical regime, translational motions are ordinary, whole-body movements in three-dimensional space in which particles move about and exchange energy in collisions. Figure 1 below shows translational motion in gases, Figure 4 below shows translational motion in solids, Zero kinetic energy remains in a substance at absolute zero. Throughout the scientific world where measurements are made in SI units, many engineering fields in the U. S. however, measure thermodynamic temperature using the Rankine scale. By international agreement, the kelvin and its scale are defined by two points, absolute zero, and the triple point of Vienna Standard Mean Ocean Water. Absolute zero, the lowest possible temperature, is defined as being precisely 0 K, the triple point of water is defined as being precisely 273.16 K and 0.01 °C. This definition does three things, It fixes the magnitude of the unit as being precisely 1 part in 273.15 kelvins

24.
Volume (thermodynamics)
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In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, a property, is the systems volume per unit of mass. Volume is a function of state and is interdependent with other properties such as pressure and temperature. For example, volume is related to the pressure and temperature of a gas by the ideal gas law. The physical volume of a system may or may not coincide with a control volume used to analyze the system, the volume of a thermodynamic system typically refers to the volume of the working fluid, such as, for example, the fluid within a piston. Changes to this volume may be made through an application of work, an isochoric process however operates at a constant-volume, thus no work can be produced. Many other thermodynamic processes will result in a change in volume, a polytropic process, in particular, causes changes to the system so that the quantity p V n is constant. Note that for specific polytropic indexes a polytropic process will be equivalent to a constant-property process, for instance, for very large values of n approaching infinity, the process becomes constant-volume. Gases are compressible, thus their volumes may be subject to change during thermodynamic processes, liquids, however, are nearly incompressible, thus their volumes can be often taken as constant. In general, compressibility is defined as the volume change of a fluid or solid as a response to a pressure. Similarly, thermal expansion is the tendency of matter to change in volume in response to a change in temperature, many thermodynamic cycles are made up of varying processes, some which maintain a constant volume and some which do not. A vapor-compression refrigeration cycle, for example, follows a sequence where the refrigerant fluid transitions between the liquid and vapor states of matter, typical units for volume are m 3, l, and f t 3. Mechanical work performed on a working fluid causes a change in the constraints of the system, in other words, for work to occur. Hence volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved, volume is one of a pair of conjugate variables, the other being pressure. As with all pairs, the product is a form of energy. The product p V is the energy lost to a due to mechanical work. This product is one term which makes up enthalpy H, H = U + p V, the second law of thermodynamics describes constraints on the amount of useful work which can be extracted from a thermodynamic system. Similarly, the value of heat capacity to use in a given process depends on whether the process produces a change in volume

25.
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

26.
Heat capacity
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Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change. The unit of capacity is joule per kelvin J K. Specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 kelvin, Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. The molar heat capacity is the capacity per unit amount of a pure substance. In some engineering contexts, the heat capacity is used. Other contributions can come from magnetic and electronic degrees of freedom in solids, for quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available, to store thermal energy. In such cases, the capacity is a fraction of the maximum. As the temperature approaches zero, the heat capacity of a system approaches zero. Quantum theory can be used to predict the heat capacity of simple systems. In a previous theory of common in the early modern period, heat was thought to be a measurement of an invisible fluid. Bodies were capable of holding an amount of this fluid, hence the term heat capacity, named. Heat is no longer considered a fluid, but rather a transfer of disordered energy, nevertheless, at least in English, the term heat capacity survives. In some other languages, the thermal capacity is preferred. In the International System of Units, heat capacity has the unit joules per kelvin, if the temperature change is sufficiently small the heat capacity may be assumed to be constant, C = Q Δ T. Heat capacity is a property, meaning it depends on the extent or size of the physical system studied. A sample containing twice the amount of substance as another sample requires the transfer of twice the amount of heat to achieve the change in temperature. For many purposes it is convenient to report heat capacity as an intensive property. In practice, this is most often an expression of the property in relation to a unit of mass, in science and engineering, International standards now recommend that specific heat capacity always refer to division by mass

27.
Compressibility
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In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change. β = −1 V ∂ V ∂ p where V is volume, the specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal. Accordingly, isothermal compressibility is defined, β T = −1 V T where the subscript T indicates that the differential is to be taken at constant temperature. Isentropic compressibility is defined, β S = −1 V S where S is entropy, for a solid, the distinction between the two is usually negligible. The minus sign makes the compressibility positive in the case that an increase in pressure induces a reduction in volume, the speed of sound is defined in classical mechanics as, c 2 = S where ρ is the density of the material. It follows, by replacing partial derivatives, that the compressibility can be expressed as, β S =1 ρ c 2 The inverse of the compressibility is called the bulk modulus. That page also contains some examples for different materials, the compressibility equation relates the isothermal compressibility to the structure of the liquid. The term compressibility is also used in thermodynamics to describe the deviance in the properties of a real gas from those expected from an ideal gas. The compressibility factor is defined as Z = p V _ R T where p is the pressure of the gas, T is its temperature, and V _ is its molar volume. The deviation from ideal gas behavior tends to become particularly significant near the critical point, in these cases, a generalized compressibility chart or an alternative equation of state better suited to the problem must be utilized to produce accurate results. This pressure dependent transition occurs for atmospheric oxygen in the 2500 K to 4000 K temperature range, in transition regions, where this pressure dependent dissociation is incomplete, both beta and the differential, constant pressure heat capacity greatly increase. For moderate pressures, above 10,000 K the gas further dissociates into free electrons and ions, Z for the resulting plasma can similarly be computed for a mole of initial air, producing values between 2 and 4 for partially or singly ionized gas. Each dissociation absorbs a great deal of energy in a reversible process, ions or free radicals transported to the object surface by diffusion may release this extra energy if the surface catalyzes the slower recombination process. The isothermal compressibility is related to the isentropic compressibility by the relation, more simply stated, β T β S = γ where, γ is the heat capacity ratio. The Earth sciences use compressibility to quantify the ability of a soil or rock to reduce in volume under applied pressure and this concept is important for specific storage, when estimating groundwater reserves in confined aquifers. Geologic materials are made up of two portions, solids and voids, the void space can be full of liquid or gas. Geologic materials reduces in volume only when the spaces are reduced. This can happen over a period of time, resulting in settlement and it is an important concept in geotechnical engineering in the design of certain structural foundations

28.
Thermal expansion
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Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a change in temperature. Temperature is a function of the average molecular kinetic energy of a substance. When a substance is heated, the energy of its molecules increases. Thus, the molecules begin vibrating/moving more and usually maintain an average separation. Materials which contract with increasing temperature are unusual, this effect is limited in size, the degree of expansion divided by the change in temperature is called the materials coefficient of thermal expansion and generally varies with temperature. If an equation of state is available, it can be used to predict the values of the expansion at all the required temperatures and pressures. A number of contract on heating within certain temperature ranges. For example, the coefficient of expansion of water drops to zero as it is cooled to 3. Also, fairly pure silicon has a coefficient of thermal expansion for temperatures between about 18 and 120 Kelvin. Unlike gases or liquids, solid materials tend to keep their shape when undergoing thermal expansion, in general, liquids expand slightly more than solids. The thermal expansion of glasses is higher compared to that of crystals, at the glass transition temperature, rearrangements that occur in an amorphous material lead to characteristic discontinuities of coefficient of thermal expansion and specific heat. These discontinuities allow detection of the transition temperature where a supercooled liquid transforms to a glass. Absorption or desorption of water can change the size of common materials. Common plastics exposed to water can, in the long term, the coefficient of thermal expansion describes how the size of an object changes with a change in temperature. Specifically, it measures the change in size per degree change in temperature at a constant pressure. Several types of coefficients have been developed, volumetric, area, which is used depends on the particular application and which dimensions are considered important. For solids, one might only be concerned with the change along a length, the volumetric thermal expansion coefficient is the most basic thermal expansion coefficient, and the most relevant for fluids. In general, substances expand or contract when their temperature changes, substances that expand at the same rate in every direction are called isotropic

29.
Thermodynamic potential
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A thermodynamic potential is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886, Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has an interpretation is the internal energy U. It is the energy of configuration of a system of conservative forces. Expressions for all other thermodynamic potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, certain forces, such as gravity, are disregarded when formulating expressions for potentials. Five common thermodynamic potentials are, where T = temperature, S = entropy, p = pressure, the Helmholtz free energy is often denoted by the symbol F, but the use of A is preferred by IUPAC, ISO and IEC. Ni is the number of particles of type i in the system, for the sake of completeness, the set of all Ni are also included as natural variables, although they are sometimes ignored. These five common potentials are all energy potentials, but there are also entropy potentials, the thermodynamic square can be used as a tool to recall and derive some of the potentials. Gibbs energy is the capacity to do non-mechanical work, enthalpy is the capacity to do non-mechanical work plus the capacity to release heat. Helmholtz free energy is the capacity to do mechanical plus non-mechanical work, thermodynamic potentials are very useful when calculating the equilibrium results of a chemical reaction, or when measuring the properties of materials in a chemical reaction. Just as in mechanics, the system will tend towards lower values of potential and at equilibrium, under these constraints, the thermodynamic potentials can also be used to estimate the total amount of energy available from a thermodynamic system under the appropriate constraint. In particular, When the entropy and external parameters of a system are held constant. This follows from the first and second laws of thermodynamics and is called the principle of minimum energy, the following three statements are directly derivable from this principle. When the temperature and external parameters of a system are held constant. When the pressure and external parameters of a system are held constant. When the temperature, pressure and external parameters of a system are held constant. The variables that are constant in this process are termed the natural variables of that potential

30.
Enthalpy
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Enthalpy /ˈɛnθəlpi/ is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the heat content of a system. It is equal to the energy of the system plus the product of pressure. Enthalpy is defined as a function that depends only on the prevailing equilibrium state identified by the systems internal energy, pressure. The unit of measurement for enthalpy in the International System of Units is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating or work other than expansion work, the total enthalpy, H, of a system cannot be measured directly. The same situation exists in classical mechanics, only a change or difference in energy carries physical meaning. Enthalpy itself is a potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point, therefore what we measure is the change in enthalpy. The ΔH is a change in endothermic reactions, and negative in heat-releasing exothermic processes. For processes under constant pressure, ΔH is equal to the change in the energy of the system. This means that the change in enthalpy under such conditions is the heat absorbed by the material through a reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure assume standard state, most commonly 1 bar pressure, standard state does not, strictly speaking, specify a temperature, but expressions for enthalpy generally reference the standard heat of formation at 25 °C. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy, real materials at common temperatures and pressures usually closely approximate this behavior, which greatly simplifies enthalpy calculation and use in practical designs and analyses. The word enthalpy stems from the Ancient Greek verb enthalpein, which means to warm in and it combines the Classical Greek prefix ἐν- en-, meaning to put into, and the verb θάλπειν thalpein, meaning to heat. The word enthalpy is often attributed to Benoît Paul Émile Clapeyron. This misconception was popularized by the 1927 publication of The Mollier Steam Tables, however, neither the concept, the word, nor the symbol for enthalpy existed until well after Clapeyrons death. The earliest writings to contain the concept of enthalpy did not appear until 1875, however, Gibbs did not use the word enthalpy in his writings. The actual word first appears in the literature in a 1909 publication by J. P. Dalton

31.
Internal energy
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It keeps account of the gains and losses of energy of the system that are due to changes in its internal state. The internal energy of a system can be changed by transfers of matter or heat or by doing work, when matter transfer is prevented by impermeable containing walls, the system is said to be closed. Then the first law of thermodynamics states that the increase in energy is equal to the total heat added plus the work done on the system by its surroundings. If the containing walls pass neither matter nor energy, the system is said to be isolated, the first law of thermodynamics may be regarded as establishing the existence of the internal energy. The internal energy is one of the two cardinal state functions of the variables of a thermodynamic system. The internal energy of a state of a system cannot be directly measured. Such a chain, or path, can be described by certain extensive state variables of the system, namely, its entropy, S, its volume, V. The internal energy, U, is a function of those, sometimes, to that list are appended other extensive state variables, for example electric dipole moment. Customarily, thermodynamic descriptions include only items relevant to the processes under study, Thermodynamics is chiefly concerned only with changes in the internal energy, not with its absolute value. The internal energy is a function of a system, because its value depends only on the current state of the system. It is the one and only cardinal thermodynamic potential, through it, by use of Legendre transforms, are mathematically constructed the other thermodynamic potentials. These are functions of variable lists in which some extensive variables are replaced by their conjugate intensive variables, Legendre transformation is necessary because mere substitutive replacement of extensive variables by intensive variables does not lead to thermodynamic potentials. Mere substitution leads to a less informative formula, an equation of state, though it is a macroscopic quantity, internal energy can be explained in microscopic terms by two theoretical virtual components. One is the kinetic energy due to the microscopic motion of the systems particles. The other is the energy associated with the microscopic forces, including the chemical bonds. If thermonuclear reactions are specified as a topic of concern, then the static rest mass energy of the constituents of matter is also counted. There is no simple relation between these quantities of microscopic energy and the quantities of energy gained or lost by the system in work, heat. The SI unit of energy is the joule, sometimes it is convenient to use a corresponding density called specific internal energy which is internal energy per unit of mass of the system in question

32.
Ideal gas law
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The ideal gas law is the equation of state of a hypothetical ideal gas. It is an approximation of the behavior of many gases under many conditions. It was first stated by Émile Clapeyron in 1834 as a combination of the empirical Boyles law, Charless law and it can also be derived microscopically from kinetic theory, as was achieved by August Krönig in 1856 and Rudolf Clausius in 1857. The state of an amount of gas is determined by its pressure, volume, the modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature, in SI units, P is measured in pascals, V is measured in cubic metres, n is measured in moles, and T in kelvins. R has the value 8.314 J/ ≈2 cal/, how much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, a form of the ideal gas law may be useful. The chemical amount is equal to the mass of the gas divided by the molar mass. By replacing n with m/M and subsequently introducing density ρ = m/V, we get, defining the specific gas constant Rspecific as the ratio R/M, P = ρ R specific T. This form of the gas law is very useful because it links pressure, density. Alternatively, the law may be written in terms of the specific volume v and it is common, especially in engineering applications, to represent the specific gas constant by the symbol R. In such cases, the gas constant is usually given a different symbol such as R ¯ to distinguish it. In any case, the context and/or units of the gas constant should make it clear as to whether the universal or specific gas constant is being referred to. KB =R/NA The number density contrasts to the formulation, which uses n, the number of moles and V. This relation implies that R = NAkB, where NA is Avogadros constant, in extreme conditions the principles of statistical mechanics may break down as some of the assumptions relating a real life example to an ideal gas become untrue. In SI units, P is measured in pascals, V in cubic metres, Y is a dimensionless number, KB has the value 1. 38·10−23 J/K in SI units. According to the assumptions of the theory of gases, we assumed that there are no inter molecular attractions between the molecules of an ideal gas its potential energy is zero. Hence, all the energy possessed by the gas is kinetic energy, E =32 R T This is the kinetic energy of one mole of a gas

33.
Fundamental thermodynamic relation
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D U = T d S − P d V Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume. This relation applies to a change, or to a change in a closed system of uniform temperature and pressure at constant composition. This is only one expression of the thermodynamic relation. It may be expressed in other ways, using different variables, However, since U, S, and V are thermodynamic state functions, the above relation holds also for non-reversible changes in a system of uniform pressure and temperature at constant composition. The last term must be zero for a reversible process, the above derivation uses the first and second laws of thermodynamics. The first law of thermodynamics is essentially a definition of heat, However, the second law of thermodynamics is not a defining relation for the entropy. The fundamental definition of entropy of a system containing an amount of energy of E is. Here δ E is a small energy interval that is kept fixed. Strictly speaking this means that the entropy depends on the choice of δ E. However, in the thermodynamic limit, the specific entropy does not depend on δ E. The entropy is thus a measure of the uncertainty about exactly which quantum state the system is in and this allows us to extract all the thermodynamical quantities of interest. Suppose that the system has some external parameter, x, that can be changed, in general, the energy eigenstates of the system will depend on x. The generalized force, X, corresponding to the external parameter x is defined such that X d x is the performed by the system if x is increased by an amount dx. E. g. if x is the volume, then X is the pressure, suppose we change x to x + dx. Since these energy eigenstates increase in energy by Y dx, all such energy eigenstates that are in the interval ranging from E - Y dx to E move from below E to above E, there are N Y = Ω Y δ E Y d x such energy eigenstates. If Y d x ≤ δ E, all these energy eigenstates will move into the range between E and E + δ E and contribute to an increase in Ω. The number of energy eigenstates that move from below E + δ E to above E + δ E is, of course, the difference N Y − N Y is thus the net contribution to the increase in Ω. Note that if Y dx is larger than δ E there will be energy eigenstates that move from below E to above E + δ E and they are counted in both N Y and N Y, therefore the above expression is also valid in that case. e. It does not scale with system size, in contrast, the last term scales as the inverse system size and thus vanishes in the thermodynamic limit

34.
Heat engine
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In thermodynamics, a heat engine is a system that converts heat or thermal energy—and chemical energy—to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state, the working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a heat capacity. During this process, a lot of heat is lost to the surroundings, in general an engine converts energy to mechanical work. Heat engines distinguish themselves from other types of engines by the fact that their efficiency is limited by Carnots theorem. Since the heat source that supplies energy to the engine can thus be powered by virtually any kind of energy. Heat engines are often confused with the cycles they attempt to implement, typically, the term engine is used for a physical device and cycle for the model. In thermodynamics, heat engines are often modeled using an engineering model such as the Otto cycle. The theoretical model can be refined and augmented with data from an operating engine. Since very few implementations of heat engines exactly match their underlying thermodynamic cycles. In general terms, the larger the difference in temperature between the hot source and the sink, the larger is the potential thermal efficiency of the cycle. The efficiency of heat engines proposed or used today has a large range. 25% for most automotive gasoline engines 49% for a supercritical coal-fired power station such as the Avedøre Power Station, all these processes gain their efficiency from the temperature drop across them. Significant energy may be used for equipment, such as pumps. Heat engines can be characterized by their power, which is typically given in kilowatts per litre of engine displacement. The result offers an approximation of the power output of an engine

35.
Thermodynamic cycle
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In the process of passing through a cycle, the working fluid may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source, during a closed cycle, the system returns to its original thermodynamic state of temperature and pressure. Process quantities, such as heat and work are process dependent, ein might be the work and heat input during the cycle and Eout would be the work and heat output during the cycle. The first law of thermodynamics also dictates that the net heat input is equal to the net work output over a cycle, the repeating nature of the process path allows for continuous operation, making the cycle an important concept in thermodynamics. Thermodynamic cycles are often represented mathematically as quasistatic processes in the modeling of the workings of an actual device, two primary classes of thermodynamic cycles are power cycles and heat pump cycles. Power cycles are cycles which convert some heat input into a mechanical work output, cycles composed entirely of quasistatic processes can operate as power or heat pump cycles by controlling the process direction. On a pressure-volume diagram or temperature-entropy diagram, the clockwise and counterclockwise directions indicate power and heat pump cycles, because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a PV diagram. A PV diagrams Y axis shows pressure and X axis shows volume, if the cyclic process moves clockwise around the loop, then W will be positive, and it represents a heat engine. If it moves counterclockwise, then W will be negative, and this does not exclude energy transfer as work. Isothermal, The process is at a constant temperature during that part of the cycle and this does not exclude energy transfer as heat or work. Isobaric, Pressure in that part of the cycle will remain constant and this does not exclude energy transfer as heat or work. Isochoric, The process is constant volume and this does not exclude energy transfer as heat or work. Isentropic, The process is one of constant entropy and this excludes the transfer of heat but not work. Thermodynamic power cycles are the basis for the operation of heat engines, power cycles can be organized into two categories, real cycles and ideal cycles. Cycles encountered in real world devices are difficult to analyze because of the presence of complicating effects, power cycles can also be divided according to the type of heat engine they seek to model. The most common used to model internal combustion engines are the Otto cycle, which models gasoline engines, and the Diesel cycle. There is no difference between the two except the purpose of the refrigerator is to cool a very small space while the heat pump is intended to warm a house. Both work by moving heat from a space to a warm space