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
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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
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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
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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
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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
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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
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Quasistatic process
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In thermodynamics, a quasi-static process is a thermodynamic process that happens slowly enough for the system to remain in internal equilibrium. An example of this is quasi-static compression, where the volume of a system changes at a slow enough to allow the pressure to remain uniform. Any reversible process is necessarily a quasi-static one, however, quasi-static processes involving entropy production are irreversible. Some ambiguity exists in the literature concerning the distinction between quasi-static and reversible processes, as these are taken as synonyms. The reason is the theorem that any process is also a quasi-static one. The definition given above is closer to the understanding of the word “quasi-” “static”
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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
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Free expansion
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Free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber. It is also called Joule expansion, real gases experience a temperature change during free expansion. Since the gas expands, Vf > Vi, which implies that the pressure does drop, during free expansion, no work is done by the gas. The gas goes through states that are not in thermodynamic equilibrium before reaching its final state, for example, the pressure changes locally from point to point, and the volume occupied by the gas is not a well defined quantity. A free expansion is achieved by opening a stopcock that allows the gas to expand into a vacuum. Although it would be difficult to achieve in reality, it is instructive to imagine a free expansion caused by moving a piston faster than virtually any atom, no work is done because there is no pressure on the piston. No heat energy leaves or enters the piston, nevertheless, there is an entropy change. But the well-known formula for change, Δ S = ∫ d Q r e v T
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Reversible process (thermodynamics)
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Throughout the entire reversible process, the system is in thermodynamic equilibrium with its surroundings. Since it would take an infinite amount of time for the process to finish. However, if the system undergoing the changes responds much faster than the applied change, in a reversible cycle, a reversible process which is cyclic, the system and its surroundings will be returned to their original states if the forward cycle is followed by the reverse cycle. Thermodynamic processes can be carried out in one of two ways, reversibly or irreversibly, reversibility refers to performing a reaction continuously at equilibrium. The phenomenon of maximized work and minimized heat can be visualized on a curve, as the area beneath the equilibrium curve. In order to work, one must follow the equilibrium curve closely. When described in terms of pressure and volume, it occurs when the pressure or the volume of a system changes so dramatically and instantaneously that the other does not have time to catch up. A classic example of irreversibility is allowing a certain volume of gas to be released into a vacuum. By releasing pressure on a sample and thus allowing it to occupy a large space, however, significant work will be required, with a corresponding amount of energy dissipated as heat flow to the environment, in order to reverse the process. An alternative definition of a process is a process that, after it has taken place, can be reversed and. In thermodynamic terms, a process taking place would refer to its transition from its state to its final state. In an irreversible process, finite changes are made, therefore the system is not at equilibrium throughout the process, at the same point in an irreversible cycle, the system will be in the same state, but the surroundings are permanently changed after each cycle. A reversible process changes the state of a system in such a way that the net change in the entropy of the system. In some cases, it is important to distinguish between reversible and quasistatic processes, Reversible processes are always quasistatic, but the converse is not always true. For example, a compression of a gas in a cylinder where there exists friction between the piston and the cylinder is a quasistatic, but not reversible process. Historically, the term Tesla principle was used to describe certain reversible processes invented by Nikola Tesla, however, this phrase is no longer in conventional use. The principle stated that some systems could be reversed and operated in a complementary manner and it was developed during Teslas research in alternating currents where the currents magnitude and direction varied cyclically. During a demonstration of the Tesla turbine, the disks revolved, if the turbines operation was reversed, the disks acted as a pump
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Irreversible process
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In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics, a system that undergoes an irreversible process may still be capable of returning to its initial state, however, the impossibility occurs in restoring the environment to its own initial conditions. An irreversible process increases the entropy of the universe, however, because entropy is a state function, the change in entropy of the system is the same whether the process is reversible or irreversible. The second law of thermodynamics can be used to determine whether a process is reversible or not, all complex natural processes are irreversible. A certain amount of energy will be used as the molecules of the working body do work on each other when they change from one state to another. Many biological processes that were thought to be reversible have been found to actually be a pairing of two irreversible processes. Thermodynamics defines the behaviour of large numbers of entities, whose exact behavior is given by more specific laws. The irreversibility of thermodynamics must be statistical in nature, that is, that it must be highly unlikely, but not impossible. The German physicist Rudolf Clausius, in the 1850s, was the first to quantify the discovery of irreversibility in nature through his introduction of the concept of entropy. For example, a cup of hot coffee placed in an area of temperature will transfer heat to its surroundings. However, that same initial cup of coffee will never absorb heat from its surroundings causing it to grow even hotter with the temperature of the room decreasing, therefore, the process of the coffee cooling down is irreversible unless extra energy is added to the system. However, a paradox arose when attempting to reconcile microanalysis of a system with observations of its macrostate, many processes are mathematically reversible in their microstate when analyzed using classical Newtonian mechanics. His formulas quantified the work done by William Thomson, 1st Baron Kelvin who had argued that, in 1890, he published his first explanation of nonlinear dynamics, also called chaos theory. Sensitivity to initial conditions relating to the system and its environment at the compounds into an exhibition of irreversible characteristics within the observable. In the physical realm, many processes are present to which the inability to achieve 100% efficiency in energy transfer can be attributed. The following is a list of events which contribute to the irreversibility of processes. The internal energy of the gas remains the same, while the volume increases, the original state cannot be recovered by simply compressing the gas to its original volume, since the internal energy will be increased by this compression. The original state can only be recovered by then cooling the re-compressed system, the diagram to the right applies only if the first expansion is free
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Endoreversible thermodynamics
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Endoreversible thermodynamics is a subset of irreversible thermodynamics aimed at making more realistic assumptions about heat transfer than are typically made in reversible thermodynamics. Endoreversible thermodynamics was discovered in simultaneous work by Novikov and Chambadal, for some typical cycles, the above equation gives the following results, As shown, the endoreversible efficiency much more closely models the observed data. However, such an engine violates Carnots principle which states that work can be any time there is a difference in temperature. The fact that the hot and cold reservoirs are not at the temperature as the working fluid they are in contact with means that work can and is done at the hot. The result is tantamount to coupling the high and low temperature parts of the cycle, so that the cycle collapses. It is well known that the temperature is the geometric mean temperature T H T L so that the efficiency is the Carnot efficiency for an engine working between T H and T H T L. Due to occasional confusion about the origins of the above equation, heat engine An introduction to endoreversible thermodynamics is given in the thesis by Katharina Wagner. It is also introduced by Hoffman et al, a thorough discussion of the concept, together with many applications in engineering, is given in the book by Hans Ulrich Fuchs
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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
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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
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Heat pump and refrigeration cycle
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Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pumps and refrigerators. A heat pump is a machine or device that moves heat from one location at a temperature to another location at a higher temperature using mechanical work or a high-temperature heat source. Thus a heat pump may be thought of as a heater if the objective is to warm the heat sink, in either case, the operating principles are identical. Heat is moved from a place to a warm place. According to the law of thermodynamics heat cannot spontaneously flow from a colder location to a hotter area. An air conditioner requires work to cool a space, moving heat from the cooler interior to the warmer outdoors. Similarly, a refrigerator moves heat from inside the cold icebox to the warmer room-temperature air of the kitchen, the operating principle of the refrigeration cycle was described mathematically by Sadi Carnot in 1824 as a heat engine. A heat pump can be thought of as an engine which is operating in reverse. Heat pump and refrigeration cycles can be classified as vapor compression, vapor absorption, gas cycle, the vapor-compression cycle is used in most household refrigerators as well as in many large commercial and industrial refrigeration systems. Figure 1 provides a schematic diagram of the components of a typical vapor-compression refrigeration system, the thermodynamics of the cycle can be analysed on a diagram as shown in Figure 2. In this cycle, a refrigerant such as Freon enters the compressor as a vapor. The vapor is compressed at constant entropy and exits the compressor superheated, the liquid refrigerant goes through the expansion valve where its pressure abruptly decreases, causing flash evaporation and auto-refrigeration of, typically, less than half of the liquid. That results in a mixture of liquid and vapor at a temperature and pressure. The cold liquid-vapor mixture then travels through the coil or tubes and is completely vaporized by cooling the warm air being blown by a fan across the evaporator coil or tubes. The resulting refrigerant vapor returns to the inlet to complete the thermodynamic cycle. The absorption cycle is similar to the cycle, except for the method of raising the pressure of the refrigerant vapor. Some work is required by the pump but, for a given quantity of refrigerant. In an absorption refrigerator, a combination of refrigerant and absorbent is used
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Conjugate variables (thermodynamics)
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In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume. In fact, all thermodynamic potentials are expressed in terms of conjugate pairs, the product of two quantities that are conjugate has units of energy or sometimes power. For a mechanical system, an increment of energy is the product of a force times a small displacement. A similar situation exists in thermodynamics and these forces and their associated displacements are called conjugate variables. The thermodynamic force is always a variable and the displacement is always an extensive variable. The intensive variable is the derivative of the energy with respect to the extensive variable, while all other extensive variables are held constant. The thermodynamic square can be used as a tool to recall, in the above description, the product of two conjugate variables yields an energy. In other words, the pairs are conjugate with respect to energy. In general, conjugate pairs can be defined with respect to any state function. Conjugate pairs with respect to entropy are often used, in which the product of the conjugate pairs yields an entropy, such conjugate pairs are particularly useful in the analysis of irreversible processes, as exemplified in the derivation of the Onsager reciprocal relations. The present article is concerned only with energy-conjugate variables and these forces and their associated displacements are called conjugate variables. For example, consider the p V conjugate pair, the pressure p acts as a generalized force, Pressure differences force a change in volume d V, and their product is the energy lost by the system due to work. Here, pressure is the force, volume is the associated displacement. In a similar way, temperature differences drive changes in entropy, the thermodynamic force is always an intensive variable and the displacement is always an extensive variable, yielding an extensive energy. The intensive variable is the derivative of the energy with respect to the extensive variable. The theory of thermodynamic potentials is not complete until one considers the number of particles in a system as a variable on par with the other quantities such as volume. The number of particles is, like volume and entropy, the displacement variable in a conjugate pair, the generalized force component of this pair is the chemical potential. The chemical potential may be thought of as a force which, in cases where there are a mixture of chemicals and phases, this is a useful concept
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Thermodynamic diagrams
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Thermodynamic diagrams are diagrams used to represent the thermodynamic states of a material and the consequences of manipulating this material. For instance, a diagram may be used to demonstrate the behavior of a fluid as it is changed by a compressor. Especially in meteorology they are used to analyze the state of the atmosphere derived from the measurements of radiosondes. In such diagrams, temperature and humidity values are displayed with respect to pressure, thus the diagram gives at a first glance the actual atmospheric stratification and vertical water vapor distribution. Further analysis gives the base and top height of convective clouds or possible instabilities in the stratification. The main feature of thermodynamic diagrams is the equivalence between the area in the diagram and energy, the P-alpha-diagram shows a strong deformation of the grid for atmospheric conditions and is therefore not useful in atmospheric sciences. The three diagrams are constructed from the P-alpha-diagram by using appropriate coordinate transformations, not a thermodynamic diagram in a strict sense since it does not display the energy - area equivalence is the Stüve diagram Due to its simpler construction it is preferred in education. With the help of these lines, parameters such as cloud condensation level, level of free convection, etc. can be derived from the soundings. The Physics of Atmospheres by John Houghton, Cambridge University Press 2002, www. met. tamu. edu/. /aws-tr79-006. pdf A very large technical manual how to use the diagrams. Www. comet. ucar. edu/. /sld010. htm A course on how to use diagrams at Comet, the Cooperative Program for Operational Meteorology, Education and Training
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Intensive and extensive properties
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Physical properties of materials and systems can often be categorized as being either intensive or extensive quantities, according to how the property changes when the size of the system changes. According to IUPAC, a property is one whose magnitude is independent of the size of the system. An extensive property is one whose magnitude is additive for subsystems, an intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, T, refractive index, n, density, ρ, when a diamond is cut, the pieces maintain their intrinsic hardness, so hardness is independent of the size of the system. By contrast, a property is additive for subsystems. For example, both the mass, m, and the volume, V, of a diamond are directly proportional to the amount that is left after cutting it from the raw mineral, mass and volume are extensive properties, but hardness is intensive. The ratio of two properties of the same object or system is an intensive property. For example, the ratio of a mass and volume. The terms intensive and extensive quantities were introduced by Richard C, an intensive property is a physical quantity whose value does not depend on the amount of the substance for which it is measured. For example, the temperature of a system in equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical, the same applies to the density of a homogeneous system, if the system is divided in half, the mass and the volume change in the identical ratio and the density remains unchanged. Additionally, the point of a substance is another example of an intensive property. For example, the point of water is 100 °C at a pressure of one atmosphere. The distinction between intensive and extensive properties has some theoretical uses, other intensive properties are derived from those two variables. Examples of intensive properties include, The IUPAC Gold Book defines an extensive property as a physical quantity whose magnitude is additive for subsystems. The value of such a property is proportional to the size of the system it describes. For example, the amount of required to melt ice at constant temperature and pressure is an extensive property. The amount of required to melt one ice cube would be much less than the amount of heat required to melt an iceberg
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State function
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State functions do not depend on the path by which the system arrived at its present state. A state function describes the state of a system. In contrast, mechanical work and heat are process quantities or path functions, the mode of description breaks down for quantities exhibiting hysteresis effects. A thermodynamic system is described by a number of parameters which are not necessarily independent. The number of parameters needed to describe the system is the dimension of the space of the system. For example, a gas having a fixed number of particles is a simple case of a two-dimensional system. In this example, any system is specified by two parameters, such as pressure and volume, or perhaps pressure and temperature. They are simply different coordinate systems in the thermodynamic state space. Given pressure and temperature, the volume is calculable from them, likewise, given pressure and volume, the temperature is calculable from them. An analogous statement holds for higher-dimensional spaces, as described by the state postulate, if the state space is two-dimensional as in the above example, one may visualize the state space as a three-dimensional graph. The labels of the axes are not generally unique, since there are more variables than three in this case, and any two independent variables suffice to define the state. When a system changes state continuously, it out a path in the state space. The path can be specified by noting the values of the parameters as the system traces out the path, perhaps as a function of time. For example, we might have the pressure P and the volume V as functions of time from time t 0 to t 1 and this will specify a path in our two dimensional state space example. We can now all sorts of functions of time which we may integrate over the path. It is clear that in order to calculate the work W in the integral, we will have to know the functions P and V at each time t. A state function is a function of the parameters of the system which only depends upon the values at the endpoints of the path. For example, suppose we wish to calculate the work plus the integral of V d P over the path, the product P V is therefore a state function of the system
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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
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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
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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
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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
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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
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Vapor quality
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In thermodynamics, vapour quality is the mass fraction in a saturated mixture that is vapour, i. e. saturated vapour has a quality of 100%, and saturated liquid has a quality of 0%. Vapour quality is a property which can be used in conjunction with other independent intensive properties to specify the thermodynamic state of the working fluid of a thermodynamic system. It has no meaning for substances which are not saturated mixtures, quality χ can be calculated by dividing the mass of the vapour by the mass of the total mixture, χ = m v a p o u r m t o t a l where m indicates mass. Another definition used by chemical engineers defines quality of a fluid as the fraction that is saturated liquid, by this definition, a saturated liquid has q =0. A saturated vapour has q =1, an alternative definition is the equilibrium thermodynamic quality. It can be used only for single-component mixtures, and can take values <0 and >1, χ e q = h − h f h f g, subscripts f and g refer to saturated liquid and saturated gas respectively, and fg refers to vaporisation. Another expression of the concept is, χ = m v m l + m v where m v is the vapour mass. The genesis of the idea of quality was derived from the origins of thermodynamics. Low quality steam would contain a high moisture percentage and therefore damage components more easily, high quality steam would not corrode the steam engine. Steam engines use water vapour to drive pistons or turbines which create work, the quality of steam can be quantitatively described by steam quality, the proportion of saturated steam in a saturated water/steam mixture. A steam quality of 0 indicates 100% water while a quality of 1 indicates 100% steam. The quality of steam on which whistles are blown is variable. Steam quality determines the velocity of sound, which declines with decreasing dryness due to the inertia of the liquid phase, also, the specific volume of steam for a given temperature decreases with decreasing dryness. Steam quality is very useful in determining enthalpy of saturated water/steam mixtures since the enthalpy of steam is many orders of higher than enthalpy of water
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Reduced properties
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In thermodynamics, the reduced properties of a fluid are a set of state variables normalized by the fluids state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substances compressibility factor, reduced properties are also used to define the Peng–Robinson equation of state, a model designed to provide reasonable accuracy near the critical point. They are also used to critical exponents, which describe the behaviour of physical quantities near continuous phase transitions, both the reduced temperature and the reduced pressure are often used in thermodynamical formulas like the Peng–Robinson equation of state
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Process function
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As an example, mechanical work and heat are process functions because they describe quantitatively the transition between equilibrium states of a thermodynamic system. Path functions depend on the path taken to one state from another. Examples of path functions include work, heat and arc length, in contrast to path functions, state functions are independent of the path taken. Thermodynamic state variables are point functions, differing from path functions, for a given state, considered as a point, there is a definite value for each state variable and state function. Infinitesimal changes in a process function X are often indicated by δ X to distinguish them from changes in a state function Y which is written d Y. The quantity d Y is a differential, while δ X is not. In general, a process function X may be either holonomic or non-holonomic, for a holonomic process function, an auxiliary state function λ may be defined such that Y = λ X is a state function. For a non-holonomic process function, no such function may be defined, in other words, for a holonomic process function, λ may be defined such that d Y = λ δ X is an exact differential. For example, thermodynamic work is a process function since the integrating factor λ =1 / p will yield exact differential of the volume state function d V = δ W / p. Thermodynamics