2300:, and are mentioned by other writers also. They are selectively permeable. They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal. This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state.
2083:. It is allowed in equilibrium thermodynamics just because the initial and final states are of thermodynamic equilibrium, even though during the process there is transient departure from thermodynamic equilibrium, when neither the system nor its surroundings are in well defined states of internal equilibrium. A natural process proceeds at a finite rate for the main part of its course. It is thereby radically different from a fictive quasi-static 'process' that proceeds infinitely slowly throughout its course, and is fictively 'reversible'. Classical thermodynamics allows that even though a process may take a very long time to settle to thermodynamic equilibrium, if the main part of its course is at a finite rate, then it is considered to be natural, and to be subject to the second law of thermodynamics, and thereby irreversible. Engineered machines and artificial devices and manipulations are permitted within the surroundings. The allowance of such operations and devices in the surroundings but not in the system is the reason why Kelvin in one of his statements of the second law of thermodynamics spoke of
2374:, "The most important conception of thermodynamics is temperature." Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it.
2025:
boundary between the two systems. In the thermodynamic formalism, that surface is regarded as having specific properties of permeability. For example, the surface of contiguity may be supposed to be permeable only to heat, allowing energy to transfer only as heat. Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. When two systems are in contact equilibrium with respect to a particular kind of permeability, they have common values of the intensive variable that belongs to that particular kind of permeability. Examples of such intensive variables are temperature, pressure, chemical potential.
2461:
separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature.
2446:
thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state.
2268:." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium.
2029:
are equal and opposite. An adiabatic wall between the two systems is 'permeable' only to energy transferred as work; at mechanical equilibrium the rates of transfer of energy as work between them are equal and opposite. If the wall is a simple wall, then the rates of transfer of volume across it are also equal and opposite; and the pressures on either side of it are equal. If the adiabatic wall is more complicated, with a sort of leverage, having an area-ratio, then the pressures of the two systems in exchange equilibrium are in the inverse ratio of the volume exchange ratio; this keeps the zero balance of rates of transfer as work.
2218:
shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface.
2391:
matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed." As noted above, according to A. MĂĽnster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass.
2296:. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by
2344:
systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied.
2126:
number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature doesn't hold, and the temperature becomes undefined.
2079:
adiabatic wall may be placed or removed within the surroundings. Consequent upon such an operation restricted to the surroundings, the system may be for a time driven away from its own initial internal state of thermodynamic equilibrium. Then, according to the second law of thermodynamics, the whole undergoes changes and eventually reaches a new and final equilibrium with the surroundings. Following Planck, this consequent train of events is called a natural
2426:
of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system.
2378:
exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of
Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement.
2530:
155:
1725:
2157:
molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it to compensate for the melting, and continuously draining off the meltwater. Natural
2413:
simultaneously; some can be established before others. For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium.
2075:
unique property of temperature. It holds even in the presence of long-range forces. (That is, there is no "force" that can maintain temperature discrepancies.) For example, in a system in thermodynamic equilibrium in a vertical gravitational field, the pressure on the top wall is less than that on the bottom wall, but the temperature is the same everywhere.
2241:
by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. MĂĽnster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero.
2514:
subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods.
2513:
Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously
2441:
If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics,
2425:
To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values
2240:
For example, A. MĂĽnster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso
2141:
being emitted and absorbed by the gas do not need to be in a thermodynamic equilibrium with each other or with the massive particles of the gas for LTE to exist. In some cases, it is not considered necessary for free electrons to be in equilibrium with the much more massive atoms or molecules for LTE
2125:
If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain
2028:
A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems
2024:
Often the surroundings of a thermodynamic system may also be regarded as another thermodynamic system. In this view, one may consider the system and its surroundings as two systems in mutual contact, with long-range forces also linking them. The enclosure of the system is the surface of contiguity or
2437:
If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent
2390:
In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria. In the words of
Prigogine and Defay (1945): "It is a
2343:
if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed
2271:
A student textbook by F.H. Crawford has a section headed "Thermodynamic
Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in
2217:
The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its
2412:
When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached
2070:
The thermodynamic formalism allows that a system may have contact with several other systems at once, which may or may not also have mutual contact, the contacts having respectively different permeabilities. If these systems are all jointly isolated from the rest of the world those of them that are
2044:
from its surroundings. If it has been left undisturbed for an indefinitely long time, classical thermodynamics postulates that it is in a state in which no changes occur within it, and there are no flows within it. This is a thermodynamic state of internal equilibrium. (This postulate is sometimes,
2377:
The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative
2256:
Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like
2252:
In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness".
2244:
R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from
2460:
An explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are several occurring irreversible processes, entailing non-zero fluxes; the two systems are
2381:
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal
2156:
Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local
Maxwell–Boltzmann distribution of
2074:
If several systems are free of adiabatic walls between each other, but are jointly isolated from the rest of the world, then they reach a state of multiple contact equilibrium, and they have a common temperature, a total internal energy, and a total entropy. Amongst intensive variables, this is a
2509:
A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time.
2433:
If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too
2357:
A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent
2288:
so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow
2233:
conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn
2078:
A thermodynamic operation may occur as an event restricted to the walls that are within the surroundings, directly affecting neither the walls of contact of the system of interest with its surroundings, nor its interior, and occurring within a definitely limited time. For example, an immovable
1946:
Thermodynamic equilibrium is the unique stable stationary state that is approached or eventually reached as the system interacts with its surroundings over a long time. The above-mentioned potentials are mathematically constructed to be the thermodynamic quantities that are minimized under the
130:
body of material starts from an equilibrium state, in which portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable, then it spontaneously reaches its own new state of internal
2279:
A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is
2201:
Another author, A. MĂĽnster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical
2394:
If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general,
2429:
It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values.
2445:
The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal
2197:
writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10 years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in
2494:
to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium.
2181:
writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, generally can be ignored". He adds "In practice, the criterion for equilibrium is circular.
2328:
Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform,
2093:
It is often convenient to suppose that some of the surrounding subsystems are so much larger than the system that the process can affect the intensive variables only of the surrounding subsystems, and they are then called reservoirs for relevant intensive variables.
2403:
As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties.
2320:
J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a piece of glass that has not yet reached its
2517:
Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production.
2358:
volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some
2056:
Such states are a principal concern in what is known as classical or equilibrium thermodynamics, for they are the only states of the system that are regarded as well defined in that subject. A system in contact equilibrium with another system can by a
2173:
Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated.
2149:. The temperature inside the glass can be defined at any point, but it is colder near the ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the
2421:
In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account.
2061:
be isolated, and upon the event of isolation, no change occurs in it. A system in a relation of contact equilibrium with another system may thus also be regarded as being in its own state of internal thermodynamic equilibrium.
1444:
2306:
also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium".
2317:". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'.
2209:: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common."
2189:
J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems."
2122:(LTE) means that those intensive parameters are varying in space and time, but are varying so slowly that, for any point, one can assume thermodynamic equilibrium in some neighborhood about that point.
2153:
for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the
Maxwell–Boltzmann distribution for another temperature.
2229:: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are
93:
equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a
2102:
It can be useful to distinguish between global and local thermodynamic equilibrium. In thermodynamics, exchanges within a system and between the system and the outside are controlled by
2434:
small to see. According to
Buchdahl: "... there is no place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)."
111:
there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a
2253:
This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors".
2045:
but not often, called the "minus first" law of thermodynamics. One textbook calls it the "zeroth law", remarking that the authors think this more befitting that title than its
97:. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
2257:
interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy.
1279:
1224:
1169:
1937:
976:
929:
844:
797:
709:
662:
2289:
process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process.
1885:
4265:(March 1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam".
1754:
880:
748:
2284:." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being
1827:
1114:
4690:
3722:
1455:
613:
4398:
1343:
952:
905:
820:
773:
685:
638:
2032:
A radiative exchange can occur between two otherwise separate systems. Radiative exchange equilibrium prevails when the two systems have the same temperature.
66:
nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, not only is there an absence of
2202:
significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions."
577:
2471:
with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same.
4279:"On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam"
2165:
of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.
1433:
4852:
1466:
4501:
3545:
Velasco, S.; Román, F.L.; White, J.A. (1996). "On a paradox concerning the temperature distribution of an ideal gas in a gravitational field".
2781:
2442:
and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important.
1036:
2759:, Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C.
104:, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.
2697:
1840:), is minimized at thermodynamic equilibrium in a closed system at constant temperature and pressure, both controlled by the surroundings:
1747:
1334:
570:
448:
1003:
3502:
Román, F.L.; White, J.A.; Velasco, S. (1995). "Microcanonical single-particle distributions for an ideal gas in a gravitational field".
2193:
Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text",
386:
2487:
2150:
4683:
4096:
3960:
The
Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases
2359:
1518:
1492:
1013:
467:
101:
2821:
4918:
4391:
4330:
4262:
4043:
4003:
3925:
3890:
3875:
3860:
3631:
3025:
2802:
2773:
2608:
419:
2668:
1571:
2129:
This local equilibrium may apply only to a certain subset of particles in the system. For example, LTE is usually applied only to
5002:
4592:
1042:
441:
4364:
2370:
Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable temperature. According to
4956:
2483:
2234:
proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium.
1740:
5007:
4992:
3981:
3951:
2504:
1671:
203:
2245:
all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in
1566:
4997:
4676:
2727:
2682:
2292:
A. MĂĽnster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of
1646:
1419:
396:
4650:
4554:
4903:
4384:
2184:
Operationally, a system is in an equilibrium state if its properties are consistently described by thermodynamic theory!
2084:
2046:
1031:
234:
224:
123:
3467:
Coombes, C.A.; Laue, H. (1985). "A paradox concerning the temperature distribution of a gas in a gravitational field".
2892:
Marsland, Robert; Brown, Harvey R.; Valente, Giovanni (2015). "Time and irreversibility in axiomatic thermodynamics".
2722:
2702:
2548:
2438:
state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent.
239:
229:
4463:
3944:: 355–386. A translation may be found here. Also a mostly reliable translation is to be found at Kestin, J. (1976).
4817:
4707:
4570:
3931:
2717:
2648:
2573:
2297:
1561:
1523:
1487:
199:
4971:
4446:
2732:
1316:
1064:
510:
323:
100:
A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its
4619:
4614:
4575:
4926:
4031:, edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp. 55–353.
3370:
3345:
2237:
Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other.
4359:
5012:
4951:
4936:
4882:
2578:
2058:
1772:
1728:
1556:
1353:
1056:
995:
531:
520:
186:
94:
2757:
Statistical
Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases
4638:
4528:
1661:
1581:
1378:
462:
216:
191:
82:
51:, or a relation between several thermodynamic systems connected by more or less permeable or impermeable
4797:
4757:
4631:
4626:
4604:
4549:
4456:
4436:
3955:
3936:
2628:
2593:
2080:
1784:
1596:
1173:
486:
332:
181:
90:
4213:, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.
3996:
Generalized
Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics
4941:
4513:
4496:
4407:
4122:
4103:
Lieb, E. H.; Yngvason, J. (1999). "The
Physics and Mathematics of the Second Law of Thermodynamics".
4070:
4049:
4016:
3805:
3749:
3511:
3476:
3394:
3357:
3288:
2995:
2901:
2603:
2371:
2336:
1940:
1676:
1601:
1591:
391:
265:
253:
86:
52:
48:
4946:
4847:
4699:
4609:
4587:
4473:
4431:
4150:
4011:
Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems
2742:
2712:
2692:
2618:
2613:
2598:
2464:
2455:
2158:
1768:
1621:
1616:
1383:
405:
371:
366:
279:
78:
4803:
4597:
4488:
4421:
4138:
4112:
3716:
3562:
3527:
3410:
2927:
2161:
may lead a system from local to global thermodynamic equilibrium. Going back to our example, the
2115:
2103:
2005:
1710:
1373:
1321:
1234:
1179:
1124:
553:
537:
424:
376:
361:
351:
160:
154:
59:
4301:
2362:. For example, a relatively dense component of a mixture can be concentrated by centrifugation.
2206:
1970:
For a closed system at controlled constant temperature and pressure without an applied voltage,
1913:
1368:
958:
911:
826:
779:
691:
644:
1846:
17:
4966:
4788:
4643:
4523:
4451:
4441:
4326:
4237:
4092:
4039:
3999:
3977:
3921:
3886:
3871:
3856:
3831:
3627:
3601:
2798:
2777:
2769:
2643:
2638:
1833:
1705:
1666:
1656:
1228:
1026:
862:
854:
727:
356:
346:
288:
4370:
4908:
4582:
4468:
4311:
4251:
4130:
3896:
3821:
3813:
3757:
3554:
3519:
3484:
3454:
3402:
3365:
3313:
2944:
2917:
2909:
2623:
2535:
2222:
2130:
1797:
1626:
1611:
1551:
1546:
1363:
1358:
1084:
1008:
476:
341:
4931:
4544:
4353:
4182:
4165:
3234:
3116:
2658:
2468:
2310:
2261:
2226:
2050:
2041:
1576:
1424:
1078:
719:
542:
303:
270:
127:
108:
44:
3794:"Self-Assembled Wiggling Nano-Structures and the Principle of Maximum Entropy Production"
2339:
and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of
4126:
3809:
3753:
3515:
3480:
3398:
3361:
2905:
595:
4898:
4857:
4842:
4827:
4762:
4752:
4747:
4722:
4655:
4226:
4216:
3913:
3826:
3793:
2737:
2663:
2333:
is said to exist." He is not here considering the presence of an external force field.
2178:
1791:), for a closed system at constant volume and temperature (controlled by a heat bath):
1631:
1401:
937:
890:
805:
758:
670:
623:
501:
381:
318:
308:
176:
146:
40:
4134:
2760:
4986:
4961:
4877:
4832:
4793:
4767:
4737:
4732:
4508:
4336:
4278:
4247:
4196:
4142:
3566:
3558:
3531:
3523:
3414:
3309:
3222:
2931:
2303:
2194:
2107:
1700:
1018:
587:
548:
260:
2417:
Fluctuations within an isolated system in its own internal thermodynamic equilibrium
4867:
4862:
4837:
4783:
4742:
2653:
2560:
1651:
1636:
1586:
1069:
131:
thermodynamic equilibrium and this is accompanied by an increase in the sum of the
3385:
Akmaev, R.A. (2008). "On the energetics of maximum-entropy temperature profiles".
3976:, North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York,
4367:
Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere
4067:, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.
3661:
2707:
2475:
1606:
414:
67:
56:
2490:
would be in thermal equilibrium. This outcome allows a single temperature and
2090:
Otherwise, a thermodynamic operation may directly affect a wall of the system.
1771:. The state of a system at thermodynamic equilibrium is the one for which some
4872:
4518:
4206:
3276:
2861:
2687:
2633:
2588:
2525:
1695:
1641:
4426:
2479:
2162:
2134:
293:
122:
of thermodynamics that there exist states of thermodynamic equilibrium. The
3835:
3762:
3737:
27:
State of thermodynamic systems where no net flow of matter or energy occurs
4036:
Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)
2795:
Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics)
2145:
As an example, LTE will exist in a glass of water that contains a melting
4117:
2922:
2583:
2491:
2146:
1994:
1409:
1326:
1118:
526:
298:
77:
Systems in mutual thermodynamic equilibrium are simultaneously in mutual
2395:
additional variables are needed to describe the spatial non-uniformity.
4668:
4356:
George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15
2554:
1776:
515:
132:
4376:
4203:, reprinted with corrections 1966, Cambridge University Press, London.
3817:
2913:
2478:
thermal observables have ceased to change with time. For example, an
2071:
in contact then reach respective contact equilibria with one another.
1775:
is minimized (in the absence of an applied voltage), or for which the
3903:, translated by S.G. Brush, University of California Press, Berkeley.
2138:
2012:
63:
3488:
1783:) is maximized, for specified conditions. One such potential is the
4365:
Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres
3406:
1963:
For a closed system at controlled constant temperature and volume,
119:
36:
4054:
Thermodynamics. An Advanced Treatment for Chemists and Physicists
3445:
Chapman, S., Cowling, T.G. (1939/1970), Section 4.14, pp. 75–78.
2348:
Characteristics of a state of internal thermodynamic equilibrium
2015:
are balanced and there is no significant external driving force.
491:
4672:
4380:
2408:
Approach to thermodynamic equilibrium within an isolated system
1943:
under these conditions (in the absence of an applied voltage).
3969:, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.
3934:(1909). Untersuchungen ĂĽber die Grundlagen der Thermodynamik,
3694:
Thermodynamics of Complex Systems: Principles and applications
2118:
parameters are homogeneous throughout the whole system, while
4179:, translated by E.S. Halberstadt, Wiley–Interscience, London.
4019:(1876/1878). On the equilibrium of heterogeneous substances,
3779:
Non-equilibrium Thermodynamics and the Production of Entropy
4059:
Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of
3624:
Fundamentals of Equilibrium and Steady-State Thermodynamics
2755:
C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973)
1978:
The various types of equilibriums are achieved as follows:
4343:, fifth edition 1967, McGraw–Hill Book Company, New York.
3962:, third edition 1970, Cambridge University Press, London.
3371:
10.1175/1520-0469(2004)061<0931:omep>2.0.co;2
3920:, (1st edition 1960) 2nd edition 1985, Wiley, New York,
2266:
An equilibrium state is one which is independent of time
2036:
Thermodynamic state of internal equilibrium of a system
3918:
Thermodynamics and an Introduction to Thermostatistics
2087:; a system in thermodynamic equilibrium is inanimate.
4082:
Thermodynamics with Quantum Statistical Illustrations
1947:
particular conditions in the specified surroundings.
1916:
1849:
1800:
1237:
1182:
1127:
1087:
961:
940:
914:
893:
865:
829:
808:
782:
761:
730:
694:
673:
647:
626:
598:
4029:
The Collected Works of J. Willard Gibbs, PhD, LL. D.
4917:
4891:
4816:
4776:
4717:
4706:
4563:
4537:
4487:
4414:
2822:
Introduction to Chemical Engineering Thermodynamics
1910:the internal energy of the system. In other words,
4221:Étude Thermodynamique des Phénomènes irréversibles
4056:, fifth revised edition, North-Holland, Amsterdam.
2824:, Fifth Edition (1996), .p.34, italics in original
1931:
1879:
1821:
1273:
1218:
1163:
1108:
970:
946:
923:
899:
874:
838:
814:
791:
767:
742:
703:
679:
656:
632:
607:
4341:Heat and Thermodynamics. An Intermediate Textbook
3870:, American Institute of Physics Press, New York,
2386:Number of real variables needed for specification
55:. In thermodynamic equilibrium, there are no net
3948:, Dowden, Hutchinson & Ross, Stroudsburg PA.
3738:"Reciprocal Relations in Irreversible Processes"
3272:
3270:
2857:
2855:
2106:parameters. As an example, temperature controls
2020:Relation of exchange equilibrium between systems
1894:denotes the absolute thermodynamic temperature,
4318:, American Mathematical Society, Providence RI.
4191:Fundamental Principles. The Properties of Gases
4172:, second edition, W.A. Benjamin, Inc, New York.
4371:Thermodynamic Equilibrium, Local and otherwise
4267:Transactions of the Royal Society of Edinburgh
2955:
2953:
2313:writes that thermodynamics is concerned with "
2225:of the theory of thermodynamics. According to
1767:Classical thermodynamics deals with states of
4684:
4392:
3967:Heat, Thermodynamics, and Statistical Physics
3885:, Elsevier Scientific Publishing, Amsterdam,
2768:. First Edition (QB43.3.B37 2006) CRC Press
2551:(NRTL model) - Phase equilibrium calculations
2353:Homogeneity in the absence of external forces
1748:
8:
4354:Breakdown of Local Thermodynamic Equilibrium
4325:, Cambridge University Press, Cambridge UK,
4153:(1867). "On the dynamical theory of gases".
3910:, Cambridge University Press, Cambridge UK.
3591:Prigogine, I., Defay, R. (1950/1954), p. 1.
3578:
3576:
3016:Lieb, E.H., Yngvason, J. (1999), pp. 17–18.
2474:Thermal equilibrium occurs when a system's
4714:
4691:
4677:
4669:
4399:
4385:
4377:
4187:An Advanced Treatise on Physical Chemistry
4063:, pages 1–97 of volume 1, ed. W. Jost, of
3721:: CS1 maint: location missing publisher (
3264:Kirkwood, J.G., Oppenheim, I. (1961), p. 2
3055:Beattie, J.A., Oppenheim, I. (1979), p. 3.
2280:properly static, it will be said to be in
1755:
1741:
1304:
456:
275:
153:
142:
118:Though not a widely named "law," it is an
4116:
4091:, second edition, McGraw-Hill, New York,
3998:, Kluwer Academic Publishers, Dordrecht,
3825:
3761:
3369:
2921:
2845:
2843:
1915:
1848:
1799:
1236:
1181:
1126:
1086:
960:
939:
913:
892:
864:
828:
807:
781:
760:
729:
693:
672:
646:
625:
597:
4258:, Addison-Wesley Publishing, Reading MA.
4201:The Elements of Classical Thermodynamics
4065:Physical Chemistry. An Advanced Treatise
4038:, Cambridge University Press, New York
3908:The Concepts of Classical Thermodynamics
3682:de Groot, S.R., Mazur, P. (1962), p. 43.
3673:de Groot, S.R., Mazur, P. (1962), p. 44.
3094:
3092:
2837:, 3rd ed., p. 157, Academic Press, 2008.
2820:J.M. Smith, H.C. Van Ness, M.M. Abbott.
2797:, Cambridge University Press, New York
1974:is minimum at thermodynamic equilibrium.
1967:is minimum at thermodynamic equilibrium.
1960:is maximum at thermodynamic equilibrium.
70:change, but there is an “absence of any
4853:Homogeneous charge compression ignition
2813:
2790:, Second Edition, John Wiley & Sons
2040:A collection of matter may be entirely
1501:
1478:
1432:
1392:
1342:
1307:
500:
475:
404:
331:
278:
145:
74:toward change on a macroscopic scale.”
3855:, third edition, McGraw-Hill, London,
3714:
2557:model - Phase equilibrium calculations
2177:For example, one widely cited writer,
4077:, McGraw-Hill Book Company, New York.
3881:Beattie, J.A., Oppenheim, I. (1979).
3344:Verkley, W.T.M.; Gerkema, T. (2004).
3300:Gibbs, J.W. (1876/1878), pp. 144-150.
2977:Landsberg, P. T. (1961), pp. 128–142.
2399:Stability against small perturbations
1986:when their temperatures are the same.
7:
4244:, fourth edition, Wiley, Hoboken NJ.
2049:, which apparently was suggested by
4233:, Longmans, Green & Co, London.
4223:, Dunod, Paris, and Desoers, Liège.
2315:states of thermodynamic equilibrium
4193:, Longmans, Green and Co., London.
3989:Thermodynamics of the Steady State
3972:de Groot, S.R., Mazur, P. (1962).
3709:An Introduction to Thermomechanics
3604:, Bawendi, M.G. (1955/2005), p. 4.
3436:Boltzmann, L. (1896/1964), p. 143.
2325:thermodynamic equilibrium state".
1956:For a completely isolated system,
1917:
962:
915:
830:
783:
695:
648:
468:Intensive and extensive properties
107:In systems that are at a state of
25:
4316:Lectures in Statistical Mechanics
4027:: 108–248, 343–524, reprinted in
3792:Belkin, Andrey; et., al. (2015).
3781:(Heidelberg: Springer. ed.).
3064:Callen, H.B. (1960/1985), p. 485.
2609:Markov chain approximation method
3946:The Second Law of Thermodynamics
3325:Münster, A. (1970), pp. 309–310.
3177:Partington, J.R. (1949), p. 161.
3155:Callen, H.B. (1960/1985), p. 13.
3086:Pippard, A.B. (1957/1966), p. 6.
3046:Callen, H.B. (1960/1985), p. 15.
2882:Callen, H.B. (1960/1985), p. 26.
2528:
2467:is achieved when two systems in
2112:Global thermodynamic equilibrium
1724:
1723:
1043:Table of thermodynamic equations
4360:Local Thermodynamic Equilibrium
3334:Bailyn, M. (1994), pp. 254-256.
3213:Adkins, C.J. (1968/1983), p. 8.
2221:Thermodynamic equilibrium is a
2120:local thermodynamic equilibrium
1519:Maxwell's thermodynamic surface
18:Local thermodynamic equilibrium
3974:Non-equilibrium Thermodynamics
3777:Kleidon, A.; et., al. (2005).
3696:. IOP Publishing, Bristol, UK.
3204:Buchdahl, H.A. (1966), p. 111.
2505:Non-equilibrium thermodynamics
2488:Maxwell–Boltzmann distribution
2151:Maxwell–Boltzmann distribution
1253:
1241:
1198:
1186:
1143:
1131:
1103:
1091:
1:
4277:Thomson, W. (December 1852).
4240:, Bawendi, M.G. (1955/2005).
4135:10.1016/S0370-1573(98)00082-9
3692:Pokrovskii, Vladimir (2020).
3643:Buchdahl, H.A. (1966), p. 16.
3346:"On maximum entropy profiles"
3164:Adkins, C.J. (1968/1983), p.
3073:Adkins, C.J. (1968/1983), p.
2728:People in systems and control
2683:Automation and remote control
2486:has stabilised to a specific
1939:is a necessary condition for
1420:Mechanical equivalent of heat
4323:The Theory of Thermodynamics
4308:, M.I.T Press, Cambridge MA.
4273:(part II): 261–268, 289–298.
4211:The Theory of Heat Radiation
3883:Principles of Thermodynamics
3613:Denbigh, K.G. (1951), p. 42.
3195:Buchdahl, H.A. (1966), p. 8.
3186:Crawford, F.H. (1963), p. 5.
2968:Prigogine, I. (1947), p. 48.
2669:Youla–Kucera parametrization
2098:Local and global equilibrium
2066:Multiple contact equilibrium
1032:Onsager reciprocal relations
124:second law of thermodynamics
4758:Stirling (pseudo/adiabatic)
4373:lecture by Michael Richmond
3711:. North Holland, Amsterdam.
3246:Waldram, J.R. (1985), p. 5.
3007:Levine, I.N. (1983), p. 40.
2894:American Journal of Physics
2723:Negative feedback amplifier
2703:Controller (control theory)
2698:Control–feedback–abort loop
2549:Non-random two-liquid model
1524:Entropy as energy dispersal
1335:"Perpetual motion" machines
1274:{\displaystyle G(T,p)=H-TS}
1219:{\displaystyle A(T,V)=U-TS}
1164:{\displaystyle H(S,p)=U+pV}
5029:
4306:Generalized Thermodynamics
4256:Elements of Thermodynamics
3868:A Survey of Thermodynamics
3853:Equilibrium Thermodynamics
3851:Adkins, C.J. (1968/1983).
3582:Fitts, D.D. (1962), p. 43.
3559:10.1088/0143-0807/17/1/008
3524:10.1088/0143-0807/16/2/008
3146:Haase, R. (1971), pp. 3–4.
3137:MĂĽnster, A. (1970), p. 52.
3098:MĂĽnster, A. (1970), p. 53.
2947:, Ford, G.W. (1963), p. 5.
2849:MĂĽnster, A. (1970), p. 49.
2718:Mathematical system theory
2649:State space representation
2574:Coefficient diagram method
2502:
2453:
2274:thermodynamic—equilibrium.
1932:{\displaystyle \Delta G=0}
971:{\displaystyle \partial T}
924:{\displaystyle \partial V}
839:{\displaystyle \partial p}
792:{\displaystyle \partial V}
704:{\displaystyle \partial T}
657:{\displaystyle \partial S}
4479:Thermodynamic equilibrium
4229:, Defay, R. (1950/1954).
4155:Phil. Trans. R. Soc. Lond
4084:, Interscience, New York.
3652:Eu, B.C. (2002), page 13.
3255:Bailyn, M. (1994), p. 21.
3128:Bailyn, M. (1994), p. 20.
3107:Tisza, L. (1966), p. 119.
2986:Tisza, L. (1966), p. 108.
2766:Fundamentals of Astronomy
2733:Perceptual control theory
2341:thermodynamic equilibrium
2331:thermodynamic equilibrium
2260:Another textbook author,
2047:more customary definition
1880:{\displaystyle G=U-TS+PV}
1445:An Inquiry Concerning the
33:Thermodynamic equilibrium
4632:Distribution coefficient
4576:Hammett acidity function
4555:Liquid–liquid extraction
4464:Le Chatelier's principle
4177:Classical Thermodynamics
4080:Landsberg, P.T. (1961).
4073:, Oppenheim, I. (1961).
4013:, McGraw-Hill, New York.
2959:Carathéodory, C. (1909).
2567:Topics in control theory
1458:Heterogeneous Substances
875:{\displaystyle \alpha =}
743:{\displaystyle \beta =-}
5003:Thermodynamic processes
4231:Chemical Thermodynamics
4075:Chemical Thermodynamics
3965:Crawford, F.H. (1963).
3906:Buchdahl, H.A. (1966).
3626:, Elsevier, Amsterdam,
3622:Tschoegl, N.W. (2000).
2873:Haase, R. (1971), p. 4.
2764:Cesare Barbieri (2007)
2579:Control reconfiguration
2114:(GTE) means that those
2059:thermodynamic operation
1832:Another potential, the
1773:thermodynamic potential
113:meta-stable equilibrium
95:thermodynamic operation
4593:Coordination complexes
4529:Thermodynamic activity
4321:Waldram, J.R. (1985).
3987:Denbigh, K.G. (1951).
3901:Lectures on Gas Theory
3763:10.1103/PhysRev.37.405
3736:Onsager, Lars (1931).
3387:Q. J. R. Meteorol. Soc
1991:mechanical equilibrium
1933:
1881:
1823:
1822:{\displaystyle A=U-TS}
1275:
1220:
1165:
1110:
1109:{\displaystyle U(S,V)}
972:
948:
925:
901:
876:
840:
816:
793:
769:
744:
705:
681:
658:
634:
609:
588:Specific heat capacity
192:Quantum thermodynamics
5008:Thermodynamic systems
4993:Equilibrium chemistry
4605:Dissociation constant
4550:Equilibrium unfolding
4437:Equilibrium chemistry
4314:, Ford, G.W. (1963).
4087:Levine, I.N. (1983),
3937:Mathematische Annalen
3427:Maxwell, J.C. (1867).
2793:Hans R. Griem (2005)
2629:Radial basis function
2594:Hankel singular value
2484:distribution function
2081:thermodynamic process
2002:diffusive equilibrium
1934:
1882:
1824:
1785:Helmholtz free energy
1456:On the Equilibrium of
1276:
1221:
1174:Helmholtz free energy
1166:
1111:
973:
949:
926:
902:
877:
841:
817:
794:
770:
745:
706:
682:
659:
635:
610:
4998:Thermodynamic cycles
4942:Regenerative cooling
4820:combustion / thermal
4719:Without phase change
4710:combustion / thermal
4700:Thermodynamic cycles
4514:Predominance diagram
4497:Equilibrium constant
4175:MĂĽnster, A. (1970).
4034:Griem, H.R. (2005).
4009:Fitts, D.D. (1962).
3707:Ziegler, H. (1983).
3457:(1949), pp. 275–278.
3316:(1966), pp. 127–130.
2998:(1949/1967), § 1.12.
2676:Other related topics
2604:Lead-lag compensator
2543:Thermodynamic models
1941:chemical equilibrium
1914:
1847:
1798:
1469:Motive Power of Fire
1235:
1180:
1125:
1085:
1037:Bridgman's equations
1014:Fundamental relation
959:
938:
912:
891:
863:
827:
806:
780:
759:
728:
692:
671:
645:
624:
596:
126:states that when an
102:intensive properties
49:thermodynamic system
43:. It is an internal
4588:Binding selectivity
4564:Specific equilibria
4474:Reversible reaction
4432:Dynamic equilibrium
4408:Chemical equilibria
4127:1999PhR...310....1L
3866:Bailyn, M. (1994).
3810:2015NatSR...5E8323B
3754:1931PhRv...37..405O
3516:1995EJPh...16...83R
3481:1985AmJPh..53..272C
3399:2008QJRMS.134..187A
3362:2004JAtS...61..931V
3225:(1937/1968), p. 27.
2906:2015AmJPh..83..628M
2788:Statistical Physics
2743:Time scale calculus
2713:Intelligent control
2693:Control engineering
2619:Multi-loop feedback
2614:Minor loop feedback
2465:Thermal equilibrium
2456:Thermal equilibrium
2450:Thermal equilibrium
2366:Uniform temperature
2360:intensive variables
2294:contact equilibrium
2159:transport phenomena
2006:chemical potentials
2000:Two systems are in
1989:Two systems are in
1984:thermal equilibrium
1982:Two systems are in
1769:dynamic equilibrium
1447:Source ... Friction
1379:Loschmidt's paradox
571:Material properties
449:Conjugate variables
4598:Macrocyclic effect
4422:Chemical stability
4275:Also published in
4242:Physical Chemistry
4089:Physical Chemistry
4021:Trans. Conn. Acad.
3991:, Methuen, London.
3846:Cited bibliography
3237:(1969), pp. 6, 37.
2835:Physical Chemistry
2750:General references
2639:Signal-flow graphs
2085:"inanimate" agency
1929:
1877:
1819:
1711:Order and disorder
1467:Reflections on the
1374:Heat death paradox
1271:
1216:
1161:
1106:
968:
944:
921:
897:
872:
836:
812:
789:
765:
740:
701:
677:
654:
630:
608:{\displaystyle c=}
605:
578:Property databases
554:Reduced properties
538:Chemical potential
502:Functions of state
425:Thermal efficiency
161:Carnot heat engine
4980:
4979:
4957:Vapor-compression
4883:Staged combustion
4812:
4811:
4777:With phase change
4666:
4665:
4644:Common-ion effect
4571:Acid dissociation
4524:Reaction quotient
4442:Equilibrium stage
3994:Eu, B.C. (2002).
3818:10.1038/srep08323
3291:(1949/1967), p.5.
3279:(1897/1927), p.3.
2914:10.1119/1.4914528
2782:978-0-7503-0886-1
2644:Stable polynomial
2131:massive particles
1834:Gibbs free energy
1765:
1764:
1706:Self-organization
1531:
1530:
1229:Gibbs free energy
1027:Maxwell relations
985:
984:
981:
980:
947:{\displaystyle V}
900:{\displaystyle 1}
855:Thermal expansion
849:
848:
815:{\displaystyle V}
768:{\displaystyle 1}
714:
713:
680:{\displaystyle N}
633:{\displaystyle T}
561:
560:
477:Process functions
463:Property diagrams
442:System properties
432:
431:
397:Endoreversibility
289:Equation of state
135:of the portions.
16:(Redirected from
5020:
4952:Vapor absorption
4715:
4693:
4686:
4679:
4670:
4583:Binding constant
4469:Phase separation
4401:
4394:
4387:
4378:
4298:
4296:
4294:
4274:
4183:Partington, J.R.
4162:
4146:
4120:
4118:cond-mat/9708200
4050:Guggenheim, E.A.
3932:Carathéodory, C.
3840:
3839:
3829:
3789:
3783:
3782:
3774:
3768:
3767:
3765:
3733:
3727:
3726:
3720:
3712:
3704:
3698:
3697:
3689:
3683:
3680:
3674:
3671:
3665:
3659:
3653:
3650:
3644:
3641:
3635:
3620:
3614:
3611:
3605:
3598:
3592:
3589:
3583:
3580:
3571:
3570:
3542:
3536:
3535:
3499:
3493:
3492:
3464:
3458:
3455:Partington, J.R.
3452:
3446:
3443:
3437:
3434:
3428:
3425:
3419:
3418:
3393:(630): 187–197.
3382:
3376:
3375:
3373:
3341:
3335:
3332:
3326:
3323:
3317:
3307:
3301:
3298:
3292:
3289:Guggenheim, E.A.
3286:
3280:
3274:
3265:
3262:
3256:
3253:
3247:
3244:
3238:
3232:
3226:
3220:
3214:
3211:
3205:
3202:
3196:
3193:
3187:
3184:
3178:
3175:
3169:
3162:
3156:
3153:
3147:
3144:
3138:
3135:
3129:
3126:
3120:
3114:
3108:
3105:
3099:
3096:
3087:
3084:
3078:
3071:
3065:
3062:
3056:
3053:
3047:
3044:
3038:
3037:H.R. Griem, 2005
3035:
3029:
3023:
3017:
3014:
3008:
3005:
2999:
2996:Guggenheim, E.A.
2993:
2987:
2984:
2978:
2975:
2969:
2966:
2960:
2957:
2948:
2942:
2936:
2935:
2925:
2889:
2883:
2880:
2874:
2871:
2865:
2859:
2850:
2847:
2838:
2833:Mortimer, R. G.
2831:
2825:
2818:
2786:F. Mandl (1988)
2624:Positive systems
2599:Krener's theorem
2538:
2536:Chemistry portal
2533:
2532:
2531:
2223:primitive notion
1938:
1936:
1935:
1930:
1906:the volume, and
1886:
1884:
1883:
1878:
1828:
1826:
1825:
1820:
1757:
1750:
1743:
1727:
1726:
1434:Key publications
1415:
1414:("living force")
1364:Brownian ratchet
1359:Entropy and life
1354:Entropy and time
1305:
1280:
1278:
1277:
1272:
1225:
1223:
1222:
1217:
1170:
1168:
1167:
1162:
1115:
1113:
1112:
1107:
1009:Clausius theorem
1004:Carnot's theorem
977:
975:
974:
969:
953:
951:
950:
945:
930:
928:
927:
922:
906:
904:
903:
898:
885:
884:
881:
879:
878:
873:
845:
843:
842:
837:
821:
819:
818:
813:
798:
796:
795:
790:
774:
772:
771:
766:
753:
752:
749:
747:
746:
741:
710:
708:
707:
702:
686:
684:
683:
678:
663:
661:
660:
655:
639:
637:
636:
631:
618:
617:
614:
612:
611:
606:
584:
583:
457:
276:
157:
143:
21:
5028:
5027:
5023:
5022:
5021:
5019:
5018:
5017:
4983:
4982:
4981:
4976:
4913:
4887:
4819:
4808:
4798:Organic Rankine
4772:
4726:
4723:hot air engines
4720:
4709:
4702:
4697:
4667:
4662:
4615:Self-ionization
4559:
4545:Buffer solution
4533:
4483:
4410:
4405:
4350:
4312:Uhlenbeck, G.E.
4292:
4290:
4276:
4261:
4170:Thermal Physics
4149:
4102:
3848:
3843:
3791:
3790:
3786:
3776:
3775:
3771:
3735:
3734:
3730:
3713:
3706:
3705:
3701:
3691:
3690:
3686:
3681:
3677:
3672:
3668:
3660:
3656:
3651:
3647:
3642:
3638:
3621:
3617:
3612:
3608:
3599:
3595:
3590:
3586:
3581:
3574:
3544:
3543:
3539:
3501:
3500:
3496:
3489:10.1119/1.14138
3466:
3465:
3461:
3453:
3449:
3444:
3440:
3435:
3431:
3426:
3422:
3384:
3383:
3379:
3343:
3342:
3338:
3333:
3329:
3324:
3320:
3308:
3304:
3299:
3295:
3287:
3283:
3275:
3268:
3263:
3259:
3254:
3250:
3245:
3241:
3233:
3229:
3221:
3217:
3212:
3208:
3203:
3199:
3194:
3190:
3185:
3181:
3176:
3172:
3163:
3159:
3154:
3150:
3145:
3141:
3136:
3132:
3127:
3123:
3115:
3111:
3106:
3102:
3097:
3090:
3085:
3081:
3072:
3068:
3063:
3059:
3054:
3050:
3045:
3041:
3036:
3032:
3024:
3020:
3015:
3011:
3006:
3002:
2994:
2990:
2985:
2981:
2976:
2972:
2967:
2963:
2958:
2951:
2945:Uhlenbeck, G.E.
2943:
2939:
2891:
2890:
2886:
2881:
2877:
2872:
2868:
2860:
2853:
2848:
2841:
2832:
2828:
2819:
2815:
2811:
2752:
2747:
2673:
2659:Transient state
2534:
2529:
2527:
2524:
2507:
2501:
2499:Non-equilibrium
2469:thermal contact
2458:
2452:
2419:
2410:
2401:
2388:
2372:E.A. Guggenheim
2368:
2355:
2350:
2298:C. Carathéodory
2272:a single word,
2264:, writes: "(i)
2262:J.R. Partington
2215:
2171:
2100:
2068:
2038:
2022:
1953:
1912:
1911:
1845:
1844:
1796:
1795:
1761:
1716:
1715:
1691:
1683:
1682:
1681:
1541:
1533:
1532:
1511:
1497:
1472:
1468:
1461:
1457:
1450:
1446:
1413:
1406:
1388:
1369:Maxwell's demon
1331:
1302:
1301:
1285:
1284:
1283:
1233:
1232:
1231:
1178:
1177:
1176:
1123:
1122:
1121:
1083:
1082:
1081:
1079:Internal energy
1074:
1059:
1049:
1048:
1023:
998:
988:
987:
986:
957:
956:
936:
935:
910:
909:
889:
888:
861:
860:
825:
824:
804:
803:
778:
777:
757:
756:
726:
725:
720:Compressibility
690:
689:
669:
668:
643:
642:
622:
621:
594:
593:
573:
563:
562:
543:Particle number
496:
455:
444:
434:
433:
392:Irreversibility
304:State of matter
271:Isolated system
256:
246:
245:
244:
219:
209:
208:
204:Non-equilibrium
196:
171:
163:
141:
109:non-equilibrium
28:
23:
22:
15:
12:
11:
5:
5026:
5024:
5016:
5015:
5013:Thermodynamics
5010:
5005:
5000:
4995:
4985:
4984:
4978:
4977:
4975:
4974:
4969:
4964:
4959:
4954:
4949:
4944:
4939:
4934:
4929:
4923:
4921:
4915:
4914:
4912:
4911:
4906:
4901:
4895:
4893:
4889:
4888:
4886:
4885:
4880:
4875:
4870:
4865:
4860:
4855:
4850:
4845:
4840:
4835:
4830:
4824:
4822:
4814:
4813:
4810:
4809:
4807:
4806:
4801:
4791:
4786:
4780:
4778:
4774:
4773:
4771:
4770:
4765:
4760:
4755:
4750:
4745:
4740:
4735:
4729:
4727:
4718:
4712:
4704:
4703:
4698:
4696:
4695:
4688:
4681:
4673:
4664:
4663:
4661:
4660:
4659:
4658:
4648:
4647:
4646:
4636:
4635:
4634:
4624:
4623:
4622:
4612:
4607:
4602:
4601:
4600:
4590:
4585:
4580:
4579:
4578:
4567:
4565:
4561:
4560:
4558:
4557:
4552:
4547:
4541:
4539:
4535:
4534:
4532:
4531:
4526:
4521:
4516:
4511:
4506:
4505:
4504:
4493:
4491:
4485:
4484:
4482:
4481:
4476:
4471:
4466:
4461:
4460:
4459:
4454:
4444:
4439:
4434:
4429:
4424:
4418:
4416:
4412:
4411:
4406:
4404:
4403:
4396:
4389:
4381:
4375:
4374:
4368:
4362:
4357:
4349:
4348:External links
4346:
4345:
4344:
4334:
4319:
4309:
4299:
4259:
4245:
4236:Silbey, R.J.,
4234:
4224:
4214:
4204:
4199:(1957/1966).
4194:
4180:
4173:
4163:
4147:
4100:
4097:978-0072538625
4085:
4078:
4071:Kirkwood, J.G.
4068:
4061:Thermodynamics
4057:
4047:
4032:
4014:
4007:
3992:
3985:
3970:
3963:
3949:
3929:
3911:
3904:
3894:
3879:
3864:
3847:
3844:
3842:
3841:
3784:
3769:
3748:(4): 405–426.
3728:
3699:
3684:
3675:
3666:
3654:
3645:
3636:
3615:
3606:
3600:Silbey, R.J.,
3593:
3584:
3572:
3537:
3494:
3475:(3): 272–273.
3459:
3447:
3438:
3429:
3420:
3407:10.1002/qj.209
3377:
3356:(8): 931–936.
3336:
3327:
3318:
3302:
3293:
3281:
3266:
3257:
3248:
3239:
3227:
3215:
3206:
3197:
3188:
3179:
3170:
3157:
3148:
3139:
3130:
3121:
3109:
3100:
3088:
3079:
3066:
3057:
3048:
3039:
3030:
3018:
3009:
3000:
2988:
2979:
2970:
2961:
2949:
2937:
2900:(7): 628–634.
2884:
2875:
2866:
2864:(1914), p. 40.
2851:
2839:
2826:
2812:
2810:
2807:
2806:
2805:
2791:
2784:
2762:
2751:
2748:
2746:
2745:
2740:
2738:Systems theory
2735:
2730:
2725:
2720:
2715:
2710:
2705:
2700:
2695:
2690:
2685:
2679:
2678:
2677:
2672:
2671:
2666:
2664:Underactuation
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2586:
2581:
2576:
2570:
2569:
2568:
2564:
2563:
2558:
2552:
2545:
2544:
2540:
2539:
2523:
2520:
2503:Main article:
2500:
2497:
2454:Main article:
2451:
2448:
2418:
2415:
2409:
2406:
2400:
2397:
2387:
2384:
2367:
2364:
2354:
2351:
2349:
2346:
2286:in equilibrium
2214:
2211:
2198:equilibrium."
2170:
2167:
2108:heat exchanges
2099:
2096:
2067:
2064:
2037:
2034:
2021:
2018:
2017:
2016:
2009:
1998:
1987:
1976:
1975:
1968:
1961:
1952:
1949:
1928:
1925:
1922:
1919:
1898:the pressure,
1888:
1887:
1876:
1873:
1870:
1867:
1864:
1861:
1858:
1855:
1852:
1830:
1829:
1818:
1815:
1812:
1809:
1806:
1803:
1763:
1762:
1760:
1759:
1752:
1745:
1737:
1734:
1733:
1732:
1731:
1718:
1717:
1714:
1713:
1708:
1703:
1698:
1692:
1689:
1688:
1685:
1684:
1680:
1679:
1674:
1669:
1664:
1659:
1654:
1649:
1644:
1639:
1634:
1629:
1624:
1619:
1614:
1609:
1604:
1599:
1594:
1589:
1584:
1579:
1574:
1569:
1564:
1559:
1554:
1549:
1543:
1542:
1539:
1538:
1535:
1534:
1529:
1528:
1527:
1526:
1521:
1513:
1512:
1510:
1509:
1506:
1502:
1499:
1498:
1496:
1495:
1490:
1488:Thermodynamics
1484:
1481:
1480:
1476:
1475:
1474:
1473:
1464:
1462:
1453:
1451:
1442:
1437:
1436:
1430:
1429:
1428:
1427:
1422:
1417:
1405:
1404:
1402:Caloric theory
1398:
1395:
1394:
1390:
1389:
1387:
1386:
1381:
1376:
1371:
1366:
1361:
1356:
1350:
1347:
1346:
1340:
1339:
1338:
1337:
1330:
1329:
1324:
1319:
1313:
1310:
1309:
1303:
1300:
1299:
1296:
1292:
1291:
1290:
1287:
1286:
1282:
1281:
1270:
1267:
1264:
1261:
1258:
1255:
1252:
1249:
1246:
1243:
1240:
1226:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1171:
1160:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1116:
1105:
1102:
1099:
1096:
1093:
1090:
1075:
1073:
1072:
1067:
1061:
1060:
1055:
1054:
1051:
1050:
1047:
1046:
1039:
1034:
1029:
1022:
1021:
1016:
1011:
1006:
1000:
999:
994:
993:
990:
989:
983:
982:
979:
978:
967:
964:
954:
943:
932:
931:
920:
917:
907:
896:
882:
871:
868:
858:
851:
850:
847:
846:
835:
832:
822:
811:
800:
799:
788:
785:
775:
764:
750:
739:
736:
733:
723:
716:
715:
712:
711:
700:
697:
687:
676:
665:
664:
653:
650:
640:
629:
615:
604:
601:
591:
582:
581:
580:
574:
569:
568:
565:
564:
559:
558:
557:
556:
551:
546:
535:
524:
505:
504:
498:
497:
495:
494:
489:
483:
480:
479:
473:
472:
471:
470:
465:
446:
445:
440:
439:
436:
435:
430:
429:
428:
427:
422:
417:
409:
408:
402:
401:
400:
399:
394:
389:
384:
382:Free expansion
379:
374:
369:
364:
359:
354:
349:
344:
336:
335:
329:
328:
327:
326:
321:
319:Control volume
316:
311:
309:Phase (matter)
306:
301:
296:
291:
283:
282:
274:
273:
268:
263:
257:
252:
251:
248:
247:
243:
242:
237:
232:
227:
221:
220:
215:
214:
211:
210:
207:
206:
195:
194:
189:
184:
179:
173:
172:
169:
168:
165:
164:
159:The classical
158:
150:
149:
147:Thermodynamics
140:
137:
41:thermodynamics
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5025:
5014:
5011:
5009:
5006:
5004:
5001:
4999:
4996:
4994:
4991:
4990:
4988:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4948:
4947:Transcritical
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4927:Hampson–Linde
4925:
4924:
4922:
4920:
4919:Refrigeration
4916:
4910:
4907:
4905:
4902:
4900:
4897:
4896:
4894:
4890:
4884:
4881:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4849:
4848:Gas-generator
4846:
4844:
4841:
4839:
4836:
4834:
4833:Brayton/Joule
4831:
4829:
4826:
4825:
4823:
4821:
4815:
4805:
4802:
4799:
4795:
4792:
4790:
4787:
4785:
4782:
4781:
4779:
4775:
4769:
4766:
4764:
4761:
4759:
4756:
4754:
4751:
4749:
4746:
4744:
4741:
4739:
4738:Brayton/Joule
4736:
4734:
4731:
4730:
4728:
4724:
4716:
4713:
4711:
4705:
4701:
4694:
4689:
4687:
4682:
4680:
4675:
4674:
4671:
4657:
4654:
4653:
4652:
4649:
4645:
4642:
4641:
4640:
4637:
4633:
4630:
4629:
4628:
4625:
4621:
4618:
4617:
4616:
4613:
4611:
4608:
4606:
4603:
4599:
4596:
4595:
4594:
4591:
4589:
4586:
4584:
4581:
4577:
4574:
4573:
4572:
4569:
4568:
4566:
4562:
4556:
4553:
4551:
4548:
4546:
4543:
4542:
4540:
4536:
4530:
4527:
4525:
4522:
4520:
4517:
4515:
4512:
4510:
4509:Phase diagram
4507:
4503:
4502:determination
4500:
4499:
4498:
4495:
4494:
4492:
4490:
4486:
4480:
4477:
4475:
4472:
4470:
4467:
4465:
4462:
4458:
4455:
4453:
4450:
4449:
4448:
4445:
4443:
4440:
4438:
4435:
4433:
4430:
4428:
4425:
4423:
4420:
4419:
4417:
4413:
4409:
4402:
4397:
4395:
4390:
4388:
4383:
4382:
4379:
4372:
4369:
4366:
4363:
4361:
4358:
4355:
4352:
4351:
4347:
4342:
4339:(1937/1968).
4338:
4335:
4332:
4331:0-521-24575-3
4328:
4324:
4320:
4317:
4313:
4310:
4307:
4303:
4300:
4288:
4284:
4280:
4272:
4268:
4264:
4260:
4257:
4253:
4252:Wergeland, H.
4249:
4246:
4243:
4239:
4238:Alberty, R.A.
4235:
4232:
4228:
4227:Prigogine, I.
4225:
4222:
4218:
4217:Prigogine, I.
4215:
4212:
4208:
4205:
4202:
4198:
4197:Pippard, A.B.
4195:
4192:
4188:
4184:
4181:
4178:
4174:
4171:
4167:
4164:
4160:
4156:
4152:
4151:Maxwell, J.C.
4148:
4144:
4140:
4136:
4132:
4128:
4124:
4119:
4114:
4110:
4106:
4101:
4098:
4094:
4090:
4086:
4083:
4079:
4076:
4072:
4069:
4066:
4062:
4058:
4055:
4052:(1949/1967).
4051:
4048:
4045:
4044:0-521-61941-6
4041:
4037:
4033:
4030:
4026:
4022:
4018:
4015:
4012:
4008:
4005:
4004:1-4020-0788-4
4001:
3997:
3993:
3990:
3986:
3983:
3979:
3975:
3971:
3968:
3964:
3961:
3958:(1939/1970).
3957:
3956:Cowling, T.G.
3953:
3950:
3947:
3943:
3939:
3938:
3933:
3930:
3927:
3926:0-471-86256-8
3923:
3919:
3916:(1960/1985).
3915:
3912:
3909:
3905:
3902:
3899:(1896/1964).
3898:
3897:Boltzmann, L.
3895:
3892:
3891:0-444-41806-7
3888:
3884:
3880:
3877:
3876:0-88318-797-3
3873:
3869:
3865:
3862:
3861:0-521-25445-0
3858:
3854:
3850:
3849:
3845:
3837:
3833:
3828:
3823:
3819:
3815:
3811:
3807:
3803:
3799:
3795:
3788:
3785:
3780:
3773:
3770:
3764:
3759:
3755:
3751:
3747:
3743:
3739:
3732:
3729:
3724:
3718:
3710:
3703:
3700:
3695:
3688:
3685:
3679:
3676:
3670:
3667:
3663:
3662:R. K. Pathria
3658:
3655:
3649:
3646:
3640:
3637:
3633:
3632:0-444-50426-5
3629:
3625:
3619:
3616:
3610:
3607:
3603:
3602:Alberty, R.A.
3597:
3594:
3588:
3585:
3579:
3577:
3573:
3568:
3564:
3560:
3556:
3552:
3548:
3541:
3538:
3533:
3529:
3525:
3521:
3517:
3513:
3509:
3505:
3498:
3495:
3490:
3486:
3482:
3478:
3474:
3470:
3463:
3460:
3456:
3451:
3448:
3442:
3439:
3433:
3430:
3424:
3421:
3416:
3412:
3408:
3404:
3400:
3396:
3392:
3388:
3381:
3378:
3372:
3367:
3363:
3359:
3355:
3351:
3350:J. Atmos. Sci
3347:
3340:
3337:
3331:
3328:
3322:
3319:
3315:
3314:Wergeland, H.
3311:
3306:
3303:
3297:
3294:
3290:
3285:
3282:
3278:
3273:
3271:
3267:
3261:
3258:
3252:
3249:
3243:
3240:
3236:
3231:
3228:
3224:
3219:
3216:
3210:
3207:
3201:
3198:
3192:
3189:
3183:
3180:
3174:
3171:
3167:
3161:
3158:
3152:
3149:
3143:
3140:
3134:
3131:
3125:
3122:
3119:(1969), p. 7.
3118:
3113:
3110:
3104:
3101:
3095:
3093:
3089:
3083:
3080:
3076:
3070:
3067:
3061:
3058:
3052:
3049:
3043:
3040:
3034:
3031:
3027:
3022:
3019:
3013:
3010:
3004:
3001:
2997:
2992:
2989:
2983:
2980:
2974:
2971:
2965:
2962:
2956:
2954:
2950:
2946:
2941:
2938:
2933:
2929:
2924:
2923:11311/1043322
2919:
2915:
2911:
2907:
2903:
2899:
2895:
2888:
2885:
2879:
2876:
2870:
2867:
2863:
2858:
2856:
2852:
2846:
2844:
2840:
2836:
2830:
2827:
2823:
2817:
2814:
2808:
2804:
2803:0-521-61941-6
2800:
2796:
2792:
2789:
2785:
2783:
2779:
2775:
2774:0-7503-0886-9
2771:
2767:
2763:
2761:
2758:
2754:
2753:
2749:
2744:
2741:
2739:
2736:
2734:
2731:
2729:
2726:
2724:
2721:
2719:
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2689:
2686:
2684:
2681:
2680:
2675:
2674:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2572:
2571:
2566:
2565:
2562:
2559:
2556:
2553:
2550:
2547:
2546:
2542:
2541:
2537:
2526:
2521:
2519:
2515:
2511:
2506:
2498:
2496:
2493:
2489:
2485:
2481:
2477:
2472:
2470:
2466:
2462:
2457:
2449:
2447:
2443:
2439:
2435:
2431:
2427:
2423:
2416:
2414:
2407:
2405:
2398:
2396:
2392:
2385:
2383:
2382:equilibrium.
2379:
2375:
2373:
2365:
2363:
2361:
2352:
2347:
2345:
2342:
2338:
2337:J.G. Kirkwood
2334:
2332:
2326:
2324:
2318:
2316:
2312:
2308:
2305:
2301:
2299:
2295:
2290:
2287:
2283:
2277:
2275:
2269:
2267:
2263:
2258:
2254:
2250:
2248:
2242:
2238:
2235:
2232:
2228:
2224:
2219:
2212:
2210:
2208:
2205:According to
2203:
2199:
2196:
2191:
2187:
2185:
2180:
2175:
2168:
2166:
2164:
2160:
2154:
2152:
2148:
2143:
2140:
2136:
2132:
2127:
2123:
2121:
2117:
2113:
2109:
2105:
2097:
2095:
2091:
2088:
2086:
2082:
2076:
2072:
2065:
2063:
2060:
2054:
2052:
2048:
2043:
2035:
2033:
2030:
2026:
2019:
2014:
2010:
2008:are the same.
2007:
2003:
1999:
1997:are the same.
1996:
1992:
1988:
1985:
1981:
1980:
1979:
1973:
1969:
1966:
1962:
1959:
1955:
1954:
1950:
1948:
1944:
1942:
1926:
1923:
1920:
1909:
1905:
1902:the entropy,
1901:
1897:
1893:
1874:
1871:
1868:
1865:
1862:
1859:
1856:
1853:
1850:
1843:
1842:
1841:
1839:
1835:
1816:
1813:
1810:
1807:
1804:
1801:
1794:
1793:
1792:
1790:
1786:
1782:
1778:
1774:
1770:
1758:
1753:
1751:
1746:
1744:
1739:
1738:
1736:
1735:
1730:
1722:
1721:
1720:
1719:
1712:
1709:
1707:
1704:
1702:
1701:Self-assembly
1699:
1697:
1694:
1693:
1687:
1686:
1678:
1675:
1673:
1672:van der Waals
1670:
1668:
1665:
1663:
1660:
1658:
1655:
1653:
1650:
1648:
1645:
1643:
1640:
1638:
1635:
1633:
1630:
1628:
1625:
1623:
1620:
1618:
1615:
1613:
1610:
1608:
1605:
1603:
1600:
1598:
1597:von Helmholtz
1595:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1544:
1537:
1536:
1525:
1522:
1520:
1517:
1516:
1515:
1514:
1507:
1504:
1503:
1500:
1494:
1491:
1489:
1486:
1485:
1483:
1482:
1477:
1471:
1470:
1463:
1460:
1459:
1452:
1449:
1448:
1441:
1440:
1439:
1438:
1435:
1431:
1426:
1423:
1421:
1418:
1416:
1412:
1408:
1407:
1403:
1400:
1399:
1397:
1396:
1391:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1357:
1355:
1352:
1351:
1349:
1348:
1345:
1341:
1336:
1333:
1332:
1328:
1325:
1323:
1320:
1318:
1315:
1314:
1312:
1311:
1306:
1297:
1294:
1293:
1289:
1288:
1268:
1265:
1262:
1259:
1256:
1250:
1247:
1244:
1238:
1230:
1227:
1213:
1210:
1207:
1204:
1201:
1195:
1192:
1189:
1183:
1175:
1172:
1158:
1155:
1152:
1149:
1146:
1140:
1137:
1134:
1128:
1120:
1117:
1100:
1097:
1094:
1088:
1080:
1077:
1076:
1071:
1068:
1066:
1063:
1062:
1058:
1053:
1052:
1045:
1044:
1040:
1038:
1035:
1033:
1030:
1028:
1025:
1024:
1020:
1019:Ideal gas law
1017:
1015:
1012:
1010:
1007:
1005:
1002:
1001:
997:
992:
991:
965:
955:
941:
934:
933:
918:
908:
894:
887:
886:
883:
869:
866:
859:
856:
853:
852:
833:
823:
809:
802:
801:
786:
776:
762:
755:
754:
751:
737:
734:
731:
724:
721:
718:
717:
698:
688:
674:
667:
666:
651:
641:
627:
620:
619:
616:
602:
599:
592:
589:
586:
585:
579:
576:
575:
572:
567:
566:
555:
552:
550:
549:Vapor quality
547:
545:
544:
539:
536:
534:
533:
528:
525:
522:
518:
517:
512:
509:
508:
507:
506:
503:
499:
493:
490:
488:
485:
484:
482:
481:
478:
474:
469:
466:
464:
461:
460:
459:
458:
454:
450:
443:
438:
437:
426:
423:
421:
418:
416:
413:
412:
411:
410:
407:
403:
398:
395:
393:
390:
388:
387:Reversibility
385:
383:
380:
378:
375:
373:
370:
368:
365:
363:
360:
358:
355:
353:
350:
348:
345:
343:
340:
339:
338:
337:
334:
330:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
286:
285:
284:
281:
277:
272:
269:
267:
264:
262:
261:Closed system
259:
258:
255:
250:
249:
241:
238:
236:
233:
231:
228:
226:
223:
222:
218:
213:
212:
205:
201:
198:
197:
193:
190:
188:
185:
183:
180:
178:
175:
174:
167:
166:
162:
156:
152:
151:
148:
144:
138:
136:
134:
129:
125:
121:
116:
114:
110:
105:
103:
98:
96:
92:
88:
84:
80:
75:
73:
69:
65:
61:
58:
54:
50:
46:
42:
38:
34:
30:
19:
4804:Regenerative
4733:Bell Coleman
4651:Vapor–liquid
4538:Applications
4478:
4340:
4337:Zemansky, M.
4322:
4315:
4305:
4291:. Retrieved
4286:
4282:
4270:
4266:
4255:
4248:ter Haar, D.
4241:
4230:
4220:
4210:
4200:
4190:
4189:, volume 1,
4186:
4176:
4169:
4158:
4154:
4108:
4104:
4088:
4081:
4074:
4064:
4060:
4053:
4035:
4028:
4024:
4020:
4010:
3995:
3988:
3973:
3966:
3959:
3945:
3941:
3935:
3917:
3914:Callen, H.B.
3907:
3900:
3882:
3867:
3852:
3801:
3797:
3787:
3778:
3772:
3745:
3741:
3731:
3708:
3702:
3693:
3687:
3678:
3669:
3657:
3648:
3639:
3623:
3618:
3609:
3596:
3587:
3550:
3547:Eur. J. Phys
3546:
3540:
3510:(2): 83–90.
3507:
3504:Eur. J. Phys
3503:
3497:
3472:
3468:
3462:
3450:
3441:
3432:
3423:
3390:
3386:
3380:
3353:
3349:
3339:
3330:
3321:
3310:ter Haar, D.
3305:
3296:
3284:
3260:
3251:
3242:
3230:
3223:Zemansky, M.
3218:
3209:
3200:
3191:
3182:
3173:
3165:
3160:
3151:
3142:
3133:
3124:
3112:
3103:
3082:
3074:
3069:
3060:
3051:
3042:
3033:
3021:
3012:
3003:
2991:
2982:
2973:
2964:
2940:
2897:
2893:
2887:
2878:
2869:
2834:
2829:
2816:
2794:
2787:
2765:
2756:
2654:Steady state
2561:Time crystal
2516:
2512:
2508:
2473:
2463:
2459:
2444:
2440:
2436:
2432:
2428:
2424:
2420:
2411:
2402:
2393:
2389:
2380:
2376:
2369:
2356:
2340:
2335:
2330:
2327:
2322:
2319:
2314:
2309:
2302:
2293:
2291:
2285:
2281:
2278:
2273:
2270:
2265:
2259:
2255:
2251:
2246:
2243:
2239:
2236:
2230:
2220:
2216:
2204:
2200:
2195:A.B. Pippard
2192:
2188:
2183:
2179:H. B. Callen
2176:
2172:
2169:Reservations
2155:
2144:
2128:
2124:
2119:
2111:
2101:
2092:
2089:
2077:
2073:
2069:
2055:
2039:
2031:
2027:
2023:
2001:
1990:
1983:
1977:
1971:
1964:
1957:
1945:
1907:
1903:
1899:
1895:
1891:
1889:
1837:
1831:
1788:
1780:
1766:
1562:Carathéodory
1493:Heat engines
1465:
1454:
1443:
1425:Motive power
1410:
1070:Free entropy
1041:
541:
540: /
530:
529: /
521:introduction
514:
513: /
452:
415:Heat engines
313:
202: /
117:
112:
106:
99:
76:
71:
47:of a single
32:
31:
29:
4972:Ionocaloric
4967:Vuilleumier
4789:Hygroscopic
4656:Henry's law
4447:Free energy
4263:Thomson, W.
4166:Morse, P.M.
4111:(1): 1–96.
4017:Gibbs, J.W.
3952:Chapman, S.
3469:Am. J. Phys
3235:Morse, P.M.
3117:Morse, P.M.
3026:Thomson, W.
2708:Cybernetics
2476:macroscopic
2304:M. Zemansky
2282:equilibrium
2247:equilibrium
2213:Definitions
2004:when their
1993:when their
1384:Synergetics
1065:Free energy
511:Temperature
372:Quasistatic
367:Isenthalpic
324:Instruments
314:Equilibrium
266:Open system
200:Equilibrium
182:Statistical
68:macroscopic
57:macroscopic
39:concept of
4987:Categories
4937:Pulse tube
4909:Mixed/dual
4639:Solubility
4610:Hydrolysis
4519:Phase rule
4289:(22): 8–21
4207:Planck. M.
3982:0486647412
3277:Planck, M.
2862:Planck. M.
2809:References
2688:Bond graph
2634:Root locus
2589:H infinity
2311:P.M. Morse
2227:P.M. Morse
2142:to exist.
1951:Conditions
1696:Nucleation
1540:Scientists
1344:Philosophy
1057:Potentials
420:Heat pumps
377:Polytropic
362:Isentropic
352:Isothermal
83:mechanical
4932:Kleemenko
4818:Internal
4627:Partition
4457:Helmholtz
4427:Chelation
4302:Tisza, L.
4283:Phil. Mag
4143:119620408
4105:Phys. Rep
3742:Phys. Rev
3717:cite book
3567:250885860
3553:: 43–44.
3532:250840083
3415:122759570
2932:117173742
2480:ideal gas
2163:diffusion
2137:gas, the
2135:radiating
2116:intensive
2104:intensive
1995:pressures
1918:Δ
1860:−
1811:−
1677:Waterston
1627:von Mayer
1582:de Donder
1572:Clapeyron
1552:Boltzmann
1547:Bernoulli
1508:Education
1479:Timelines
1263:−
1208:−
996:Equations
963:∂
916:∂
867:α
831:∂
784:∂
738:−
732:β
696:∂
649:∂
357:Adiabatic
347:Isochoric
333:Processes
294:Ideal gas
177:Classical
133:entropies
91:radiative
37:axiomatic
4899:Combined
4858:Humphrey
4843:Expander
4828:Atkinson
4763:Stoddard
4753:Stirling
4748:Ericsson
4708:External
4620:of water
4415:Concepts
4304:(1966).
4254:(1966).
4219:(1947).
4209:(1914).
4185:(1949).
4168:(1969).
4161:: 49–88.
3836:25662746
3804:: 8323.
3798:Sci. Rep
3634:, p. 21.
2584:Feedback
2522:See also
2492:pressure
2207:L. Tisza
2147:ice cube
2042:isolated
1729:Category
1667:Thompson
1577:Clausius
1557:Bridgman
1411:Vis viva
1393:Theories
1327:Gas laws
1119:Enthalpy
527:Pressure
342:Isobaric
299:Real gas
187:Chemical
170:Branches
139:Overview
128:isolated
87:chemical
72:tendency
4962:Siemens
4878:Scuderi
4794:Rankine
4293:25 June
4123:Bibcode
3827:4321171
3806:Bibcode
3750:Bibcode
3512:Bibcode
3477:Bibcode
3395:Bibcode
3358:Bibcode
3028:(1851).
2902:Bibcode
2555:UNIQUAC
2139:photons
2133:. In a
1777:entropy
1652:Smeaton
1647:Rankine
1637:Onsager
1622:Maxwell
1617:Massieu
1322:Entropy
1317:General
1308:History
1298:Culture
1295:History
519: (
516:Entropy
453:italics
254:Systems
79:thermal
4868:Miller
4863:Lenoir
4838:Diesel
4784:Kalina
4768:Manson
4743:Carnot
4489:Models
4329:
4141:
4095:
4042:
4002:
3980:
3924:
3889:
3874:
3859:
3834:
3824:
3664:, 1996
3630:
3565:
3530:
3413:
2930:
2801:
2780:
2772:
2482:whose
2051:Fowler
2013:forces
1890:where
1642:Planck
1632:Nernst
1607:Kelvin
1567:Carnot
857:
722:
590:
532:Volume
447:Note:
406:Cycles
235:Second
225:Zeroth
89:, and
64:matter
35:is an
4892:Mixed
4452:Gibbs
4285:. 4.
4139:S2CID
4113:arXiv
3563:S2CID
3528:S2CID
3411:S2CID
2928:S2CID
1690:Other
1657:Stahl
1612:Lewis
1602:Joule
1592:Gibbs
1587:Duhem
280:State
240:Third
230:First
120:axiom
60:flows
53:walls
45:state
4904:HEHC
4873:Otto
4327:ISBN
4295:2012
4093:ISBN
4040:ISBN
4000:ISBN
3978:ISBN
3922:ISBN
3887:ISBN
3872:ISBN
3857:ISBN
3832:PMID
3723:link
3628:ISBN
3075:xiii
2799:ISBN
2778:ISBN
2770:ISBN
2323:full
2011:All
1662:Tait
492:Heat
487:Work
217:Laws
4159:157
4131:doi
4109:310
3822:PMC
3814:doi
3758:doi
3555:doi
3520:doi
3485:doi
3403:doi
3391:134
3366:doi
2918:hdl
2910:doi
2231:not
2053:.)
1505:Art
451:in
62:of
4989::
4287:IV
4281:.
4271:XX
4269:.
4250:,
4157:.
4137:.
4129:.
4121:.
4107:.
4023:,
3954:,
3942:67
3940:,
3830:.
3820:.
3812:.
3800:.
3796:.
3756:.
3746:37
3744:.
3740:.
3719:}}
3715:{{
3575:^
3561:.
3551:17
3549:.
3526:.
3518:.
3508:16
3506:.
3483:.
3473:53
3471:.
3409:.
3401:.
3389:.
3364:.
3354:61
3352:.
3348:.
3312:,
3269:^
3091:^
2952:^
2926:.
2916:.
2908:.
2898:83
2896:.
2854:^
2842:^
2776:,
2276:"
2249:.
2186:"
2110:.
115:.
85:,
81:,
4800:)
4796:(
4725:)
4721:(
4692:e
4685:t
4678:v
4400:e
4393:t
4386:v
4333:.
4297:.
4145:.
4133::
4125::
4115::
4099:.
4046:.
4025:3
4006:.
3984:.
3928:.
3893:.
3878:.
3863:.
3838:.
3816::
3808::
3802:5
3766:.
3760::
3752::
3725:)
3569:.
3557::
3534:.
3522::
3514::
3491:.
3487::
3479::
3417:.
3405::
3397::
3374:.
3368::
3360::
3168:.
3166:7
3077:.
2934:.
2920::
2912::
2904::
2321:"
1972:G
1965:A
1958:S
1927:0
1924:=
1921:G
1908:U
1904:V
1900:S
1896:P
1892:T
1875:V
1872:P
1869:+
1866:S
1863:T
1857:U
1854:=
1851:G
1838:G
1836:(
1817:S
1814:T
1808:U
1805:=
1802:A
1789:A
1787:(
1781:S
1779:(
1756:e
1749:t
1742:v
1269:S
1266:T
1260:H
1257:=
1254:)
1251:p
1248:,
1245:T
1242:(
1239:G
1214:S
1211:T
1205:U
1202:=
1199:)
1196:V
1193:,
1190:T
1187:(
1184:A
1159:V
1156:p
1153:+
1150:U
1147:=
1144:)
1141:p
1138:,
1135:S
1132:(
1129:H
1104:)
1101:V
1098:,
1095:S
1092:(
1089:U
966:T
942:V
919:V
895:1
870:=
834:p
810:V
787:V
763:1
735:=
699:T
675:N
652:S
628:T
603:=
600:c
523:)
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
