Willard Gibbs - founder of chemical thermodynamics

In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. Chemical thermodynamics can be generally thought of as the application of mathematical methods to the study of chemical questions. Josiah Willard Gibbs Original: Image:Wgibbs. ... Josiah Willard Gibbs Original: Image:Wgibbs. ... Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ... Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... In thermodynamics, thermodynamic work is the quantity of energy transferred from one system to another. ... Chemical reactions are also known as chemical changes. ... This article needs to be cleaned up to conform to a higher standard of quality. ... The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ...

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, more than fifty million equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.^[1] The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... Thermodynamics (Greek: thermos = heat and dynamic = change) is the physics of energy, heat, work, entropy and the spontaneity of processes. ...

History

In 1865, the German physicist Rudolf Clausius, in his Mechanical Theory of Heat, suggested that the principles of thermochemistry, e.g. such as the heat evolved in combustion reactions, could be applied to the principles of thermodynamics. Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published a series of three papers, the most famous one being the paper On the Equilibrium of Heterogeneous Substances. In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both the thermodynamic equilibrium of chemical reactions as well as their tendencies to occur or proceed. Gibbs’ collection of papers provided the first unified body of thermodynamic theorems from the principles developed by others, such as Clausius and Sadi Carnot. Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... In the thermodynamics and physical chemistry, thermochemistry is the study of the heat evolved or absorbed in chemical reactions. ... In physics, heat, symbolized by Q, is defined as energy in transit. ... Combustion or burning is an exothermic reaction between a substance and a gas to release heat. ... Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ... The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... Sadi Carnot Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French mathematician and engineer who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics. ...

During the early 20th century, two major publications successfully applied the principles developed by Gibbs to chemical processes, and thus established the foundation of the science of chemical thermodynamics. 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 for the term 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. In this manner, Lewis, Randall, and Guggenheim are considered as the founders of modern chemical thermodynamics because of the major contribution of these two books in unifying the application of thermodynamics to chemistry.^[1] Lewis in the Berkeley Lab Gilbert Newton Lewis (October 23, 1875-March 23, 1946) was a famous American physical chemist. ... Merle Randall was an American physical chemist famous for his work, over the period of 25 years, in measuring free energy calculations of compounds with Gilbert N. Lewis. ... Chemical affinity results from electronic properties by which dissimilar substances are capable of forming chemical compounds. ... The thermodynamic free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ... Edward Armand Guggenheim (1901 - 1970) was a English thermodynamicist and professor of chemistry at the University of Reading, noted for his 1933 publication of the Modern Thermodynamics by the Methods of Willard Gibbs, a 206 page, detailed study, with text, figures, index, and preface by F. G. Donnan, showing how... Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Chemistry (from Greek χημεία khemeia[1] meaning alchemy) is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms, such as molecules, crystals, and metals. ...

Overview

The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation.^[2] In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes: Look up Spontaneous in Wiktionary, the free dictionary. ...

1. Chemical reactions
2. Phase changes
3. The formation of solutions

The following state functions are of primary concern in chemical thermodynamics: Chemical reactions are also known as chemical changes. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... In thermodynamics, a state function (or state quantity) is a property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ...

• Internal energy (U)
• Enthalpy (H).
• Entropy (S)
• Gibbs free energy (G)

Most identities in chemical thermodynaimcs arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions. In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... In thermodynamics, the enthalpy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant pressure. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure. ... Conservation of energy states that the total amount of energy (often expressed as the sum of kinetic energy and potential energy) in an isolated system remains constant. ...

Chemical reactions

In most cases of interest in chemical thermodynamics there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which always create entropy unless they are at equilibrium, or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such as pistons or electrodes, to deliver and receive external work. Even for homogeneous "bulk" materials, the free energy functions depend on the composition, as do all the extensive thermodynamic potentials, including the internal energy. If the quantities { N_i }, the number of chemical species, are omitted from the formulae, it is impossible to describe compositional changes. Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. ... A chemical reaction occurs when vapours of hydrogen chloride and ammonia meet to form a cloud of a new substance, ammonium chloride Chemical reaction is a process that results in the interconversion of chemical substances [1]. The substance or substances initially involved in a chemical reaction are called reactants. ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... piston + connecting rod Components of a typical, four stroke cycle, DOHC piston engine. ... An electrode is a conductor used to make contact with a nonmetallic part of a circuit (e. ... A chemical compound is a chemical substance consisting of two or more different chemically bonded chemical elements, with a fixed ratio determining the composition. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Chemical species is a common, general name for atoms, molecules, molecular fragments and ions as entities being subjected to a chemical process or to a measurement. ...

Gibbs function

For a "bulk" (unstructured) system they are the last remaining extensive variables. For an unstructured, homogeneous "bulk" system, there are still various extensive compositional variables { N_i } that G depends on, which specify the composition, the amounts of each chemical substance, expressed as the numbers of molecules present or (dividing by Avogadro's number), the numbers of moles Look up substance in Wiktionary, the free dictionary. ... Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ...

For the case where only PV work is possible

in which μ_i is the chemical potential for the i-the component in the system In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist (Willard Gibbs and his partner Lauren Berkley), which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given... In thermodynamics, a component is a chemically distinct constituent of a system. ...

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 For other uses, see Life (disambiguation), Lives (disambiguation) or Living (disambiguation), Living Things (disambiguation) Look up life, living in Wiktionary, the free dictionary. ...

Chemical affinity

Main article: Chemical affinity

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 (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components ( N_i } can be changed independently. All real processes obey conservation of mass, and in addition, conservation of the numbers of atoms of each kind. Whatever molecules are transferred to or from should be considered part of the "system". Chemical affinity results from electronic properties by which dissimilar substances are capable of forming chemical compounds. ... (The Lomonosov-Lavoisier law) states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle of a chemical element that retains its chemical properties. ...

Consequently we introduce an explicit variable to represent the degree of advancement of a process, a progress variable ξ for the extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4-7; Guggenheim, p. 37.62), and to the use of the partial derivative ∂G/∂ξ (in place of the widely used "ΔG", since the quantity at issue is not a finite change). The result is an understandable expression for the dependence of dG on chemical reactions (or other processes). If there is just one reaction In computer science and mathematics, a variable (sometimes called a pronumeral) is a symbol denoting a quantity or symbolic representation. ... In a chemical reaction system the stoichiometric coefficient of the i–th component is defined as or where Ni is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. ... In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). ... An expression in the very basic sense is the noun form of the verb express. ... A chemical reaction occurs when vapours of hydrogen chloride and ammonia meet to form a cloud of a new substance, ammonium chloride Chemical reaction is a process that results in the interconversion of chemical substances [1]. The substance or substances initially involved in a chemical reaction are called reactants. ...

If we introduce the stoichiometric coefficient for the i-th component in the reaction In a chemical reaction system the stoichiometric coefficient of the i-th component is defined as or where Ni is the number of molecules of i and ξ is the progress variable or extent of reaction. ...

which tells how many molecules of i are produced or consumed, we obtain an algebraic expression for the partial derivative

where, (De Donder; Progoine & Defay, p. 69; Guggenheim, pp. 37,240), we introduce a concise and historical name for this quantity, the "affinity", symbolized by A, as introduced by Théophile de Donder in 1923. The minus sign comes from the fact the affinity was defined to represent the rule that spontaneous changes will ensue only when the change in the Gibbs free energy of the process is negative, meaning that the chemical species have a positive affinity for each other. The differential for G takes on a simple form which displays its dependence on compositional change Chemical affinity results from electronic properties by which dissimilar substances are capable of forming chemical compounds. ... Belgian mathematician and physicist who was born and died in Brussels. ...

If there are a number of chemical reactions going on simultaneously, as is usually the case

a set of reaction coordinates { ξ_j }, avoiding the notion that the amounts of the components ( N_i } can be changed independently. The expressions above are equal to zero at thermodynamic equilibrium, while in the general case for real systems, they are negative, due to the fact that all chemical reactions proceeding at a finite rate produce entropy. This can be made even more explicit by introducing the reaction rates dξ_j/dt. For each and every physically independent process (Prigogine & Defay, p. 38; Prigogine, p. 24) In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ...

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether the temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (−T times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See Constraints below.)

We now relax the requirement of a homogeneous “bulk” system by letting the chemical potentials and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the entropy production due to irreversible processes, the inequality for dG is now replace by an equality In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist (Willard Gibbs and his partner Lauren Berkley), which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given...

or

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that the extent of reaction for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such a way that one can advance only if the other one also does. The coupling may occasionally be rigid, but it is often flexible and variable. In thermodynamics the Gibbs free energy is a state function of any system defined as G = H − T·S where G is the Gibbs free energy, measured in joules H is the enthalpy, measured in joules T is the temperature, measured in kelvins S is the entropy, measured in... An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. ... An isobaric process is a thermodynamic process in which the pressure stays constant; . The heat transferred to the system does work but also changes the internal energy of the system: according to the first law of thermodynamics, where W is work done by the system, E is internal energy, and... In a thermodynamics problem, the surroundings, or environment, are anything not part of the system. ... A wave that loses amplitude is said to dissipate. ... In a chemical reaction system the stoichiometric coefficient of the i–th component is defined as or where Ni is the number of molecules of i, and ξ is the progress variable or extent of reaction (Prigogine & Defay, p. ...

Solutions

In solution chemistry and biochemistry, the Gibbs free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔG) is commonly used as a surrogate for (−T times) the entropy produced by spontaneous chemical reactions in situations where there is no work being done; or at least no "useful" work; i.e., other than perhaps some ± PdV. The assertion that all spontaneous reactions have a negative ΔG is merely a restatement of the combined law of thermodynamics, giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When there is no useful work being done, it would be less misleading to use the Legendre transforms of the entropy appropriate for constant T, or for constant T and P, the Massieu functions −F/T and −G/T respectively. Chemistry (from Greek χημεία khemeia[1] meaning alchemy) is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms, such as molecules, crystals, and metals. ... Biochemistry is the study of the chemical processes and transformations in living organisms. ... In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure. ... A chemical reaction occurs when vapours of hydrogen chloride and ammonia meet to form a cloud of a new substance, ammonium chloride Chemical reaction is a process that results in the interconversion of chemical substances [1]. The substance or substances initially involved in a chemical reaction are called reactants. ... In thermodynamics, the combined law of thermodynamics is simply a mathemtical summation of the first law of thermodynamics and the second law of thermodynamics subsumed into a single concise mathematical statement as shown below: Here, U is internal energy, T is temperature, S is entropy, P is pressure, and V... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ... In mathematics, two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: f and g are then said to be related by a Legendre transformation. ...

System constraints

In this regard, it is crucial to understand the role of walls and other constraints, and the distinction between independent processes and coupling. Contrary to the clear implications of many reference sources, the previous analysis is not restricted to homogenous, isotropic bulk systems which can deliver only PdV work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of the same, overall process. An independent process is one that could proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a “thought experiment” in chemical kinetics, but actual examples exist. Isotropy (the opposite of anisotropy) is the property of being independent of direction. ... In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... In physical chemistry, chemical kinetics or reaction kinetics study reaction rates in a chemical reaction. ...

A gas reaction which results in an increase in the number of molecules will lead to an increase in volume at constant external pressure. If it occurs inside a cylinder closed with a piston, the equilibrated reaction can proceed only by doing work against an external force on the piston. The extent variable for the reaction can increase only if the piston moves, and conversely, if the piston is pushed inward, the reaction is driven backwards.

Similarly, a redox reaction might occur in an electrochemical cell with the passage of current in wires connecting the electrodes. The half-cell reactions at the electrodes are constrained if no current is allowed to flow. The current might be dissipated as joule heating, or it might in turn run an electrical device like a motor doing mechanical work. An automobile lead-acid battery can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work. Semi-accurate illustration of a redox reaction Redox reactions include all chemical processes in which atoms have their oxidation number (oxidation state) changed. ... English chemists John Daniell (left) and Michael Faraday (right), both credited to be founders of electrochemistry as known today. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... A wire is a single, usually cylindrical, elongated strand of drawn metal. ... Alternative meanings: There is also an Electric-type Pokémon named Electrode. ... Alternative meanings: There is also an Electric-type Pokémon named Electrode. ... In electronics, and in physics more broadly, Joule heating refers to the increase in temperature of a conductor as a result of resistance to an electrical current flowing through it. ... Rotating magnetic field as a sum of magnetic vectors from 3 phase coils. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... Karl Benzs Velo model (1894) - entered into the first automobile race An automobile (or motor car) is a wheeled passenger vehicle that carries its own motor. ... General Name, Symbol, Number lead, Pb, 82 Chemical series poor metals Group, Period, Block 14, 6, p Appearance bluish white Atomic mass 207. ... For other uses, see Acid (disambiguation). ... This article or section does not cite its references or sources. ...

The hydrolysis of ATP to ADP and phosphate can drive the force times distance work delivered by living muscles, and synthesis of ATP is in turn driven by a redox chain in mitochondria and chloroplasts, which involves the transport of ions across these cellular organelles. The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of a rubber balloon. Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling coefficient, which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemical process. Hydrolysis is a chemical reaction or process in which a molecule is split into two parts by reacting with a molecule of water, which has the chemical formula H2O. One of the parts gets an OH- from the water molecule and the other part gets an H+ from the water. ... ATP may refer to: Chemistry/Biochemistry Adenosine triphosphate, the universal energy currency of all living organisms Companies Alberta Theatre Projects, a major Canadian theatre company. ... Adenosine diphosphate, abbreviated ADP, is a nucleotide. ... Above is a ball-and-stick model of the inorganic phosphate molecule (HPO42−). Colour coding: P (orange); O (red); H (white). ... In physics, force is an influence that may cause a body to accelerate. ... Distance is a numerical description of how far apart things lie. ... It has been suggested that this article or section be merged into Muscular system. ... In cell biology, a mitochondrion is an organelle found in the cells of most eukaryotes. ... Chloroplasts are organelles found in plant cells and eukaryotic algae that conduct photosynthesis. ... An ion is an atom or group of atoms that normally are electrically neutral and achieve their status as an ion by loss or addition of one or more electrons. ... Drawing of the structure of cork as it appeared under the microscope to Robert Hook from Micrographia which is the origin of the word cell. Cells in culture, stained for keratin (red) and DNA (green). ... Schematic of typical animal cell, showing subcellular components. ... Latex being collected from a tapped rubber tree Rubber is an elastic hydrocarbon polymer which occurs as a milky colloidal suspension (known as latex) in the sap of several varieties of plants. ... Balloons, like greeting cards or flowers, are given for special occasions. ... In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...

Quote

In the preface section to popular book Basic Chemical Thermodynamics by physical chemist Brian Smith, originally published in 1973, and now in the 5th edition, we find the following overview of the subject as it is perceived in college:^[3]

The first time I heard about chemical thermodynamics was when a second-year undergraduate brought me the news early in my freshman year. He told me a spine-chilling story of endless lectures with almost three-hundred numbered equations, all of which, it appeared, had to be committed to memory and reproduced in exactly the same form in subsequent examinations. Not only did these equations contain all the normal algebraic symbols but in addition they were liberally sprinkled with stars, daggers, and circles so as to stretch even the most powerful of minds.

Image File history File links Cquote1. ... Image File history File links Cquote2. ...

See also

• Thermodynamic databases for pure substances

Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. ...

References

1. ^ ^{a b} Ott, Bevan J., Boerio-Goates, Juliana (2000). Chemical Thermodynamics – Principles and Applications. Academic Press. ISBN 0-12-530990-2.
2. ^ Klotz, I. (1950). Chemical Thermodynamics. New York: Prentice-Hall, Inc.
3. ^ Smith, Brian, E. (2004). Basic Chemical Thermodynamics. Oxford University Press. ISBN 1-86094-446-9.

• Herbert B. Callen (1960). Thermodynamics. Wiley & Sons. The clearest account of the logical foundations of the subject. Library of Congress Catalog No. 60-5597
• Ilya Prigogine & R. Defay, translated by D.H. Everett; Chapter IV (1954). Chemical Thermodynamics. Longmans, Green & Co. Exceptionally clear on the logical foundations as applied to chemistry; includes non-equilibrium thermodynamics.
• Ilya Prigogine (1967). Thermodynamics of Irreversible Processed, 3rd ed.. Interscience: John Wiley & Sons. A simple, concise monograph explaining all the basic ideas. Library of Congress Catalog No. 67-29540
• E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed.. North Holland; John Wiley & Sons (Interscience). A remarkably astute treatise. Library of Congress Catalog No. 67-20003
• Th. De Donder (1922). "". Bull. Ac. Roy. Belg. (Cl. Sc.) (5) 7: 197, 205.

Non-equilibrium thermodynamics is a branch of thermodynamics concerned with studying time-dependent thermodynamic systems, irreversible transformations and open systems. ...

External links

• Early Chemical Thermodynamics - Its Duality Embodied in Van't Hoff and Gibbs
• Gibbs & Chemical Thermodynamics - An Historical Outline
• Chemical Thermodynamics - University of North Carolina