3655:, the gas is contained in an insulated container and then allowed to expand in a vacuum. Because there is no external pressure for the gas to expand against, the work done by or on the system is zero. Since this process does not involve any heat transfer or work, the first law of thermodynamics then implies that the net internal energy change of the system is zero. For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case. Since at constant temperature, the entropy is proportional to the volume, the entropy increases in this case, therefore this process is irreversible.
2030:), for which energy is added as work solely through friction or viscous dissipation within the system. A stirrer that transfers energy to a viscous fluid of an adiabatically isolated system with rigid walls, without phase change, will cause a rise in temperature of the fluid, but that work is not recoverable. Isochoric work is irreversible. The second law of thermodynamics observes that a natural process, of transfer of energy as work, always consists at least of isochoric work and often both of these extreme kinds of work. Every natural process, adiabatic or not, is irreversible, with
1772:, is called adiabatic, and such a system is said to be adiabatically isolated. The simplifying assumption frequently made is that a process is adiabatic. For example, the compression of a gas within a cylinder of an engine is assumed to occur so rapidly that on the time scale of the compression process, little of the system's energy can be transferred out as heat to the surroundings. Even though the cylinders are not insulated and are quite conductive, that process is idealized to be adiabatic. The same can be said to be true for the expansion process of such a system.
8811:; the second, an isochoric and workless heat transfer returning the system to its original state. Accordingly, Rankine measured quantity of heat in units of work, rather than as a calorimetric quantity. In 1854, Rankine used a quantity that he called "the thermodynamic function" that later was called entropy, and at that time he wrote also of the "curve of no transmission of heat", which he later called an adiabatic curve. Besides its two isothermal limbs, Carnot's cycle has two adiabatic limbs.
8894:. The idea is that the shapes of the eigenfunctions change slowly and continuously, so that no quantum jump is triggered, and the change is virtually reversible. While the occupation numbers are unchanged, nevertheless there is change in the energy levels of one-to-one corresponding, pre- and post-compression, eigenstates. Thus a perturbative element of work has been done without heat transfer and without introduction of random change within the system. For example,
38:
1608:
8624:
8819:
nineteenth century, it was recognized as a form of energy, and the law of conservation of energy was thereby also recognized. The view that eventually established itself, and is currently regarded as right, is that the law of conservation of energy is a primary axiom, and that heat is to be analyzed as consequential. In this light, heat cannot be a component of the total energy of a single body because it is not a
9958:
2868:
2186:
2614:); the compression ratio of the engine is 10:1 (that is, the 1 L volume of uncompressed gas is reduced to 0.1 L by the piston); and the uncompressed gas is at approximately room temperature and pressure (a warm room temperature of ~27 °C, or 300 K, and a pressure of 1 bar = 100 kPa, i.e. typical sea-level atmospheric pressure).
1975:). Should the work be added in such a way that friction or viscous forces are operating within the system, then the process is not isentropic, and if there is no phase change, then the temperature of the system will rise, the process is said to be "irreversible", and the work added to the system is not entirely recoverable in the form of work.
2620:
3618:
3406:
3636:
to provide a pressure boost but with a lower temperature rise would be advantageous. A diesel engine operates under even more extreme conditions, with compression ratios of 16:1 or more being typical, in order to provide a very high gas pressure, which ensures immediate ignition of the injected fuel.
2099:
occurs when the pressure on an adiabatically isolated system is decreased, allowing it to expand in size, thus causing it to do work on its surroundings. When the pressure applied on a parcel of gas is reduced, the gas in the parcel is allowed to expand; as the volume increases, the temperature falls
1966:
and is said to be "reversible". Ideally, if the process were reversed the energy could be recovered entirely as work done by the system. If the system contains a compressible gas and is reduced in volume, the uncertainty of the position of the gas is reduced, and seemingly would reduce the entropy of
8838:
is used in this article in the traditional way of thermodynamics, introduced by
Rankine. It is pointed out in the present article that, for example, if a compression of a gas is rapid, then there is little time for heat transfer to occur, even when the gas is not adiabatically isolated by a definite
2591:
can be used as an example of adiabatic compression. The model assumptions are: the uncompressed volume of the cylinder is one litre (1 L = 1000 cm = 0.001 m); the gas within is the air consisting of molecular nitrogen and oxygen only (thus a diatomic gas with 5 degrees of freedom, and
8814:
For the foundations of thermodynamics, the conceptual importance of this was emphasized by Bryan, by Carathéodory, and by Born. The reason is that calorimetry presupposes a type of temperature as already defined before the statement of the first law of thermodynamics, such as one based on empirical
3197:
or 25.1 bar. This pressure increase is more than a simple 10:1 compression ratio would indicate; this is because the gas is not only compressed, but the work done to compress the gas also increases its internal energy, which manifests itself by a rise in the gas temperature and an additional
2092:
flowing downhill over a mountain range. When a parcel of air descends, the pressure on the parcel increases. Because of this increase in pressure, the parcel's volume decreases and its temperature increases as work is done on the parcel of air, thus increasing its internal energy, which manifests
9039:
transferred) breaks down at the quantum level, and the specific form of energy (typically electromagnetic) must be considered instead. The small or negligible absorption of energy from the perturbation in a quantum adiabatic process provides a good justification for identifying it as the quantum
9054:
Thus for a mass of gas, in macroscopic thermodynamics, words are so used that a compression is sometimes loosely or approximately said to be adiabatic if it is rapid enough to avoid significant heat transfer, even if the system is not adiabatically isolated. But in quantum statistical theory, a
9034:
Recent research suggests that the power absorbed from the perturbation corresponds to the rate of these non-adiabatic transitions. This corresponds to the classical process of energy transfer in the form of heat, but with the relative time scales reversed in the quantum case. Quantum adiabatic
8818:
In the eighteenth century, the law of conservation of energy was not yet fully formulated or established, and the nature of heat was debated. One approach to these problems was to regard heat, measured by calorimetry, as a primary substance that is conserved in quantity. By the middle of the
8678:
If adiabats and isotherms are graphed at regular intervals of entropy and temperature, respectively (like altitude on a contour map), then as the eye moves towards the axes (towards the south-west), it sees the density of isotherms stay constant, but it sees the density of adiabats grow. The
2170:
In practice, no process is truly adiabatic. Many processes rely on a large difference in time scales of the process of interest and the rate of heat dissipation across a system boundary, and thus are approximated by using an adiabatic assumption. There is always some heat loss, as no perfect
3192:
3039:
7413:
5603:
2004:
The transfer of energy as work into an adiabatically isolated system can be imagined as being of two idealized extreme kinds. In one such kind, no entropy is produced within the system (no friction, viscous dissipation, etc.), and the work is only pressure-volume work (denoted by
8271:
6461:
2863:{\displaystyle {\begin{aligned}&P_{1}V_{1}^{\gamma }=\mathrm {constant} _{1}=100\,000~{\text{Pa}}\times (0.001~{\text{m}}^{3})^{\frac {7}{5}}\\&=10^{5}\times 6.31\times 10^{-5}~{\text{Pa}}\,{\text{m}}^{21/5}=6.31~{\text{Pa}}\,{\text{m}}^{21/5},\end{aligned}}}
4510:
3433:
2093:
itself by a rise in the temperature of that mass of air. The parcel of air can only slowly dissipate the energy by conduction or radiation (heat), and to a first approximation it can be considered adiabatically isolated and the process an adiabatic process.
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8117:
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6307:
8515:
6705:
3227:
8815:
scales. Such a presupposition involves making the distinction between empirical temperature and absolute temperature. Rather, the definition of absolute thermodynamic temperature is best left till the second law is available as a conceptual basis.
8898:
writes "Actually, it is usually the 'adiabatic' case with which we have to do: i.e. the limiting case where the external force (or the reaction of the parts of the system on each other) acts very slowly. In this case, to a very high approximation
2876:
The gas is now compressed to a 0.1 L (0.0001 m) volume, which we assume happens quickly enough that no heat enters or leaves the gas through the walls. The adiabatic constant remains the same, but with the resulting pressure unknown
7989:
7677:
6179:
5867:
9046:
In classical thermodynamics, such a rapid change would still be called adiabatic because the system is adiabatically isolated, and there is no transfer of energy as heat. The strong irreversibility of the change, due to viscosity or other
7792:
5982:
7558:
5748:
8806:
only as heat or work. Therefore, a quantity of work in such a system can be related almost directly to an equivalent quantity of heat in a cycle of two limbs. The first limb is an isochoric adiabatic work process increasing the system's
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6803:
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3623:
That is a final temperature of 753 K, or 479 °C, or 896 °F, well above the ignition point of many fuels. This is why a high-compression engine requires fuels specially formulated to not self-ignite (which would cause
7887:
6077:
9055:
compression is not called adiabatic if it is rapid, even if the system is adiabatically isolated in the classical thermodynamic sense of the term. The words are used differently in the two disciplines, as stated just above.
2064:
compressing a gas contained within a cylinder and raising the temperature where in many practical situations heat conduction through walls can be slow compared with the compression time. This finds practical application in
3050:
4992:
8850:, recommend using "adiathermal" to refer to processes where no heat-exchange occurs (such as Joule expansion), and "adiabatic" to reversible quasi-static adiathermal processes (so that rapid compression of a gas is
2883:
4899:
4091:
9035:
processes occur over relatively long time scales, while classical adiabatic processes occur over relatively short time scales. It should also be noted that the concept of 'heat' (in reference to the quantity of
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that is, there is no probability for a transition, and the system is in the initial state after cessation of the perturbation. Such a slow perturbation is therefore reversible, as it is classically."
1327:
1978:
If the walls of a system are not adiabatic, and energy is transferred in as heat, entropy is transferred into the system with the heat. Such a process is neither adiabatic nor isentropic, having
2625:
4205:
2566:
4282:
3613:{\displaystyle T={\frac {PV}{\mathrm {constant} _{2}}}={\frac {2.51\times 10^{6}~{\text{Pa}}\times 10^{-4}~{\text{m}}^{3}}{0.333~{\text{Pa}}\,{\text{m}}^{3}{\text{K}}^{-1}}}=753~{\text{K}}.}
2247:
2156:, the mantle temperature is approximately an adiabat. The slight decrease in temperature with shallowing depth is due to the decrease in pressure the shallower the material is in the Earth.
9015:
On the other hand, in quantum theory, if a perturbative element of compressive work is done rapidly, it changes the occupation numbers and energies of the eigenstates in proportion to the
6888:
5078:
1775:
The assumption of adiabatic isolation is useful and often combined with other such idealizations to calculate a good first approximation of a system's behaviour. For example, according to
4409:
8282:
8006:
6472:
6196:
3943:
3731:
8890:
On the one hand, in quantum theory, if a perturbative element of compressive work is done almost infinitely slowly (that is to say quasi-statically), it is said to have been done
3401:{\displaystyle {\frac {PV}{T}}=\mathrm {constant} _{2}={\frac {10^{5}~{\text{Pa}}\times 10^{-3}~{\text{m}}^{3}}{300~{\text{K}}}}=0.333~{\text{Pa}}\,{\text{m}}^{3}{\text{K}}^{-1}.}
8409:
6599:
2126:
Adiabatic expansion does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above absolute zero) is via
3835:
6944:
5134:
8672:
An adiabat looks similar to an isotherm, except that during an expansion, an adiabat loses more pressure than an isotherm, so it has a steeper inclination (more vertical).
2046:
The adiabatic compression of a gas causes a rise in temperature of the gas. Adiabatic expansion against pressure, or a spring, causes a drop in temperature. In contrast,
1722:
Some chemical and physical processes occur too rapidly for energy to enter or leave the system as heat, allowing a convenient "adiabatic approximation". For example, the
1162:
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7898:
7569:
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812:
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631:
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7451:
5641:
997:
1779:, when sound travels in a gas, there is no time for heat conduction in the medium, and so the propagation of sound is adiabatic. For such an adiabatic process, the
8823:
but, rather, a variable that describes a transfer between two bodies. The adiabatic process is important because it is a logical ingredient of this current view.
8523:
6713:
3217:
the gas constant for that gas). Our initial conditions being 100 kPa of pressure, 1 L volume, and 300 K of temperature, our experimental constant (
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496:
7132:
5322:
4639:
835:
788:
703:
656:
568:
521:
7803:
5993:
2145:
Rising magma also undergoes adiabatic expansion before eruption, particularly significant in the case of magmas that rise quickly from great depths such as
1753:
into water droplets. The change in temperature of an air undergoing pseudo-adiabatic expansion differs from air undergoing adiabatic expansion because
8675:
If isotherms are concave towards the north-east direction (45° from V-axis), then adiabats are concave towards the east north-east (31° from V-axis).
3187:{\displaystyle P_{2}=P_{1}\left({\frac {V_{1}}{V_{2}}}\right)^{\gamma }=100\,000~{\text{Pa}}\times {\text{10}}^{7/5}=2.51\times 10^{6}~{\text{Pa}}}
1637:
3034:{\displaystyle P_{2}V_{2}^{\gamma }=\mathrm {constant} _{1}=6.31~{\text{Pa}}\,{\text{m}}^{21/5}=P\times (0.0001~{\text{m}}^{3})^{\frac {7}{5}},}
4909:
1338:
9391:
1226:
4814:
1666:
3994:
9940:
8905:
7408:{\displaystyle W=P_{1}V_{1}^{\gamma }{\frac {V_{2}^{1-\gamma }-V_{1}^{1-\gamma }}{1-\gamma }}={\frac {P_{2}V_{2}-P_{1}V_{1}}{1-\gamma }}.}
6970:
5598:{\displaystyle W=P_{1}V_{1}^{\gamma }{\frac {V_{2}^{1-\gamma }-V_{1}^{1-\gamma }}{1-\gamma }}={\frac {P_{2}V_{2}-P_{1}V_{1}}{1-\gamma }}.}
5160:
2069:
which rely on the lack of heat dissipation during the compression stroke to elevate the fuel vapor temperature sufficiently to ignite it.
1737:, adiabatic expansion and cooling of moist air, which can be triggered by winds flowing up and over a mountain for example, can cause the
4299:
460:
9623:
Rankine, W. J. MacQ. (1854). "On the geometrical representation of the expansive action of heat, and theory of thermodynamic engines".
9601:
Rankine, W. J. MacQ. (1854). "On the geometrical representation of the expansive action of heat, and theory of thermodynamic engines".
7058:
5248:
2438:. Note that the above formula is only applicable to classical ideal gases (that is, gases far above absolute zero temperature) and not
2380:
2280:
9822:"Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities"
8266:{\displaystyle \alpha nR(T_{2}-T_{1})=\alpha nRT_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right).}
6456:{\displaystyle \alpha nR(T_{2}-T_{1})=\alpha nRT_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right).}
2015:). In nature, this ideal kind occurs only approximately because it demands an infinitely slow process and no sources of dissipation.
1955:), and, in a fictive idealized process, energy is added to the system in the form of frictionless, non-viscous pressure–volume work (
1316:
9365:
9023:, as well as perturbing the functional form of the eigenstates themselves. In that theory, such a rapid change is said not to be
2467:
1349:
9214:
9919:
9723:
919:
8642:
diagram are indicated. These properties may be read from the classical behaviour of ideal gases, except in the region where
9962:
1630:
1217:
886:
453:
331:
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9989:
269:
9086:
9020:
4145:
2524:
1401:
1375:
896:
350:
8872:
8776:
in 1871 (explicitly attributing the term to
Rankine). The etymological origin corresponds here to an impossibility of
9698:
9494:
9457:
9348:
9254:
4505:{\displaystyle \ln \left({\frac {P}{P_{0}}}\right)=-{\frac {\alpha +1}{\alpha }}\ln \left({\frac {V}{V_{0}}}\right).}
4223:
2211:
302:
9984:
6828:
5018:
1454:
925:
324:
8795:
The adiabatic process has been important for thermodynamics since its early days. It was important in the work of
9288:
8396:{\displaystyle T_{2}-T_{1}=T_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right),}
8112:{\displaystyle W=-\alpha nRT_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right).}
6586:{\displaystyle T_{2}-T_{1}=T_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right),}
6302:{\displaystyle W=-\alpha nRT_{1}\left(\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1\right).}
1623:
19:
This article is about adiabatic processes in thermodynamics. For the adiabatic theorem in quantum mechanics, see
3201:
We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law,
8875:, one that can at times seem almost opposite to the classical thermodynamic sense. In quantum theory, the word
1554:
86:
1449:
9512:
8865:
8769:
3898:
3686:
1529:
1302:
279:
8787:("not") and διαβατός, "passable", in turn deriving from διά ("through"), and βαῖνειν ("to walk, go, come").
8679:
exception is very near absolute zero, where the density of adiabats drops sharply and they become rare (see
8510:{\displaystyle {\frac {T_{2}}{T_{1}}}-1=\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1,}
6700:{\displaystyle {\frac {T_{2}}{T_{1}}}-1=\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}-1,}
9652:
Thermodynamics. An
Introductory Treatise dealing mainly with First Principles and their Direct Applications
2439:
2180:
2119:
Due in part to adiabatic expansion in mountainous areas, snowfall infrequently occurs in some parts of the
1994:
1962:), and there is no phase change, then the temperature of the system will rise. Such a process is called an
914:
117:
107:
6820:
At the same time, the work done by the pressure–volume changes as a result from this process, is equal to
5010:
At the same time, the work done by the pressure–volume changes as a result from this process, is equal to
3198:
rise in pressure above what would result from a simplistic calculation of 10 times the original pressure.
1916:
If the system has such rigid walls that pressure–volume work cannot be done, but the walls are adiabatic (
9081:
1858:
1723:
1712:
122:
112:
9521:
8843:, though often far from isentropic, even when the gas is not adiabatically isolated by a definite wall.
9584:
2139:
1406:
1370:
148:
82:
9611:
9180:
7682:
Using the ideal gas law and assuming a constant molar quantity (as often happens in practical cases),
5872:
Using the ideal gas law and assuming a constant molar quantity (as often happens in practical cases),
1444:
9650:
3801:
2576:
2127:
1199:
947:
393:
206:
196:
9969:
8839:
wall. In this sense, a rapid compression of a gas is sometimes approximately or loosely said to be
7984:{\displaystyle \left({\frac {P_{2}}{P_{1}}}\right)^{-{\frac {1}{\gamma }}}={\frac {V_{2}}{V_{1}}}.}
7672:{\displaystyle W=-\alpha P_{1}V_{1}\left(\left({\frac {V_{2}}{V_{1}}}\right)^{1-\gamma }-1\right).}
6914:
6174:{\displaystyle \left({\frac {P_{2}}{P_{1}}}\right)^{-{\frac {1}{\gamma }}}={\frac {V_{2}}{V_{1}}}.}
5862:{\displaystyle W=-\alpha P_{1}V_{1}\left(\left({\frac {V_{2}}{V_{1}}}\right)^{1-\gamma }-1\right).}
5104:
2383:(3 for a monatomic gas, 5 for a diatomic gas or a gas of linear molecules such as carbon dioxide).
9043:
Furthermore, in atmospheric thermodynamics, a diabatic process is one in which heat is exchanged.
2201:
undergoing a reversible (i.e., no entropy generation) adiabatic process can be represented by the
1611:
1439:
1236:
1117:
1062:
1007:
939:
878:
414:
403:
69:
7787:{\displaystyle W=-\alpha nRT_{1}\left(\left({\frac {V_{2}}{V_{1}}}\right)^{1-\gamma }-1\right).}
5977:{\displaystyle W=-\alpha nRT_{1}\left(\left({\frac {V_{2}}{V_{1}}}\right)^{1-\gamma }-1\right).}
841:
794:
709:
662:
574:
527:
9936:
9929:
9472:
9106:
9091:
8834:
This present article is written from the viewpoint of macroscopic thermodynamics, and the word
7553:{\displaystyle W=-\alpha P_{1}V_{1}^{\gamma }\left(V_{2}^{1-\gamma }-V_{1}^{1-\gamma }\right).}
5743:{\displaystyle W=-\alpha P_{1}V_{1}^{\gamma }\left(V_{2}^{1-\gamma }-V_{1}^{1-\gamma }\right).}
3974:
3880:
relate to each other as the adiabatic process proceeds. For an ideal gas (recall ideal gas law
2060:
occurs when the pressure of a gas is increased by work done on it by its surroundings, e.g., a
1659:
1544:
1261:
345:
99:
74:
1464:
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9101:
2073:
1704:
1696:
1680:
1479:
1056:
369:
215:
64:
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9411:
9040:
analogue of adiabatic processes in classical thermodynamics, and for the reuse of the term.
8608:{\displaystyle T_{2}=T_{1}\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}.}
6798:{\displaystyle T_{2}=T_{1}\left({\frac {P_{2}}{P_{1}}}\right)^{\frac {\gamma -1}{\gamma }}.}
2100:
as its internal energy decreases. Adiabatic expansion occurs in the Earth's atmosphere with
967:
9833:
9791:
9407:
9096:
8796:
4798:{\displaystyle \left({\frac {P}{P_{0}}}\right)\left({\frac {V}{V_{0}}}\right)^{\gamma }=1,}
4623:{\displaystyle \left({\frac {P}{P_{0}}}\right)=\left({\frac {V}{V_{0}}}\right)^{-\gamma },}
2443:
2164:
2109:
1776:
1692:
1559:
1484:
1474:
274:
136:
9449:
7226:{\displaystyle W=\int _{V_{1}}^{V_{2}}P_{1}\left({\frac {V_{1}}{V}}\right)^{\gamma }\,dV.}
5416:{\displaystyle W=\int _{V_{1}}^{V_{2}}P_{1}\left({\frac {V_{1}}{V}}\right)^{\gamma }\,dV.}
4709:{\displaystyle \left({\frac {P}{P_{0}}}\right)=\left({\frac {V_{0}}{V}}\right)^{\gamma }.}
8:
9557:
9158:
9133:
8884:
8773:
8680:
6813:
The change in internal energy of a system, measured from state 1 to state 2, is equal to
1804:
1504:
1266:
288:
254:
249:
162:
9837:
9795:
9670:
2134:
on a magnetic material is used to provide adiabatic expansion. Also, the contents of an
1499:
478:
9867:
9204:
9153:
9148:
9138:
9048:
8880:
2202:
2189:
For a simple substance, during an adiabatic process in which the volume increases, the
2135:
2101:
1963:
1784:
1700:
1593:
1256:
1251:
1204:
820:
773:
688:
641:
553:
506:
436:
420:
307:
259:
244:
234:
43:
37:
9740:
9284:
7882:{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {V_{2}}{V_{1}}}\right)^{-\gamma },}
6906:
Since we require the process to be adiabatic, the following equation needs to be true
6072:{\displaystyle {\frac {P_{2}}{P_{1}}}=\left({\frac {V_{2}}{V_{1}}}\right)^{-\gamma },}
5096:
Since we require the process to be adiabatic, the following equation needs to be true
1967:
the system, but the temperature of the system will rise as the process is isentropic (
9915:
9871:
9859:
9851:
9760:
9719:
9694:
9490:
9453:
9344:
9309:
9250:
9208:
9143:
8861:
3658:
2019:
1924:
1745:. Expansion and cooling beyond the saturation vapor pressure is often idealized as a
1588:
1549:
1539:
1111:
909:
737:
229:
171:
20:
3859:
does not remain constant during an adiabatic process but instead changes along with
3671:
The definition of an adiabatic process is that heat transfer to the system is zero,
9994:
9841:
9799:
9752:
9561:
9415:
9196:
9128:
8855:
8799:
because it provided a way of nearly directly relating quantities of heat and work.
8719:
2113:
1509:
1494:
1434:
1429:
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1241:
891:
359:
224:
9944:
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9535:
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8808:
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2271:
2190:
1808:
1780:
1459:
1307:
961:
602:
425:
186:
153:
9885:
9442:
8802:
Energy can enter or leave a thermodynamic system enclosed by walls that prevent
2001:
Naturally occurring adiabatic processes are irreversible (entropy is produced).
9419:
9123:
9036:
9016:
8820:
8651:
3646:
2131:
2081:
2066:
2047:
1742:
1708:
1514:
1284:
384:
264:
201:
191:
59:
29:
1938:), and there is no phase change, then the temperature of the system will rise.
1913:), and there is no phase change, then the temperature of the system will rise.
1899:
If the system has such rigid walls that work cannot be transferred in or out (
9978:
9855:
9764:
9580:
8847:
8803:
8761:
3628:
when operated under these conditions of temperature and pressure), or that a
2449:
One can also use the ideal gas law to rewrite the above relationship between
2361:
2160:
2120:
1750:
1583:
901:
470:
431:
143:
16:
Thermodynamic process in which no mass or heat is exchanged with surroundings
2138:
can be described (to first order) as an adiabatically expanding fluid. (See
1906:), and the walls are not adiabatic and energy is added in the form of heat (
9863:
9343:. Translated by Halberstadt, E. S. London: Wiley–Interscience. p. 45.
8887:, but the usage of the word is very different between the two disciplines.
3629:
2089:
1534:
1519:
1469:
952:
2873:
so the adiabatic constant for this example is about 6.31 Pa m.
9329:
Münster, A. (1970), p. 48: "mass is an adiabatically inhibited variable."
9111:
9064:
8784:
8646:
becomes small (low temperature), where quantum effects become important.
4987:{\displaystyle \Delta U=\alpha RnT_{2}-\alpha RnT_{1}=\alpha Rn\Delta T.}
3633:
2153:
1754:
1738:
1734:
1489:
297:
9542:, vol. 1, Fundamental Principles. The Properties of Gases, London:
8698:
The isotherms are the red curves and the adiabats are the black curves.
9249:. New York, New York: American Institute of Physics Press. p. 21.
9200:
9069:
2146:
2085:
2051:
1578:
1524:
9846:
9821:
9716:
Elements of classical thermodynamics: for advanced students of physics
4894:{\displaystyle P_{0}V_{0}^{\gamma }=PV^{\gamma }=\mathrm {constant} .}
1730:
temperature by assuming combustion loses no heat to its surroundings.
9804:
9779:
8663:
6808:
4086:{\displaystyle dU=\alpha nR\,dT=\alpha \,d(PV)=\alpha (P\,dV+V\,dP).}
3652:
2198:
2105:
1672:
176:
9756:
9184:
9002:{\displaystyle c_{1}^{2}=1,\,\,c_{2}^{2}=0,\,\,c_{3}^{2}=0,\,...\,,}
7029:{\displaystyle PV^{\gamma }={\text{constant}}=P_{1}V_{1}^{\gamma }.}
5219:{\displaystyle PV^{\gamma }={\text{constant}}=P_{1}V_{1}^{\gamma }.}
4139:
Now substitute equations (a2) and (a4) into equation (a1) to obtain
1927:(constant volume) work in the form of friction or the stirring of a
1703:, an adiabatic process transfers energy to the surroundings only as
9666:
9403:
8895:
8765:
4363:{\displaystyle -(\alpha +1){\frac {dV}{V}}=\alpha {\frac {dP}{P}}.}
2409:
2077:
1852:
1292:
1209:
1001:
409:
181:
8790:
9567:
9543:
8704:
Volume is the horizontal axis and pressure is the vertical axis.
8631:
8623:
7116:{\displaystyle P=P_{1}\left({\frac {V_{1}}{V}}\right)^{\gamma }.}
5306:{\displaystyle P=P_{1}\left({\frac {V_{1}}{V}}\right)^{\gamma }.}
2152:
In the Earth's convecting mantle (the asthenosphere) beneath the
1928:
398:
2341:{\displaystyle \gamma ={\frac {C_{P}}{C_{V}}}={\frac {f+2}{f}}.}
1765:
A process without transfer of heat to or from a system, so that
9957:
2413:
2061:
9366:"Snowfall in the Sahara desert: an unusual weather phenomenon"
3783:
is being supplied from the surroundings. Pressure–volume work
2038:, as friction or viscosity are always present to some extent.
1711:, the adiabatic process supports the theory that explains the
9318:(adiabatic partitions inhibit the transfer of heat and mass)
2185:
9234:. Stroudsburg, Pennsylvania: Dowden, Hutchinson & Ross.
8777:
8734:
8731:
2511:{\displaystyle P^{1-\gamma }T^{\gamma }={\text{constant}},}
1727:
1688:
1684:
374:
8858:
has summarized the complicated etymology of "adiabatic".
8826:
8749:
8743:
8725:
9939:". Daphne – A Palomar College Web Server., 21 July 1995.
9525:, edited by W. J. Millar, 1881, Charles Griffin, London.
8695:
diagram with a superposition of adiabats and isotherms:
1726:
uses this approximation to calculate the upper limit of
3755:
is the change in the internal energy of the system and
9185:"Untersuchungen über die Grundlagen der Thermodynamik"
3771:) done must be done at the expense of internal energy
3678:. Then, according to the first law of thermodynamics,
2041:
9820:
Mandal, Anirban; Hunt, Katharine L. C. (2020-03-14).
9693:. New York, New York: American Institute of Physics.
9439:
8908:
8768:
of rivers). It is used in the thermodynamic sense by
8752:
8722:
8526:
8412:
8285:
8131:
8009:
7901:
7806:
7691:
7572:
7454:
7245:
7135:
7061:
6973:
6917:
6831:
6716:
6602:
6475:
6321:
6199:
6091:
5996:
5881:
5762:
5644:
5435:
5325:
5251:
5163:
5107:
5021:
4912:
4817:
4728:
4642:
4553:
4412:
4302:
4226:
4148:
3997:
3901:
3804:
3689:
3436:
3230:
3053:
2886:
2623:
2527:
2470:
2283:
2214:
2159:
Such temperature changes can be quantified using the
1120:
1065:
1010:
970:
844:
823:
797:
776:
748:
712:
691:
665:
644:
613:
577:
556:
530:
509:
481:
9392:"Temperature changes in ascending kimberlite magmas"
8746:
8740:
8728:
8122:
Substituting this expression and (c1) in (c3) gives
6312:
Substituting this expression and (b1) in (b3) gives
3640:
1883:
denotes the change of the system's internal energy,
9316:. Cambridge, Massachusetts: MIT Press. p. 48.
8737:
8669:
Each adiabat intersects each isotherm exactly once.
3983:is the number of moles in the system (a constant).
2582:
9448:. Cambridge: Cambridge University Press. pp.
9001:
8607:
8509:
8395:
8265:
8111:
7983:
7881:
7786:
7671:
7552:
7407:
7225:
7115:
7028:
6938:
6882:
6809:Derivation of discrete formula and work expression
6797:
6699:
6585:
6455:
6301:
6173:
6071:
5976:
5861:
5742:
5597:
5415:
5305:
5218:
5128:
5072:
4986:
4893:
4797:
4708:
4622:
4504:
4362:
4276:
4199:
4085:
3967:is the number of degrees of freedom divided by 2,
3937:
3829:
3725:
3612:
3400:
3186:
3033:
2862:
2560:
2510:
2340:
2241:
1156:
1101:
1046:
991:
853:
829:
806:
782:
757:
721:
697:
674:
650:
625:
586:
562:
539:
515:
490:
4200:{\displaystyle -P\,dV=\alpha P\,dV+\alpha V\,dP,}
2561:{\displaystyle TV^{\gamma -1}={\text{constant}}.}
2174:
1895:the work done by the system on its surroundings.
9976:
9515:(1866). On the theory of explosive gas engines,
4373:After integrating the left and right sides from
3667:relation for adiabatic compression and expansion
1889:the quantity of energy added to it as heat, and
1853:Various applications of the adiabatic assumption
9519:, July 27, 1866; at page 467 of the reprint in
9508:
9506:
8791:Conceptual significance in thermodynamic theory
8634:in a diagram. Some properties of adiabats on a
7236:Integrating we obtain the expression for work,
5426:Integrating we obtain the expression for work,
4277:{\displaystyle -(\alpha +1)P\,dV=\alpha V\,dP,}
2242:{\displaystyle PV^{\gamma }={\text{constant}},}
9684:
9682:
9528:
9484:
9389:
9175:
9173:
7994:Substituting into the previous expression for
6184:Substituting into the previous expression for
2373:is the specific heat for constant volume, and
6883:{\displaystyle W=\int _{V_{1}}^{V_{2}}P\,dV.}
5073:{\displaystyle W=\int _{V_{1}}^{V_{2}}P\,dV.}
1631:
9503:
9179:
9051:, does not impinge on this classical usage.
9679:
9540:An Advanced Treatise on Physical Chemistry.
9270:
9268:
9266:
9170:
8780:and of transfer of matter across the wall.
9914:. Hoboken, New Jersey: Wiley. p. 55.
9819:
9534:
9390:Kavanagh, J. L.; Sparks, R. S. J. (2009).
4633:and eliminate the negative sign to obtain
1638:
1624:
36:
9845:
9803:
9489:(8th ed.). W.H.Freeman. p. 48.
8995:
8985:
8960:
8959:
8934:
8933:
7213:
6870:
5403:
5060:
4264:
4248:
4187:
4171:
4155:
4070:
4057:
4029:
4016:
3817:
3562:
3367:
3122:
2962:
2832:
2797:
2696:
9777:
9485:Atkins, Peter; de Paula, Giulio (2006).
9263:
9238:
8783:The Greek word ἀδιάβατος is formed from
8622:
3868:It is desired to know how the values of
3044:We can now solve for the final pressure
2184:
9910:Silbey, Robert J.; et al. (2004).
9780:"Physical aspects of quantum mechanics"
9738:
9713:
9622:
9600:
9556:
9383:
9338:
3938:{\displaystyle U=\alpha nRT=\alpha PV,}
3726:{\displaystyle dU+\delta W=\delta Q=0,}
2193:of the working substance must decrease
1857:For a closed system, one may write the
9977:
9909:
9718:(Repr ed.). Cambridge: Univ. Pr.
9688:
9672:Natural Philosophy of Cause and Chance
9634:Miscellaneous Scientific Papers p. 341
9612:Miscellaneous Scientific Papers p. 339
9363:
9244:
9229:
3651:For an adiabatic free expansion of an
1715:. The opposite term to "adiabatic" is
9970:Article in HyperPhysics Encyclopaedia
9645:
9308:
8764:term ἀδιάβατος "impassable" (used by
4403:and changing the sides respectively,
3986:Differentiating equation (a3) yields
1749:whereby excess vapor instantaneously
9810:(Translation by Robert Oppenheimer.)
9665:
8618:
6964:
6908:
6822:
5154:
5098:
5012:
4903:
4515:Exponentiate both sides, substitute
4109:Equation (a4) is often expressed as
3988:
3892:
3795:
3680:
2072:Adiabatic compression occurs in the
9396:Earth and Planetary Science Letters
3427:, so we can solve for temperature:
2042:Adiabatic compression and expansion
1941:If the system walls are adiabatic (
13:
9675:. London: Oxford University Press.
9364:Knight, Jasper (31 January 2022).
9087:Entropy (classical thermodynamics)
9021:time-dependent perturbation theory
8630:An adiabat is a curve of constant
7126:Substituting this into (c2) gives
6918:
5316:Substituting this into (b2) gives
5108:
4975:
4913:
4884:
4881:
4878:
4875:
4872:
4869:
4866:
4863:
3890:) the internal energy is given by
3476:
3473:
3470:
3467:
3464:
3461:
3458:
3455:
3272:
3269:
3266:
3263:
3260:
3257:
3254:
3251:
2938:
2935:
2932:
2929:
2926:
2923:
2920:
2917:
2680:
2677:
2674:
2671:
2668:
2665:
2662:
2659:
2408:, and for a diatomic gas (such as
2274:or heat capacity ratio defined as
2018:The other extreme kind of work is
845:
798:
713:
666:
578:
531:
351:Intensive and extensive properties
14:
10006:
9951:
9888:. American Meteorological Society
3641:Adiabatic free expansion of a gas
2197:The mathematical equation for an
1683:that occurs without transferring
1679: 'impassable') is a type of
9956:
9739:Laidler, Keith J. (1994-03-01).
9689:Bailyn, M. (1994). "Chapter 3".
9625:Proceedings of the Royal Society
9603:Proceedings of the Royal Society
9232:The Second Law of Thermodynamics
8879:can mean something perhaps near
8718:
2583:Example of adiabatic compression
1607:
1606:
926:Table of thermodynamic equations
9878:
9826:The Journal of Chemical Physics
9813:
9771:
9732:
9707:
9659:
9639:
9616:
9594:
9574:
9550:
9522:Miscellaneous Scientific Papers
9478:
9466:
9433:
9289:American Meteorological Society
9118:Related thermodynamic processes
3830:{\displaystyle \delta W=P\,dV.}
3411:We know the compressed gas has
2416:, the main components of air),
1402:Maxwell's thermodynamic surface
9513:Rankine, William John MacQuorn
9440:Turcotte and Schubert (2002).
9357:
9332:
9323:
9302:
9277:
8167:
8141:
6357:
6331:
4318:
4306:
4242:
4230:
4077:
4051:
4042:
4033:
3213:is amount of gas in moles and
3014:
2992:
2733:
2711:
2175:Ideal gas (reversible process)
1760:
1757:is released by precipitation.
1136:
1124:
1081:
1069:
1026:
1014:
986:
974:
1:
9745:Canadian Journal of Chemistry
9591:, Clarendon Press, Oxford UK.
9274:Bailyn, M. (1994), pp. 52–53.
9213:. A translation may be found
9164:
8866:quantum statistical mechanics
8827:Divergent usages of the word
8760:) is an anglicization of the
8701:The adiabats are isentropic.
6939:{\displaystyle \Delta U+W=0.}
5129:{\displaystyle \Delta U+W=0.}
1303:Mechanical equivalent of heat
9741:"The meaning of "adiabatic""
8707:
7042:
6962:By the previous derivation,
6952:
6896:
5232:
5152:By the previous derivation,
5142:
5086:
5000:
4099:
3951:
3843:
3739:
2587:The compression stroke in a
2181:Reversible adiabatic process
2080:descends, for example, in a
1995:second law of thermodynamics
1849:is the pressure of the gas.
1807:at constant pressure and at
915:Onsager reciprocal relations
7:
9714:Pippard, Alfred B. (1981).
9082:First law of thermodynamics
9058:
7797:By the continuous formula,
5987:By the continuous formula,
2386:For a monatomic ideal gas,
2167:for atmospheric processes.
1859:first law of thermodynamics
1724:adiabatic flame temperature
1713:first law of thermodynamics
1407:Entropy as energy dispersal
1218:"Perpetual motion" machines
1157:{\displaystyle G(T,p)=H-TS}
1102:{\displaystyle A(T,V)=U-TS}
1047:{\displaystyle H(S,p)=U+pV}
10:
10011:
9990:Atmospheric thermodynamics
9691:A Survey of Thermodynamics
9566:(first ed.), London:
9487:Atkins' Physical Chemistry
9420:10.1016/j.epsl.2009.07.011
9314:Generalized Thermodynamics
9247:A Survey of Thermodynamics
9226:translation is to be found
9017:transition moment integral
8778:transfer of energy as heat
4544:, the heat capacity ratio
3644:
2178:
2140:heat death of the universe
2054:process for an ideal gas.
1923:), and energy is added as
1665:
854:{\displaystyle \partial T}
807:{\displaystyle \partial V}
722:{\displaystyle \partial p}
675:{\displaystyle \partial V}
587:{\displaystyle \partial T}
540:{\displaystyle \partial S}
18:
9935:Thorngren, Dr. Jane R.. "
9655:. Leipzig: B. G. Teubner.
9285:"pseudoadiabatic process"
9224:. Also a mostly reliable
8873:in a very different sense
4287:and divide both sides by
3793:the system is defined as
2577:thermodynamic temperature
2128:adiabatic demagnetisation
1931:fluid within the system (
1743:saturation vapor pressure
1328:An Inquiry Concerning the
9341:Classical Thermodynamics
9027:, and the contrary word
8868:, however, use the word
1747:pseudo-adiabatic process
1341:Heterogeneous Substances
758:{\displaystyle \alpha =}
626:{\displaystyle \beta =-}
9985:Thermodynamic processes
9589:A Greek-English Lexicon
9568:Longmans, Green and Co.
9544:Longmans, Green and Co.
9412:2009E&PSL.286..404K
9019:and in accordance with
8772:(1866), and adopted by
8687:The right diagram is a
7052:Rearranging (c4) gives
5242:Rearranging (b4) gives
3415: = 0.1 L and
2364:for constant pressure,
1805:ratio of specific heats
1741:pressure to exceed the
9107:Magnetic refrigeration
9092:Adiabatic conductivity
9076:Related physics topics
9003:
8627:
8609:
8511:
8397:
8267:
8113:
7985:
7883:
7788:
7673:
7554:
7409:
7227:
7117:
7030:
6940:
6884:
6799:
6701:
6587:
6457:
6303:
6175:
6073:
5978:
5863:
5744:
5599:
5417:
5307:
5220:
5130:
5074:
4988:
4895:
4799:
4710:
4624:
4506:
4364:
4278:
4201:
4087:
3975:universal gas constant
3939:
3831:
3765:the system. Any work (
3727:
3614:
3402:
3188:
3035:
2864:
2562:
2512:
2342:
2243:
2194:
2130:, where the change in
1787:) can be expressed as
1707:. As a key concept in
1158:
1103:
1048:
993:
992:{\displaystyle U(S,V)}
855:
831:
808:
784:
759:
723:
699:
676:
652:
627:
588:
564:
541:
517:
492:
471:Specific heat capacity
75:Quantum thermodynamics
9965:at Wikimedia Commons
9189:Mathematische Annalen
9102:Total air temperature
9004:
8626:
8610:
8512:
8398:
8268:
8114:
7986:
7884:
7789:
7674:
7555:
7410:
7228:
7118:
7031:
6941:
6885:
6800:
6702:
6588:
6458:
6304:
6176:
6074:
5979:
5864:
5745:
5600:
5418:
5308:
5221:
5131:
5075:
4989:
4896:
4800:
4711:
4625:
4507:
4365:
4279:
4202:
4088:
3940:
3832:
3728:
3615:
3403:
3189:
3036:
2865:
2563:
2513:
2343:
2244:
2188:
2058:Adiabatic compression
1781:modulus of elasticity
1681:thermodynamic process
1339:On the Equilibrium of
1159:
1104:
1057:Helmholtz free energy
1049:
994:
856:
832:
809:
785:
760:
724:
700:
677:
653:
628:
589:
565:
542:
518:
493:
9339:Münster, A. (1970).
9097:Adiabatic lapse rate
8906:
8654:approaches both the
8524:
8410:
8283:
8129:
8007:
7899:
7804:
7689:
7570:
7452:
7243:
7133:
7059:
6971:
6915:
6829:
6714:
6600:
6473:
6319:
6197:
6089:
5994:
5879:
5760:
5642:
5433:
5323:
5249:
5161:
5105:
5019:
4910:
4815:
4726:
4640:
4551:
4410:
4300:
4224:
4146:
3995:
3899:
3802:
3687:
3434:
3228:
3051:
2884:
2621:
2525:
2468:
2281:
2212:
2165:hydrostatic equation
2108:, and this can form
1693:thermodynamic system
1352:Motive Power of Fire
1118:
1063:
1008:
968:
920:Bridgman's equations
897:Fundamental relation
842:
821:
795:
774:
746:
710:
689:
663:
642:
611:
575:
554:
528:
507:
479:
9963:Adiabatic processes
9937:Adiabatic Processes
9930:Adiabatic Processes
9838:2020JChPh.152j4110M
9796:1927Natur.119..354B
9473:Adiabatic Processes
9245:Bailyn, M. (1994).
9230:Kestin, J. (1976).
9159:Quasistatic process
9134:Isenthalpic process
8975:
8949:
8923:
8846:Some authors, like
7541:
7517:
7491:
7324:
7300:
7276:
7170:
7022:
6866:
5731:
5707:
5681:
5514:
5490:
5466:
5360:
5212:
5056:
4842:
2911:
2653:
2575:is the absolute or
2097:Adiabatic expansion
1330:Source ... Friction
1262:Loschmidt's paradox
454:Material properties
332:Conjugate variables
9943:2011-05-09 at the
9912:Physical chemistry
9886:"diabatic process"
9220:2019-10-12 at the
9201:10.1007/BF01450409
9154:Polytropic process
9149:Isothermal process
9139:Isentropic process
9049:entropy production
9031:is applied to it.
8999:
8961:
8935:
8909:
8883:, or perhaps near
8854:"adiabatic"). And
8628:
8605:
8507:
8393:
8263:
8109:
7981:
7879:
7784:
7669:
7550:
7521:
7497:
7477:
7405:
7304:
7280:
7262:
7223:
7142:
7113:
7026:
7008:
6936:
6880:
6838:
6795:
6697:
6583:
6453:
6299:
6171:
6069:
5974:
5859:
5740:
5711:
5687:
5667:
5595:
5494:
5470:
5452:
5413:
5332:
5303:
5216:
5198:
5126:
5070:
5028:
4984:
4891:
4828:
4795:
4706:
4620:
4502:
4360:
4274:
4197:
4083:
3935:
3827:
3723:
3610:
3398:
3184:
3031:
2897:
2860:
2858:
2639:
2558:
2508:
2381:degrees of freedom
2338:
2239:
2203:polytropic process
2195:
2171:insulators exist.
2136:expanding universe
2102:orographic lifting
2074:Earth's atmosphere
1964:isentropic process
1701:isothermal process
1594:Order and disorder
1350:Reflections on the
1257:Heat death paradox
1154:
1099:
1044:
989:
851:
827:
804:
780:
755:
719:
695:
672:
648:
623:
584:
560:
537:
513:
491:{\displaystyle c=}
488:
461:Property databases
437:Reduced properties
421:Chemical potential
385:Functions of state
308:Thermal efficiency
44:Carnot heat engine
9961:Media related to
9928:Nave, Carl Rod. "
9921:978-0-471-21504-2
9847:10.1063/1.5140009
9790:(2992): 354–357.
9778:Born, M. (1927).
9725:978-0-521-09101-5
9536:Partington, J. R.
9144:Isochoric process
8862:Quantum mechanics
8619:Graphing adiabats
8599:
8577:
8495:
8473:
8435:
8376:
8354:
8246:
8224:
8092:
8070:
7976:
7947:
7929:
7861:
7829:
7752:
7637:
7400:
7337:
7201:
7098:
7050:
7049:
6993:
6960:
6959:
6904:
6903:
6789:
6767:
6685:
6663:
6625:
6566:
6544:
6436:
6414:
6282:
6260:
6166:
6137:
6119:
6051:
6019:
5942:
5827:
5590:
5527:
5391:
5288:
5240:
5239:
5183:
5150:
5149:
5094:
5093:
5008:
5007:
4774:
4748:
4691:
4662:
4602:
4573:
4493:
4466:
4438:
4355:
4334:
4107:
4106:
3959:
3958:
3851:
3850:
3747:
3746:
3605:
3601:
3591:
3579:
3567:
3560:
3556:
3541:
3536:
3516:
3512:
3486:
3384:
3372:
3365:
3361:
3351:
3348:
3344:
3329:
3324:
3304:
3300:
3244:
3182:
3178:
3141:
3132:
3128:
3104:
3025:
3005:
3000:
2967:
2960:
2956:
2837:
2830:
2826:
2802:
2795:
2791:
2744:
2724:
2719:
2706:
2702:
2553:
2503:
2379:is the number of
2333:
2312:
2234:
2114:lenticular clouds
1993:according to the
1948:) but not rigid (
1652:adiabatic process
1648:
1647:
1589:Self-organization
1414:
1413:
1112:Gibbs free energy
910:Maxwell relations
868:
867:
864:
863:
830:{\displaystyle V}
783:{\displaystyle 1}
738:Thermal expansion
732:
731:
698:{\displaystyle V}
651:{\displaystyle 1}
597:
596:
563:{\displaystyle N}
516:{\displaystyle T}
444:
443:
360:Process functions
346:Property diagrams
325:System properties
315:
314:
280:Endoreversibility
172:Equation of state
21:adiabatic theorem
10002:
9960:
9932:". HyperPhysics.
9925:
9898:
9897:
9895:
9893:
9882:
9876:
9875:
9849:
9817:
9811:
9809:
9807:
9805:10.1038/119354a0
9775:
9769:
9768:
9736:
9730:
9729:
9711:
9705:
9704:
9686:
9677:
9676:
9663:
9657:
9656:
9643:
9637:
9632:
9620:
9614:
9610:
9598:
9592:
9578:
9572:
9571:
9554:
9548:
9547:
9532:
9526:
9510:
9501:
9500:
9482:
9476:
9470:
9464:
9463:
9447:
9437:
9431:
9430:
9428:
9426:
9387:
9381:
9380:
9378:
9376:
9370:The Conversation
9361:
9355:
9354:
9336:
9330:
9327:
9321:
9320:
9306:
9300:
9299:
9297:
9295:
9281:
9275:
9272:
9261:
9260:
9242:
9236:
9235:
9212:
9181:Carathéodory, C.
9177:
9129:Isobaric process
9008:
9006:
9005:
9000:
8974:
8969:
8948:
8943:
8922:
8917:
8759:
8758:
8755:
8754:
8751:
8748:
8745:
8742:
8739:
8736:
8733:
8730:
8727:
8724:
8681:Nernst's theorem
8662:axis (just like
8614:
8612:
8611:
8606:
8601:
8600:
8595:
8584:
8582:
8578:
8576:
8575:
8566:
8565:
8556:
8549:
8548:
8536:
8535:
8516:
8514:
8513:
8508:
8497:
8496:
8491:
8480:
8478:
8474:
8472:
8471:
8462:
8461:
8452:
8436:
8434:
8433:
8424:
8423:
8414:
8402:
8400:
8399:
8394:
8389:
8385:
8378:
8377:
8372:
8361:
8359:
8355:
8353:
8352:
8343:
8342:
8333:
8321:
8320:
8308:
8307:
8295:
8294:
8272:
8270:
8269:
8264:
8259:
8255:
8248:
8247:
8242:
8231:
8229:
8225:
8223:
8222:
8213:
8212:
8203:
8191:
8190:
8166:
8165:
8153:
8152:
8118:
8116:
8115:
8110:
8105:
8101:
8094:
8093:
8088:
8077:
8075:
8071:
8069:
8068:
8059:
8058:
8049:
8037:
8036:
7999:
7990:
7988:
7987:
7982:
7977:
7975:
7974:
7965:
7964:
7955:
7950:
7949:
7948:
7940:
7934:
7930:
7928:
7927:
7918:
7917:
7908:
7888:
7886:
7885:
7880:
7875:
7874:
7866:
7862:
7860:
7859:
7850:
7849:
7840:
7830:
7828:
7827:
7818:
7817:
7808:
7793:
7791:
7790:
7785:
7780:
7776:
7769:
7768:
7757:
7753:
7751:
7750:
7741:
7740:
7731:
7719:
7718:
7678:
7676:
7675:
7670:
7665:
7661:
7654:
7653:
7642:
7638:
7636:
7635:
7626:
7625:
7616:
7604:
7603:
7594:
7593:
7559:
7557:
7556:
7551:
7546:
7542:
7540:
7529:
7516:
7505:
7490:
7485:
7476:
7475:
7445:in second term,
7444:
7443:
7441:
7440:
7435:
7432:
7414:
7412:
7411:
7406:
7401:
7399:
7388:
7387:
7386:
7377:
7376:
7364:
7363:
7354:
7353:
7343:
7338:
7336:
7325:
7323:
7312:
7299:
7288:
7278:
7275:
7270:
7261:
7260:
7232:
7230:
7229:
7224:
7212:
7211:
7206:
7202:
7197:
7196:
7187:
7180:
7179:
7169:
7168:
7167:
7157:
7156:
7155:
7122:
7120:
7119:
7114:
7109:
7108:
7103:
7099:
7094:
7093:
7084:
7077:
7076:
7044:
7035:
7033:
7032:
7027:
7021:
7016:
7007:
7006:
6994:
6991:
6986:
6985:
6965:
6954:
6945:
6943:
6942:
6937:
6909:
6898:
6889:
6887:
6886:
6881:
6865:
6864:
6863:
6853:
6852:
6851:
6823:
6804:
6802:
6801:
6796:
6791:
6790:
6785:
6774:
6772:
6768:
6766:
6765:
6756:
6755:
6746:
6739:
6738:
6726:
6725:
6706:
6704:
6703:
6698:
6687:
6686:
6681:
6670:
6668:
6664:
6662:
6661:
6652:
6651:
6642:
6626:
6624:
6623:
6614:
6613:
6604:
6592:
6590:
6589:
6584:
6579:
6575:
6568:
6567:
6562:
6551:
6549:
6545:
6543:
6542:
6533:
6532:
6523:
6511:
6510:
6498:
6497:
6485:
6484:
6462:
6460:
6459:
6454:
6449:
6445:
6438:
6437:
6432:
6421:
6419:
6415:
6413:
6412:
6403:
6402:
6393:
6381:
6380:
6356:
6355:
6343:
6342:
6308:
6306:
6305:
6300:
6295:
6291:
6284:
6283:
6278:
6267:
6265:
6261:
6259:
6258:
6249:
6248:
6239:
6227:
6226:
6189:
6180:
6178:
6177:
6172:
6167:
6165:
6164:
6155:
6154:
6145:
6140:
6139:
6138:
6130:
6124:
6120:
6118:
6117:
6108:
6107:
6098:
6078:
6076:
6075:
6070:
6065:
6064:
6056:
6052:
6050:
6049:
6040:
6039:
6030:
6020:
6018:
6017:
6008:
6007:
5998:
5983:
5981:
5980:
5975:
5970:
5966:
5959:
5958:
5947:
5943:
5941:
5940:
5931:
5930:
5921:
5909:
5908:
5868:
5866:
5865:
5860:
5855:
5851:
5844:
5843:
5832:
5828:
5826:
5825:
5816:
5815:
5806:
5794:
5793:
5784:
5783:
5749:
5747:
5746:
5741:
5736:
5732:
5730:
5719:
5706:
5695:
5680:
5675:
5666:
5665:
5635:in second term,
5634:
5633:
5631:
5630:
5625:
5622:
5604:
5602:
5601:
5596:
5591:
5589:
5578:
5577:
5576:
5567:
5566:
5554:
5553:
5544:
5543:
5533:
5528:
5526:
5515:
5513:
5502:
5489:
5478:
5468:
5465:
5460:
5451:
5450:
5422:
5420:
5419:
5414:
5402:
5401:
5396:
5392:
5387:
5386:
5377:
5370:
5369:
5359:
5358:
5357:
5347:
5346:
5345:
5312:
5310:
5309:
5304:
5299:
5298:
5293:
5289:
5284:
5283:
5274:
5267:
5266:
5234:
5225:
5223:
5222:
5217:
5211:
5206:
5197:
5196:
5184:
5181:
5176:
5175:
5155:
5144:
5135:
5133:
5132:
5127:
5099:
5088:
5079:
5077:
5076:
5071:
5055:
5054:
5053:
5043:
5042:
5041:
5013:
5002:
4993:
4991:
4990:
4985:
4962:
4961:
4940:
4939:
4904:
4900:
4898:
4897:
4892:
4887:
4858:
4857:
4841:
4836:
4827:
4826:
4804:
4802:
4801:
4796:
4785:
4784:
4779:
4775:
4773:
4772:
4760:
4753:
4749:
4747:
4746:
4734:
4715:
4713:
4712:
4707:
4702:
4701:
4696:
4692:
4687:
4686:
4677:
4667:
4663:
4661:
4660:
4648:
4629:
4627:
4626:
4621:
4616:
4615:
4607:
4603:
4601:
4600:
4588:
4578:
4574:
4572:
4571:
4559:
4543:
4537:
4536:
4534:
4533:
4528:
4525:
4511:
4509:
4508:
4503:
4498:
4494:
4492:
4491:
4479:
4467:
4462:
4451:
4443:
4439:
4437:
4436:
4424:
4402:
4396:
4387:
4381:
4369:
4367:
4366:
4361:
4356:
4351:
4343:
4335:
4330:
4322:
4292:
4283:
4281:
4280:
4275:
4216:
4206:
4204:
4203:
4198:
4135:
4122:
4101:
4092:
4090:
4089:
4084:
3989:
3982:
3972:
3966:
3953:
3944:
3942:
3941:
3936:
3893:
3889:
3879:
3873:
3864:
3858:
3845:
3836:
3834:
3833:
3828:
3796:
3788:
3782:
3777:, since no heat
3776:
3770:
3760:
3754:
3741:
3732:
3730:
3729:
3724:
3681:
3677:
3619:
3617:
3616:
3611:
3606:
3603:
3599:
3592:
3590:
3589:
3588:
3580:
3577:
3574:
3573:
3568:
3565:
3561:
3558:
3554:
3549:
3548:
3547:
3542:
3539:
3534:
3533:
3532:
3517:
3514:
3510:
3509:
3508:
3492:
3487:
3485:
3484:
3479:
3452:
3444:
3426:
3424:
3418:
3414:
3407:
3405:
3404:
3399:
3394:
3393:
3385:
3382:
3379:
3378:
3373:
3370:
3366:
3363:
3359:
3352:
3350:
3349:
3346:
3342:
3337:
3336:
3335:
3330:
3327:
3322:
3321:
3320:
3305:
3302:
3298:
3297:
3296:
3286:
3281:
3280:
3275:
3245:
3240:
3232:
3193:
3191:
3190:
3185:
3183:
3180:
3176:
3175:
3174:
3156:
3155:
3151:
3142:
3139:
3133:
3130:
3126:
3115:
3114:
3109:
3105:
3103:
3102:
3093:
3092:
3083:
3076:
3075:
3063:
3062:
3040:
3038:
3037:
3032:
3027:
3026:
3018:
3012:
3011:
3006:
3003:
2998:
2982:
2981:
2977:
2968:
2965:
2961:
2958:
2954:
2947:
2946:
2941:
2910:
2905:
2896:
2895:
2869:
2867:
2866:
2861:
2859:
2852:
2851:
2847:
2838:
2835:
2831:
2828:
2824:
2817:
2816:
2812:
2803:
2800:
2796:
2793:
2789:
2788:
2787:
2766:
2765:
2750:
2746:
2745:
2737:
2731:
2730:
2725:
2722:
2717:
2707:
2704:
2700:
2689:
2688:
2683:
2652:
2647:
2638:
2637:
2627:
2613:
2612:
2610:
2609:
2606:
2603:
2567:
2565:
2564:
2559:
2554:
2551:
2546:
2545:
2517:
2515:
2514:
2509:
2504:
2501:
2496:
2495:
2486:
2485:
2460:
2454:
2437:
2436:
2434:
2433:
2430:
2427:
2407:
2406:
2404:
2403:
2400:
2397:
2378:
2372:
2359:
2347:
2345:
2344:
2339:
2334:
2329:
2318:
2313:
2311:
2310:
2301:
2300:
2291:
2269:
2263:
2257:
2248:
2246:
2245:
2240:
2235:
2232:
2227:
2226:
2037:
2029:
2014:
1992:
1984:
1974:
1961:
1954:
1947:
1937:
1922:
1912:
1905:
1894:
1888:
1882:
1875:
1848:
1842:
1841:
1839:
1838:
1830:
1827:
1802:
1796:
1771:
1676:
1669:
1640:
1633:
1626:
1610:
1609:
1317:Key publications
1298:
1297:("living force")
1247:Brownian ratchet
1242:Entropy and life
1237:Entropy and time
1188:
1187:
1163:
1161:
1160:
1155:
1108:
1106:
1105:
1100:
1053:
1051:
1050:
1045:
998:
996:
995:
990:
892:Clausius theorem
887:Carnot's theorem
860:
858:
857:
852:
836:
834:
833:
828:
813:
811:
810:
805:
789:
787:
786:
781:
768:
767:
764:
762:
761:
756:
728:
726:
725:
720:
704:
702:
701:
696:
681:
679:
678:
673:
657:
655:
654:
649:
636:
635:
632:
630:
629:
624:
593:
591:
590:
585:
569:
567:
566:
561:
546:
544:
543:
538:
522:
520:
519:
514:
501:
500:
497:
495:
494:
489:
467:
466:
340:
339:
159:
158:
40:
26:
25:
10010:
10009:
10005:
10004:
10003:
10001:
10000:
9999:
9975:
9974:
9954:
9945:Wayback Machine
9922:
9901:
9891:
9889:
9884:
9883:
9879:
9818:
9814:
9776:
9772:
9757:10.1139/v94-121
9737:
9733:
9726:
9712:
9708:
9701:
9687:
9680:
9664:
9660:
9644:
9640:
9621:
9617:
9599:
9595:
9579:
9575:
9555:
9551:
9533:
9529:
9511:
9504:
9497:
9483:
9479:
9471:
9467:
9460:
9438:
9434:
9424:
9422:
9388:
9384:
9374:
9372:
9362:
9358:
9351:
9337:
9333:
9328:
9324:
9307:
9303:
9293:
9291:
9283:
9282:
9278:
9273:
9264:
9257:
9243:
9239:
9222:Wayback Machine
9178:
9171:
9167:
9061:
8970:
8965:
8944:
8939:
8918:
8913:
8907:
8904:
8903:
8832:
8809:internal energy
8793:
8721:
8717:
8710:
8621:
8585:
8583:
8571:
8567:
8561:
8557:
8555:
8551:
8550:
8544:
8540:
8531:
8527:
8525:
8522:
8521:
8481:
8479:
8467:
8463:
8457:
8453:
8451:
8447:
8446:
8429:
8425:
8419:
8415:
8413:
8411:
8408:
8407:
8362:
8360:
8348:
8344:
8338:
8334:
8332:
8328:
8327:
8326:
8322:
8316:
8312:
8303:
8299:
8290:
8286:
8284:
8281:
8280:
8232:
8230:
8218:
8214:
8208:
8204:
8202:
8198:
8197:
8196:
8192:
8186:
8182:
8161:
8157:
8148:
8144:
8130:
8127:
8126:
8078:
8076:
8064:
8060:
8054:
8050:
8048:
8044:
8043:
8042:
8038:
8032:
8028:
8008:
8005:
8004:
7995:
7970:
7966:
7960:
7956:
7954:
7939:
7935:
7923:
7919:
7913:
7909:
7907:
7903:
7902:
7900:
7897:
7896:
7867:
7855:
7851:
7845:
7841:
7839:
7835:
7834:
7823:
7819:
7813:
7809:
7807:
7805:
7802:
7801:
7758:
7746:
7742:
7736:
7732:
7730:
7726:
7725:
7724:
7720:
7714:
7710:
7690:
7687:
7686:
7643:
7631:
7627:
7621:
7617:
7615:
7611:
7610:
7609:
7605:
7599:
7595:
7589:
7585:
7571:
7568:
7567:
7530:
7525:
7506:
7501:
7496:
7492:
7486:
7481:
7471:
7467:
7453:
7450:
7449:
7436:
7433:
7427:
7426:
7424:
7419:
7389:
7382:
7378:
7372:
7368:
7359:
7355:
7349:
7345:
7344:
7342:
7326:
7313:
7308:
7289:
7284:
7279:
7277:
7271:
7266:
7256:
7252:
7244:
7241:
7240:
7207:
7192:
7188:
7186:
7182:
7181:
7175:
7171:
7163:
7159:
7158:
7151:
7147:
7146:
7134:
7131:
7130:
7104:
7089:
7085:
7083:
7079:
7078:
7072:
7068:
7060:
7057:
7056:
7017:
7012:
7002:
6998:
6990:
6981:
6977:
6972:
6969:
6968:
6916:
6913:
6912:
6859:
6855:
6854:
6847:
6843:
6842:
6830:
6827:
6826:
6811:
6775:
6773:
6761:
6757:
6751:
6747:
6745:
6741:
6740:
6734:
6730:
6721:
6717:
6715:
6712:
6711:
6671:
6669:
6657:
6653:
6647:
6643:
6641:
6637:
6636:
6619:
6615:
6609:
6605:
6603:
6601:
6598:
6597:
6552:
6550:
6538:
6534:
6528:
6524:
6522:
6518:
6517:
6516:
6512:
6506:
6502:
6493:
6489:
6480:
6476:
6474:
6471:
6470:
6422:
6420:
6408:
6404:
6398:
6394:
6392:
6388:
6387:
6386:
6382:
6376:
6372:
6351:
6347:
6338:
6334:
6320:
6317:
6316:
6268:
6266:
6254:
6250:
6244:
6240:
6238:
6234:
6233:
6232:
6228:
6222:
6218:
6198:
6195:
6194:
6185:
6160:
6156:
6150:
6146:
6144:
6129:
6125:
6113:
6109:
6103:
6099:
6097:
6093:
6092:
6090:
6087:
6086:
6057:
6045:
6041:
6035:
6031:
6029:
6025:
6024:
6013:
6009:
6003:
5999:
5997:
5995:
5992:
5991:
5948:
5936:
5932:
5926:
5922:
5920:
5916:
5915:
5914:
5910:
5904:
5900:
5880:
5877:
5876:
5833:
5821:
5817:
5811:
5807:
5805:
5801:
5800:
5799:
5795:
5789:
5785:
5779:
5775:
5761:
5758:
5757:
5720:
5715:
5696:
5691:
5686:
5682:
5676:
5671:
5661:
5657:
5643:
5640:
5639:
5626:
5623:
5617:
5616:
5614:
5609:
5579:
5572:
5568:
5562:
5558:
5549:
5545:
5539:
5535:
5534:
5532:
5516:
5503:
5498:
5479:
5474:
5469:
5467:
5461:
5456:
5446:
5442:
5434:
5431:
5430:
5397:
5382:
5378:
5376:
5372:
5371:
5365:
5361:
5353:
5349:
5348:
5341:
5337:
5336:
5324:
5321:
5320:
5294:
5279:
5275:
5273:
5269:
5268:
5262:
5258:
5250:
5247:
5246:
5207:
5202:
5192:
5188:
5180:
5171:
5167:
5162:
5159:
5158:
5106:
5103:
5102:
5049:
5045:
5044:
5037:
5033:
5032:
5020:
5017:
5016:
4957:
4953:
4935:
4931:
4911:
4908:
4907:
4862:
4853:
4849:
4837:
4832:
4822:
4818:
4816:
4813:
4812:
4780:
4768:
4764:
4759:
4755:
4754:
4742:
4738:
4733:
4729:
4727:
4724:
4723:
4697:
4682:
4678:
4676:
4672:
4671:
4656:
4652:
4647:
4643:
4641:
4638:
4637:
4608:
4596:
4592:
4587:
4583:
4582:
4567:
4563:
4558:
4554:
4552:
4549:
4548:
4539:
4529:
4526:
4520:
4519:
4517:
4516:
4487:
4483:
4478:
4474:
4452:
4450:
4432:
4428:
4423:
4419:
4411:
4408:
4407:
4398:
4395:
4389:
4383:
4380:
4374:
4344:
4342:
4323:
4321:
4301:
4298:
4297:
4288:
4225:
4222:
4221:
4211:
4147:
4144:
4143:
4129:
4124:
4119:
4110:
3996:
3993:
3992:
3978:
3968:
3962:
3900:
3897:
3896:
3881:
3875:
3869:
3860:
3854:
3803:
3800:
3799:
3784:
3778:
3772:
3766:
3756:
3750:
3688:
3685:
3684:
3672:
3669:
3649:
3643:
3626:engine knocking
3602:
3581:
3576:
3575:
3569:
3564:
3563:
3557:
3550:
3543:
3538:
3537:
3525:
3521:
3513:
3504:
3500:
3493:
3491:
3480:
3454:
3453:
3445:
3443:
3435:
3432:
3431:
3422:
3420:
3416:
3412:
3386:
3381:
3380:
3374:
3369:
3368:
3362:
3345:
3338:
3331:
3326:
3325:
3313:
3309:
3301:
3292:
3288:
3287:
3285:
3276:
3250:
3249:
3233:
3231:
3229:
3226:
3225:
3179:
3170:
3166:
3147:
3143:
3138:
3137:
3129:
3110:
3098:
3094:
3088:
3084:
3082:
3078:
3077:
3071:
3067:
3058:
3054:
3052:
3049:
3048:
3017:
3013:
3007:
3002:
3001:
2973:
2969:
2964:
2963:
2957:
2942:
2916:
2915:
2906:
2901:
2891:
2887:
2885:
2882:
2881:
2857:
2856:
2843:
2839:
2834:
2833:
2827:
2808:
2804:
2799:
2798:
2792:
2780:
2776:
2761:
2757:
2748:
2747:
2736:
2732:
2726:
2721:
2720:
2703:
2684:
2658:
2657:
2648:
2643:
2633:
2629:
2624:
2622:
2619:
2618:
2607:
2604:
2601:
2600:
2598:
2593:
2589:gasoline engine
2585:
2550:
2535:
2531:
2526:
2523:
2522:
2500:
2491:
2487:
2475:
2471:
2469:
2466:
2465:
2456:
2450:
2431:
2428:
2425:
2424:
2422:
2417:
2401:
2398:
2395:
2394:
2392:
2387:
2374:
2370:
2365:
2357:
2352:
2319:
2317:
2306:
2302:
2296:
2292:
2290:
2282:
2279:
2278:
2272:adiabatic index
2265:
2264:is volume, and
2259:
2253:
2231:
2222:
2218:
2213:
2210:
2209:
2191:internal energy
2183:
2177:
2044:
2031:
2023:
2006:
1986:
1979:
1968:
1956:
1949:
1942:
1932:
1917:
1907:
1900:
1890:
1884:
1877:
1862:
1855:
1844:
1836:
1831:
1828:
1825:
1820:
1819:
1817:
1812:
1809:constant volume
1798:
1788:
1785:Young's modulus
1766:
1763:
1644:
1599:
1598:
1574:
1566:
1565:
1564:
1424:
1416:
1415:
1394:
1380:
1355:
1351:
1344:
1340:
1333:
1329:
1296:
1289:
1271:
1252:Maxwell's demon
1214:
1185:
1184:
1168:
1167:
1166:
1119:
1116:
1115:
1114:
1064:
1061:
1060:
1059:
1009:
1006:
1005:
1004:
969:
966:
965:
964:
962:Internal energy
957:
942:
932:
931:
906:
881:
871:
870:
869:
843:
840:
839:
822:
819:
818:
796:
793:
792:
775:
772:
771:
747:
744:
743:
711:
708:
707:
690:
687:
686:
664:
661:
660:
643:
640:
639:
612:
609:
608:
603:Compressibility
576:
573:
572:
555:
552:
551:
529:
526:
525:
508:
505:
504:
480:
477:
476:
456:
446:
445:
426:Particle number
379:
338:
327:
317:
316:
275:Irreversibility
187:State of matter
154:Isolated system
139:
129:
128:
127:
102:
92:
91:
87:Non-equilibrium
79:
54:
46:
24:
17:
12:
11:
5:
10008:
9998:
9997:
9992:
9987:
9973:
9972:
9953:
9952:External links
9950:
9949:
9948:
9933:
9926:
9920:
9906:
9905:
9900:
9899:
9877:
9832:(10): 104110.
9812:
9770:
9751:(3): 936–938.
9731:
9724:
9706:
9699:
9678:
9658:
9638:
9615:
9593:
9573:
9563:Theory of Heat
9558:Maxwell, J. C.
9549:
9527:
9502:
9495:
9477:
9465:
9458:
9432:
9382:
9356:
9349:
9331:
9322:
9301:
9276:
9262:
9255:
9237:
9195:(3): 355–386.
9168:
9166:
9163:
9162:
9161:
9156:
9151:
9146:
9141:
9136:
9131:
9126:
9124:Cyclic process
9120:
9119:
9115:
9114:
9109:
9104:
9099:
9094:
9089:
9084:
9078:
9077:
9073:
9072:
9067:
9060:
9057:
9037:thermal energy
9010:
9009:
8998:
8994:
8991:
8988:
8984:
8981:
8978:
8973:
8968:
8964:
8958:
8955:
8952:
8947:
8942:
8938:
8932:
8929:
8926:
8921:
8916:
8912:
8831:
8825:
8821:state variable
8792:
8789:
8709:
8706:
8685:
8684:
8676:
8673:
8670:
8667:
8652:asymptotically
8650:Every adiabat
8620:
8617:
8616:
8615:
8604:
8598:
8594:
8591:
8588:
8581:
8574:
8570:
8564:
8560:
8554:
8547:
8543:
8539:
8534:
8530:
8518:
8517:
8506:
8503:
8500:
8494:
8490:
8487:
8484:
8477:
8470:
8466:
8460:
8456:
8450:
8445:
8442:
8439:
8432:
8428:
8422:
8418:
8404:
8403:
8392:
8388:
8384:
8381:
8375:
8371:
8368:
8365:
8358:
8351:
8347:
8341:
8337:
8331:
8325:
8319:
8315:
8311:
8306:
8302:
8298:
8293:
8289:
8274:
8273:
8262:
8258:
8254:
8251:
8245:
8241:
8238:
8235:
8228:
8221:
8217:
8211:
8207:
8201:
8195:
8189:
8185:
8181:
8178:
8175:
8172:
8169:
8164:
8160:
8156:
8151:
8147:
8143:
8140:
8137:
8134:
8120:
8119:
8108:
8104:
8100:
8097:
8091:
8087:
8084:
8081:
8074:
8067:
8063:
8057:
8053:
8047:
8041:
8035:
8031:
8027:
8024:
8021:
8018:
8015:
8012:
7992:
7991:
7980:
7973:
7969:
7963:
7959:
7953:
7946:
7943:
7938:
7933:
7926:
7922:
7916:
7912:
7906:
7890:
7889:
7878:
7873:
7870:
7865:
7858:
7854:
7848:
7844:
7838:
7833:
7826:
7822:
7816:
7812:
7795:
7794:
7783:
7779:
7775:
7772:
7767:
7764:
7761:
7756:
7749:
7745:
7739:
7735:
7729:
7723:
7717:
7713:
7709:
7706:
7703:
7700:
7697:
7694:
7680:
7679:
7668:
7664:
7660:
7657:
7652:
7649:
7646:
7641:
7634:
7630:
7624:
7620:
7614:
7608:
7602:
7598:
7592:
7588:
7584:
7581:
7578:
7575:
7561:
7560:
7549:
7545:
7539:
7536:
7533:
7528:
7524:
7520:
7515:
7512:
7509:
7504:
7500:
7495:
7489:
7484:
7480:
7474:
7470:
7466:
7463:
7460:
7457:
7416:
7415:
7404:
7398:
7395:
7392:
7385:
7381:
7375:
7371:
7367:
7362:
7358:
7352:
7348:
7341:
7335:
7332:
7329:
7322:
7319:
7316:
7311:
7307:
7303:
7298:
7295:
7292:
7287:
7283:
7274:
7269:
7265:
7259:
7255:
7251:
7248:
7234:
7233:
7222:
7219:
7216:
7210:
7205:
7200:
7195:
7191:
7185:
7178:
7174:
7166:
7162:
7154:
7150:
7145:
7141:
7138:
7124:
7123:
7112:
7107:
7102:
7097:
7092:
7088:
7082:
7075:
7071:
7067:
7064:
7048:
7047:
7038:
7036:
7025:
7020:
7015:
7011:
7005:
7001:
6997:
6989:
6984:
6980:
6976:
6958:
6957:
6948:
6946:
6935:
6932:
6929:
6926:
6923:
6920:
6902:
6901:
6892:
6890:
6879:
6876:
6873:
6869:
6862:
6858:
6850:
6846:
6841:
6837:
6834:
6818:
6817:
6810:
6807:
6806:
6805:
6794:
6788:
6784:
6781:
6778:
6771:
6764:
6760:
6754:
6750:
6744:
6737:
6733:
6729:
6724:
6720:
6708:
6707:
6696:
6693:
6690:
6684:
6680:
6677:
6674:
6667:
6660:
6656:
6650:
6646:
6640:
6635:
6632:
6629:
6622:
6618:
6612:
6608:
6594:
6593:
6582:
6578:
6574:
6571:
6565:
6561:
6558:
6555:
6548:
6541:
6537:
6531:
6527:
6521:
6515:
6509:
6505:
6501:
6496:
6492:
6488:
6483:
6479:
6464:
6463:
6452:
6448:
6444:
6441:
6435:
6431:
6428:
6425:
6418:
6411:
6407:
6401:
6397:
6391:
6385:
6379:
6375:
6371:
6368:
6365:
6362:
6359:
6354:
6350:
6346:
6341:
6337:
6333:
6330:
6327:
6324:
6310:
6309:
6298:
6294:
6290:
6287:
6281:
6277:
6274:
6271:
6264:
6257:
6253:
6247:
6243:
6237:
6231:
6225:
6221:
6217:
6214:
6211:
6208:
6205:
6202:
6182:
6181:
6170:
6163:
6159:
6153:
6149:
6143:
6136:
6133:
6128:
6123:
6116:
6112:
6106:
6102:
6096:
6080:
6079:
6068:
6063:
6060:
6055:
6048:
6044:
6038:
6034:
6028:
6023:
6016:
6012:
6006:
6002:
5985:
5984:
5973:
5969:
5965:
5962:
5957:
5954:
5951:
5946:
5939:
5935:
5929:
5925:
5919:
5913:
5907:
5903:
5899:
5896:
5893:
5890:
5887:
5884:
5870:
5869:
5858:
5854:
5850:
5847:
5842:
5839:
5836:
5831:
5824:
5820:
5814:
5810:
5804:
5798:
5792:
5788:
5782:
5778:
5774:
5771:
5768:
5765:
5751:
5750:
5739:
5735:
5729:
5726:
5723:
5718:
5714:
5710:
5705:
5702:
5699:
5694:
5690:
5685:
5679:
5674:
5670:
5664:
5660:
5656:
5653:
5650:
5647:
5606:
5605:
5594:
5588:
5585:
5582:
5575:
5571:
5565:
5561:
5557:
5552:
5548:
5542:
5538:
5531:
5525:
5522:
5519:
5512:
5509:
5506:
5501:
5497:
5493:
5488:
5485:
5482:
5477:
5473:
5464:
5459:
5455:
5449:
5445:
5441:
5438:
5424:
5423:
5412:
5409:
5406:
5400:
5395:
5390:
5385:
5381:
5375:
5368:
5364:
5356:
5352:
5344:
5340:
5335:
5331:
5328:
5314:
5313:
5302:
5297:
5292:
5287:
5282:
5278:
5272:
5265:
5261:
5257:
5254:
5238:
5237:
5228:
5226:
5215:
5210:
5205:
5201:
5195:
5191:
5187:
5179:
5174:
5170:
5166:
5148:
5147:
5138:
5136:
5125:
5122:
5119:
5116:
5113:
5110:
5092:
5091:
5082:
5080:
5069:
5066:
5063:
5059:
5052:
5048:
5040:
5036:
5031:
5027:
5024:
5006:
5005:
4996:
4994:
4983:
4980:
4977:
4974:
4971:
4968:
4965:
4960:
4956:
4952:
4949:
4946:
4943:
4938:
4934:
4930:
4927:
4924:
4921:
4918:
4915:
4902:
4901:
4890:
4886:
4883:
4880:
4877:
4874:
4871:
4868:
4865:
4861:
4856:
4852:
4848:
4845:
4840:
4835:
4831:
4825:
4821:
4806:
4805:
4794:
4791:
4788:
4783:
4778:
4771:
4767:
4763:
4758:
4752:
4745:
4741:
4737:
4732:
4717:
4716:
4705:
4700:
4695:
4690:
4685:
4681:
4675:
4670:
4666:
4659:
4655:
4651:
4646:
4631:
4630:
4619:
4614:
4611:
4606:
4599:
4595:
4591:
4586:
4581:
4577:
4570:
4566:
4562:
4557:
4513:
4512:
4501:
4497:
4490:
4486:
4482:
4477:
4473:
4470:
4465:
4461:
4458:
4455:
4449:
4446:
4442:
4435:
4431:
4427:
4422:
4418:
4415:
4393:
4378:
4371:
4370:
4359:
4354:
4350:
4347:
4341:
4338:
4333:
4329:
4326:
4320:
4317:
4314:
4311:
4308:
4305:
4285:
4284:
4273:
4270:
4267:
4263:
4260:
4257:
4254:
4251:
4247:
4244:
4241:
4238:
4235:
4232:
4229:
4208:
4207:
4196:
4193:
4190:
4186:
4183:
4180:
4177:
4174:
4170:
4167:
4164:
4161:
4158:
4154:
4151:
4127:
4117:
4105:
4104:
4095:
4093:
4082:
4079:
4076:
4073:
4069:
4066:
4063:
4060:
4056:
4053:
4050:
4047:
4044:
4041:
4038:
4035:
4032:
4028:
4025:
4022:
4019:
4015:
4012:
4009:
4006:
4003:
4000:
3957:
3956:
3947:
3945:
3934:
3931:
3928:
3925:
3922:
3919:
3916:
3913:
3910:
3907:
3904:
3849:
3848:
3839:
3837:
3826:
3823:
3820:
3816:
3813:
3810:
3807:
3745:
3744:
3735:
3733:
3722:
3719:
3716:
3713:
3710:
3707:
3704:
3701:
3698:
3695:
3692:
3668:
3659:Derivation of
3657:
3647:Free expansion
3642:
3639:
3621:
3620:
3609:
3598:
3595:
3587:
3584:
3572:
3553:
3546:
3531:
3528:
3524:
3520:
3507:
3503:
3499:
3496:
3490:
3483:
3478:
3475:
3472:
3469:
3466:
3463:
3460:
3457:
3451:
3448:
3442:
3439:
3409:
3408:
3397:
3392:
3389:
3377:
3358:
3355:
3341:
3334:
3319:
3316:
3312:
3308:
3295:
3291:
3284:
3279:
3274:
3271:
3268:
3265:
3262:
3259:
3256:
3253:
3248:
3243:
3239:
3236:
3195:
3194:
3173:
3169:
3165:
3162:
3159:
3154:
3150:
3146:
3136:
3125:
3121:
3118:
3113:
3108:
3101:
3097:
3091:
3087:
3081:
3074:
3070:
3066:
3061:
3057:
3042:
3041:
3030:
3024:
3021:
3016:
3010:
2997:
2994:
2991:
2988:
2985:
2980:
2976:
2972:
2953:
2950:
2945:
2940:
2937:
2934:
2931:
2928:
2925:
2922:
2919:
2914:
2909:
2904:
2900:
2894:
2890:
2871:
2870:
2855:
2850:
2846:
2842:
2823:
2820:
2815:
2811:
2807:
2786:
2783:
2779:
2775:
2772:
2769:
2764:
2760:
2756:
2753:
2751:
2749:
2743:
2740:
2735:
2729:
2716:
2713:
2710:
2699:
2695:
2692:
2687:
2682:
2679:
2676:
2673:
2670:
2667:
2664:
2661:
2656:
2651:
2646:
2642:
2636:
2632:
2628:
2626:
2584:
2581:
2569:
2568:
2557:
2549:
2544:
2541:
2538:
2534:
2530:
2519:
2518:
2507:
2499:
2494:
2490:
2484:
2481:
2478:
2474:
2368:
2355:
2349:
2348:
2337:
2332:
2328:
2325:
2322:
2316:
2309:
2305:
2299:
2295:
2289:
2286:
2250:
2249:
2238:
2230:
2225:
2221:
2217:
2179:Main article:
2176:
2173:
2132:magnetic field
2082:Katabatic wind
2067:diesel engines
2048:free expansion
2043:
2040:
1999:
1998:
1976:
1939:
1914:
1854:
1851:
1834:
1823:
1762:
1759:
1709:thermodynamics
1646:
1645:
1643:
1642:
1635:
1628:
1620:
1617:
1616:
1615:
1614:
1601:
1600:
1597:
1596:
1591:
1586:
1581:
1575:
1572:
1571:
1568:
1567:
1563:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1527:
1522:
1517:
1512:
1507:
1502:
1497:
1492:
1487:
1482:
1477:
1472:
1467:
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1426:
1425:
1422:
1421:
1418:
1417:
1412:
1411:
1410:
1409:
1404:
1396:
1395:
1393:
1392:
1389:
1385:
1382:
1381:
1379:
1378:
1373:
1371:Thermodynamics
1367:
1364:
1363:
1359:
1358:
1357:
1356:
1347:
1345:
1336:
1334:
1325:
1320:
1319:
1313:
1312:
1311:
1310:
1305:
1300:
1288:
1287:
1285:Caloric theory
1281:
1278:
1277:
1273:
1272:
1270:
1269:
1264:
1259:
1254:
1249:
1244:
1239:
1233:
1230:
1229:
1223:
1222:
1221:
1220:
1213:
1212:
1207:
1202:
1196:
1193:
1192:
1186:
1183:
1182:
1179:
1175:
1174:
1173:
1170:
1169:
1165:
1164:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1109:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1074:
1071:
1068:
1054:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1013:
999:
988:
985:
982:
979:
976:
973:
958:
956:
955:
950:
944:
943:
938:
937:
934:
933:
930:
929:
922:
917:
912:
905:
904:
899:
894:
889:
883:
882:
877:
876:
873:
872:
866:
865:
862:
861:
850:
847:
837:
826:
815:
814:
803:
800:
790:
779:
765:
754:
751:
741:
734:
733:
730:
729:
718:
715:
705:
694:
683:
682:
671:
668:
658:
647:
633:
622:
619:
616:
606:
599:
598:
595:
594:
583:
580:
570:
559:
548:
547:
536:
533:
523:
512:
498:
487:
484:
474:
465:
464:
463:
457:
452:
451:
448:
447:
442:
441:
440:
439:
434:
429:
418:
407:
388:
387:
381:
380:
378:
377:
372:
366:
363:
362:
356:
355:
354:
353:
348:
329:
328:
323:
322:
319:
318:
313:
312:
311:
310:
305:
300:
292:
291:
285:
284:
283:
282:
277:
272:
267:
265:Free expansion
262:
257:
252:
247:
242:
237:
232:
227:
219:
218:
212:
211:
210:
209:
204:
202:Control volume
199:
194:
192:Phase (matter)
189:
184:
179:
174:
166:
165:
157:
156:
151:
146:
140:
135:
134:
131:
130:
126:
125:
120:
115:
110:
104:
103:
98:
97:
94:
93:
90:
89:
78:
77:
72:
67:
62:
56:
55:
52:
51:
48:
47:
42:The classical
41:
33:
32:
30:Thermodynamics
15:
9:
6:
4:
3:
2:
10007:
9996:
9993:
9991:
9988:
9986:
9983:
9982:
9980:
9971:
9968:
9967:
9966:
9964:
9959:
9946:
9942:
9938:
9934:
9931:
9927:
9923:
9917:
9913:
9908:
9907:
9903:
9902:
9887:
9881:
9873:
9869:
9865:
9861:
9857:
9853:
9848:
9843:
9839:
9835:
9831:
9827:
9823:
9816:
9806:
9801:
9797:
9793:
9789:
9785:
9781:
9774:
9766:
9762:
9758:
9754:
9750:
9746:
9742:
9735:
9727:
9721:
9717:
9710:
9702:
9700:0-88318-797-3
9696:
9692:
9685:
9683:
9674:
9673:
9668:
9662:
9654:
9653:
9648:
9642:
9635:
9630:
9626:
9619:
9613:
9608:
9604:
9597:
9590:
9586:
9582:
9581:Liddell, H.G.
9577:
9570:, p. 129
9569:
9565:
9564:
9559:
9553:
9546:, p. 122
9545:
9541:
9537:
9531:
9524:
9523:
9518:
9514:
9509:
9507:
9498:
9496:0-7167-8759-8
9492:
9488:
9481:
9474:
9469:
9461:
9459:0-521-66624-4
9455:
9451:
9446:
9445:
9436:
9421:
9417:
9413:
9409:
9405:
9401:
9397:
9393:
9386:
9371:
9367:
9360:
9352:
9350:0-471-62430-6
9346:
9342:
9335:
9326:
9319:
9315:
9311:
9305:
9290:
9286:
9280:
9271:
9269:
9267:
9258:
9256:0-88318-797-3
9252:
9248:
9241:
9233:
9227:
9223:
9219:
9216:
9210:
9206:
9202:
9198:
9194:
9190:
9186:
9182:
9176:
9174:
9169:
9160:
9157:
9155:
9152:
9150:
9147:
9145:
9142:
9140:
9137:
9135:
9132:
9130:
9127:
9125:
9122:
9121:
9117:
9116:
9113:
9110:
9108:
9105:
9103:
9100:
9098:
9095:
9093:
9090:
9088:
9085:
9083:
9080:
9079:
9075:
9074:
9071:
9068:
9066:
9063:
9062:
9056:
9052:
9050:
9044:
9041:
9038:
9032:
9030:
9026:
9022:
9018:
9013:
8996:
8992:
8989:
8986:
8982:
8979:
8976:
8971:
8966:
8962:
8956:
8953:
8950:
8945:
8940:
8936:
8930:
8927:
8924:
8919:
8914:
8910:
8902:
8901:
8900:
8897:
8893:
8892:adiabatically
8888:
8886:
8882:
8878:
8874:
8871:
8867:
8863:
8859:
8857:
8853:
8849:
8844:
8842:
8837:
8830:
8824:
8822:
8816:
8812:
8810:
8805:
8804:mass transfer
8800:
8798:
8788:
8786:
8781:
8779:
8775:
8771:
8767:
8763:
8757:
8715:
8705:
8702:
8699:
8696:
8694:
8690:
8682:
8677:
8674:
8671:
8668:
8665:
8661:
8658:axis and the
8657:
8653:
8649:
8648:
8647:
8645:
8641:
8637:
8633:
8625:
8602:
8596:
8592:
8589:
8586:
8579:
8572:
8568:
8562:
8558:
8552:
8545:
8541:
8537:
8532:
8528:
8520:
8519:
8504:
8501:
8498:
8492:
8488:
8485:
8482:
8475:
8468:
8464:
8458:
8454:
8448:
8443:
8440:
8437:
8430:
8426:
8420:
8416:
8406:
8405:
8390:
8386:
8382:
8379:
8373:
8369:
8366:
8363:
8356:
8349:
8345:
8339:
8335:
8329:
8323:
8317:
8313:
8309:
8304:
8300:
8296:
8291:
8287:
8279:
8278:
8277:
8276:Simplifying,
8260:
8256:
8252:
8249:
8243:
8239:
8236:
8233:
8226:
8219:
8215:
8209:
8205:
8199:
8193:
8187:
8183:
8179:
8176:
8173:
8170:
8162:
8158:
8154:
8149:
8145:
8138:
8135:
8132:
8125:
8124:
8123:
8106:
8102:
8098:
8095:
8089:
8085:
8082:
8079:
8072:
8065:
8061:
8055:
8051:
8045:
8039:
8033:
8029:
8025:
8022:
8019:
8016:
8013:
8010:
8003:
8002:
8001:
7998:
7978:
7971:
7967:
7961:
7957:
7951:
7944:
7941:
7936:
7931:
7924:
7920:
7914:
7910:
7904:
7895:
7894:
7893:
7876:
7871:
7868:
7863:
7856:
7852:
7846:
7842:
7836:
7831:
7824:
7820:
7814:
7810:
7800:
7799:
7798:
7781:
7777:
7773:
7770:
7765:
7762:
7759:
7754:
7747:
7743:
7737:
7733:
7727:
7721:
7715:
7711:
7707:
7704:
7701:
7698:
7695:
7692:
7685:
7684:
7683:
7666:
7662:
7658:
7655:
7650:
7647:
7644:
7639:
7632:
7628:
7622:
7618:
7612:
7606:
7600:
7596:
7590:
7586:
7582:
7579:
7576:
7573:
7566:
7565:
7564:
7563:Rearranging,
7547:
7543:
7537:
7534:
7531:
7526:
7522:
7518:
7513:
7510:
7507:
7502:
7498:
7493:
7487:
7482:
7478:
7472:
7468:
7464:
7461:
7458:
7455:
7448:
7447:
7446:
7439:
7430:
7422:
7418:Substituting
7402:
7396:
7393:
7390:
7383:
7379:
7373:
7369:
7365:
7360:
7356:
7350:
7346:
7339:
7333:
7330:
7327:
7320:
7317:
7314:
7309:
7305:
7301:
7296:
7293:
7290:
7285:
7281:
7272:
7267:
7263:
7257:
7253:
7249:
7246:
7239:
7238:
7237:
7220:
7217:
7214:
7208:
7203:
7198:
7193:
7189:
7183:
7176:
7172:
7164:
7160:
7152:
7148:
7143:
7139:
7136:
7129:
7128:
7127:
7110:
7105:
7100:
7095:
7090:
7086:
7080:
7073:
7069:
7065:
7062:
7055:
7054:
7053:
7046:
7039:
7037:
7023:
7018:
7013:
7009:
7003:
6999:
6995:
6987:
6982:
6978:
6974:
6967:
6966:
6963:
6956:
6949:
6947:
6933:
6930:
6927:
6924:
6921:
6911:
6910:
6907:
6900:
6893:
6891:
6877:
6874:
6871:
6867:
6860:
6856:
6848:
6844:
6839:
6835:
6832:
6825:
6824:
6821:
6816:
6815:
6814:
6792:
6786:
6782:
6779:
6776:
6769:
6762:
6758:
6752:
6748:
6742:
6735:
6731:
6727:
6722:
6718:
6710:
6709:
6694:
6691:
6688:
6682:
6678:
6675:
6672:
6665:
6658:
6654:
6648:
6644:
6638:
6633:
6630:
6627:
6620:
6616:
6610:
6606:
6596:
6595:
6580:
6576:
6572:
6569:
6563:
6559:
6556:
6553:
6546:
6539:
6535:
6529:
6525:
6519:
6513:
6507:
6503:
6499:
6494:
6490:
6486:
6481:
6477:
6469:
6468:
6467:
6466:Simplifying,
6450:
6446:
6442:
6439:
6433:
6429:
6426:
6423:
6416:
6409:
6405:
6399:
6395:
6389:
6383:
6377:
6373:
6369:
6366:
6363:
6360:
6352:
6348:
6344:
6339:
6335:
6328:
6325:
6322:
6315:
6314:
6313:
6296:
6292:
6288:
6285:
6279:
6275:
6272:
6269:
6262:
6255:
6251:
6245:
6241:
6235:
6229:
6223:
6219:
6215:
6212:
6209:
6206:
6203:
6200:
6193:
6192:
6191:
6188:
6168:
6161:
6157:
6151:
6147:
6141:
6134:
6131:
6126:
6121:
6114:
6110:
6104:
6100:
6094:
6085:
6084:
6083:
6066:
6061:
6058:
6053:
6046:
6042:
6036:
6032:
6026:
6021:
6014:
6010:
6004:
6000:
5990:
5989:
5988:
5971:
5967:
5963:
5960:
5955:
5952:
5949:
5944:
5937:
5933:
5927:
5923:
5917:
5911:
5905:
5901:
5897:
5894:
5891:
5888:
5885:
5882:
5875:
5874:
5873:
5856:
5852:
5848:
5845:
5840:
5837:
5834:
5829:
5822:
5818:
5812:
5808:
5802:
5796:
5790:
5786:
5780:
5776:
5772:
5769:
5766:
5763:
5756:
5755:
5754:
5753:Rearranging,
5737:
5733:
5727:
5724:
5721:
5716:
5712:
5708:
5703:
5700:
5697:
5692:
5688:
5683:
5677:
5672:
5668:
5662:
5658:
5654:
5651:
5648:
5645:
5638:
5637:
5636:
5629:
5620:
5612:
5608:Substituting
5592:
5586:
5583:
5580:
5573:
5569:
5563:
5559:
5555:
5550:
5546:
5540:
5536:
5529:
5523:
5520:
5517:
5510:
5507:
5504:
5499:
5495:
5491:
5486:
5483:
5480:
5475:
5471:
5462:
5457:
5453:
5447:
5443:
5439:
5436:
5429:
5428:
5427:
5410:
5407:
5404:
5398:
5393:
5388:
5383:
5379:
5373:
5366:
5362:
5354:
5350:
5342:
5338:
5333:
5329:
5326:
5319:
5318:
5317:
5300:
5295:
5290:
5285:
5280:
5276:
5270:
5263:
5259:
5255:
5252:
5245:
5244:
5243:
5236:
5229:
5227:
5213:
5208:
5203:
5199:
5193:
5189:
5185:
5177:
5172:
5168:
5164:
5157:
5156:
5153:
5146:
5139:
5137:
5123:
5120:
5117:
5114:
5111:
5101:
5100:
5097:
5090:
5083:
5081:
5067:
5064:
5061:
5057:
5050:
5046:
5038:
5034:
5029:
5025:
5022:
5015:
5014:
5011:
5004:
4997:
4995:
4981:
4978:
4972:
4969:
4966:
4963:
4958:
4954:
4950:
4947:
4944:
4941:
4936:
4932:
4928:
4925:
4922:
4919:
4916:
4906:
4905:
4888:
4859:
4854:
4850:
4846:
4843:
4838:
4833:
4829:
4823:
4819:
4811:
4810:
4809:
4792:
4789:
4786:
4781:
4776:
4769:
4765:
4761:
4756:
4750:
4743:
4739:
4735:
4730:
4722:
4721:
4720:
4703:
4698:
4693:
4688:
4683:
4679:
4673:
4668:
4664:
4657:
4653:
4649:
4644:
4636:
4635:
4634:
4617:
4612:
4609:
4604:
4597:
4593:
4589:
4584:
4579:
4575:
4568:
4564:
4560:
4555:
4547:
4546:
4545:
4542:
4532:
4523:
4499:
4495:
4488:
4484:
4480:
4475:
4471:
4468:
4463:
4459:
4456:
4453:
4447:
4444:
4440:
4433:
4429:
4425:
4420:
4416:
4413:
4406:
4405:
4404:
4401:
4392:
4386:
4377:
4357:
4352:
4348:
4345:
4339:
4336:
4331:
4327:
4324:
4315:
4312:
4309:
4303:
4296:
4295:
4294:
4291:
4271:
4268:
4265:
4261:
4258:
4255:
4252:
4249:
4245:
4239:
4236:
4233:
4227:
4220:
4219:
4218:
4215:
4194:
4191:
4188:
4184:
4181:
4178:
4175:
4172:
4168:
4165:
4162:
4159:
4156:
4152:
4149:
4142:
4141:
4140:
4137:
4134:
4130:
4121:
4113:
4103:
4096:
4094:
4080:
4074:
4071:
4067:
4064:
4061:
4058:
4054:
4048:
4045:
4039:
4036:
4030:
4026:
4023:
4020:
4017:
4013:
4010:
4007:
4004:
4001:
3998:
3991:
3990:
3987:
3984:
3981:
3976:
3971:
3965:
3955:
3948:
3946:
3932:
3929:
3926:
3923:
3920:
3917:
3914:
3911:
3908:
3905:
3902:
3895:
3894:
3891:
3888:
3884:
3878:
3872:
3866:
3863:
3857:
3847:
3840:
3838:
3824:
3821:
3818:
3814:
3811:
3808:
3805:
3798:
3797:
3794:
3792:
3787:
3781:
3775:
3769:
3764:
3761:is work done
3759:
3753:
3743:
3736:
3734:
3720:
3717:
3714:
3711:
3708:
3705:
3702:
3699:
3696:
3693:
3690:
3683:
3682:
3679:
3675:
3666:
3662:
3656:
3654:
3648:
3638:
3635:
3631:
3627:
3607:
3596:
3593:
3585:
3582:
3570:
3551:
3544:
3529:
3526:
3522:
3518:
3505:
3501:
3497:
3494:
3488:
3481:
3449:
3446:
3440:
3437:
3430:
3429:
3428:
3395:
3390:
3387:
3375:
3356:
3353:
3339:
3332:
3317:
3314:
3310:
3306:
3293:
3289:
3282:
3277:
3246:
3241:
3237:
3234:
3224:
3223:
3222:
3220:
3216:
3212:
3208:
3205: =
3204:
3199:
3171:
3167:
3163:
3160:
3157:
3152:
3148:
3144:
3134:
3123:
3119:
3116:
3111:
3106:
3099:
3095:
3089:
3085:
3079:
3072:
3068:
3064:
3059:
3055:
3047:
3046:
3045:
3028:
3022:
3019:
3008:
2995:
2989:
2986:
2983:
2978:
2974:
2970:
2951:
2948:
2943:
2912:
2907:
2902:
2898:
2892:
2888:
2880:
2879:
2878:
2874:
2853:
2848:
2844:
2840:
2821:
2818:
2813:
2809:
2805:
2784:
2781:
2777:
2773:
2770:
2767:
2762:
2758:
2754:
2752:
2741:
2738:
2727:
2714:
2708:
2697:
2693:
2690:
2685:
2654:
2649:
2644:
2640:
2634:
2630:
2617:
2616:
2615:
2596:
2590:
2580:
2578:
2574:
2555:
2547:
2542:
2539:
2536:
2532:
2528:
2521:
2520:
2505:
2497:
2492:
2488:
2482:
2479:
2476:
2472:
2464:
2463:
2462:
2459:
2453:
2447:
2445:
2441:
2440:Bose–Einstein
2420:
2415:
2411:
2390:
2384:
2382:
2377:
2371:
2363:
2362:specific heat
2358:
2335:
2330:
2326:
2323:
2320:
2314:
2307:
2303:
2297:
2293:
2287:
2284:
2277:
2276:
2275:
2273:
2268:
2262:
2258:is pressure,
2256:
2236:
2228:
2223:
2219:
2215:
2208:
2207:
2206:
2204:
2200:
2192:
2187:
2182:
2172:
2168:
2166:
2162:
2161:ideal gas law
2157:
2155:
2150:
2148:
2143:
2141:
2137:
2133:
2129:
2124:
2122:
2121:Sahara desert
2117:
2115:
2111:
2107:
2103:
2098:
2094:
2091:
2087:
2083:
2079:
2075:
2070:
2068:
2063:
2059:
2055:
2053:
2049:
2039:
2035:
2027:
2021:
2016:
2013:
2009:
2002:
1996:
1990:
1982:
1977:
1972:
1965:
1959:
1952:
1945:
1940:
1935:
1930:
1926:
1920:
1915:
1910:
1903:
1898:
1897:
1896:
1893:
1887:
1881:
1874:
1870:
1866:
1860:
1850:
1847:
1837:
1826:
1815:
1810:
1806:
1801:
1795:
1791:
1786:
1782:
1778:
1773:
1769:
1758:
1756:
1752:
1748:
1744:
1740:
1736:
1731:
1729:
1725:
1720:
1718:
1714:
1710:
1706:
1702:
1698:
1694:
1690:
1686:
1682:
1678:
1675:
1668:
1664:
1661:
1660:Ancient Greek
1657:
1653:
1641:
1636:
1634:
1629:
1627:
1622:
1621:
1619:
1618:
1613:
1605:
1604:
1603:
1602:
1595:
1592:
1590:
1587:
1585:
1584:Self-assembly
1582:
1580:
1577:
1576:
1570:
1569:
1561:
1558:
1556:
1555:van der Waals
1553:
1551:
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1526:
1523:
1521:
1518:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1480:von Helmholtz
1478:
1476:
1473:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1427:
1420:
1419:
1408:
1405:
1403:
1400:
1399:
1398:
1397:
1390:
1387:
1386:
1384:
1383:
1377:
1374:
1372:
1369:
1368:
1366:
1365:
1361:
1360:
1354:
1353:
1346:
1343:
1342:
1335:
1332:
1331:
1324:
1323:
1322:
1321:
1318:
1315:
1314:
1309:
1306:
1304:
1301:
1299:
1295:
1291:
1290:
1286:
1283:
1282:
1280:
1279:
1275:
1274:
1268:
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1234:
1232:
1231:
1228:
1225:
1224:
1219:
1216:
1215:
1211:
1208:
1206:
1203:
1201:
1198:
1197:
1195:
1194:
1190:
1189:
1180:
1177:
1176:
1172:
1171:
1151:
1148:
1145:
1142:
1139:
1133:
1130:
1127:
1121:
1113:
1110:
1096:
1093:
1090:
1087:
1084:
1078:
1075:
1072:
1066:
1058:
1055:
1041:
1038:
1035:
1032:
1029:
1023:
1020:
1017:
1011:
1003:
1000:
983:
980:
977:
971:
963:
960:
959:
954:
951:
949:
946:
945:
941:
936:
935:
928:
927:
923:
921:
918:
916:
913:
911:
908:
907:
903:
902:Ideal gas law
900:
898:
895:
893:
890:
888:
885:
884:
880:
875:
874:
848:
838:
824:
817:
816:
801:
791:
777:
770:
769:
766:
752:
749:
742:
739:
736:
735:
716:
706:
692:
685:
684:
669:
659:
645:
638:
637:
634:
620:
617:
614:
607:
604:
601:
600:
581:
571:
557:
550:
549:
534:
524:
510:
503:
502:
499:
485:
482:
475:
472:
469:
468:
462:
459:
458:
455:
450:
449:
438:
435:
433:
432:Vapor quality
430:
428:
427:
422:
419:
417:
416:
411:
408:
405:
401:
400:
395:
392:
391:
390:
389:
386:
383:
382:
376:
373:
371:
368:
367:
365:
364:
361:
358:
357:
352:
349:
347:
344:
343:
342:
341:
337:
333:
326:
321:
320:
309:
306:
304:
301:
299:
296:
295:
294:
293:
290:
287:
286:
281:
278:
276:
273:
271:
270:Reversibility
268:
266:
263:
261:
258:
256:
253:
251:
248:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
222:
221:
220:
217:
214:
213:
208:
205:
203:
200:
198:
195:
193:
190:
188:
185:
183:
180:
178:
175:
173:
170:
169:
168:
167:
164:
161:
160:
155:
152:
150:
147:
145:
144:Closed system
142:
141:
138:
133:
132:
124:
121:
119:
116:
114:
111:
109:
106:
105:
101:
96:
95:
88:
84:
81:
80:
76:
73:
71:
68:
66:
63:
61:
58:
57:
50:
49:
45:
39:
35:
34:
31:
28:
27:
22:
9955:
9911:
9890:. Retrieved
9880:
9829:
9825:
9815:
9787:
9783:
9773:
9748:
9744:
9734:
9715:
9709:
9690:
9671:
9661:
9651:
9647:Bryan, G. H.
9641:
9628:
9624:
9618:
9606:
9602:
9596:
9588:
9576:
9562:
9552:
9539:
9530:
9520:
9517:The Engineer
9516:
9486:
9480:
9468:
9443:
9435:
9423:. Retrieved
9399:
9395:
9385:
9373:. Retrieved
9369:
9359:
9340:
9334:
9325:
9317:
9313:
9304:
9292:. Retrieved
9279:
9246:
9240:
9231:
9192:
9188:
9053:
9045:
9042:
9033:
9028:
9024:
9014:
9011:
8891:
8889:
8885:quasi-static
8876:
8869:
8860:
8851:
8845:
8840:
8835:
8833:
8828:
8817:
8813:
8801:
8794:
8785:privative ἀ-
8782:
8713:
8711:
8703:
8700:
8697:
8692:
8688:
8686:
8659:
8655:
8643:
8639:
8635:
8629:
8275:
8121:
7996:
7993:
7891:
7796:
7681:
7562:
7437:
7428:
7420:
7417:
7235:
7125:
7051:
7040:
6961:
6950:
6905:
6894:
6819:
6812:
6465:
6311:
6186:
6183:
6081:
5986:
5871:
5752:
5627:
5618:
5610:
5607:
5425:
5315:
5241:
5230:
5151:
5140:
5095:
5084:
5009:
4998:
4807:
4718:
4632:
4540:
4530:
4521:
4514:
4399:
4390:
4384:
4375:
4372:
4289:
4286:
4213:
4209:
4138:
4132:
4125:
4115:
4111:
4108:
4097:
3985:
3979:
3969:
3963:
3960:
3949:
3886:
3882:
3876:
3870:
3867:
3861:
3855:
3852:
3841:
3790:
3785:
3779:
3773:
3767:
3762:
3757:
3751:
3748:
3737:
3673:
3670:
3664:
3660:
3650:
3630:supercharger
3622:
3410:
3218:
3214:
3210:
3206:
3202:
3200:
3196:
3043:
2875:
2872:
2594:
2586:
2572:
2570:
2457:
2451:
2448:
2418:
2388:
2385:
2375:
2366:
2353:
2350:
2266:
2260:
2254:
2251:
2196:
2169:
2158:
2151:
2144:
2125:
2118:
2096:
2095:
2090:Chinook wind
2071:
2057:
2056:
2045:
2033:
2025:
2017:
2011:
2007:
2003:
2000:
1988:
1980:
1970:
1957:
1950:
1943:
1933:
1918:
1908:
1901:
1891:
1885:
1879:
1872:
1868:
1864:
1856:
1845:
1832:
1821:
1813:
1799:
1793:
1789:
1774:
1767:
1764:
1751:precipitates
1746:
1732:
1721:
1716:
1699:. Unlike an
1691:between the
1673:
1670:
1663:
1655:
1651:
1649:
1445:Carathéodory
1376:Heat engines
1348:
1337:
1326:
1308:Motive power
1293:
953:Free entropy
924:
424:
423: /
413:
412: /
404:introduction
397:
396: /
335:
298:Heat engines
239:
85: /
9892:24 November
9444:Geodynamics
9425:18 February
9406:: 404–413.
9294:November 3,
9112:Berry phase
9065:Fire piston
4719:Therefore,
3634:intercooler
2444:Fermi gases
2154:lithosphere
2147:kimberlites
1761:Description
1755:latent heat
1739:water vapor
1735:meteorology
1697:environment
1267:Synergetics
948:Free energy
394:Temperature
255:Quasistatic
250:Isenthalpic
207:Instruments
197:Equilibrium
149:Open system
83:Equilibrium
65:Statistical
9979:Categories
9631:: 115–175.
9609:: 115–175.
9165:References
9070:Heat burst
8881:isentropic
4210:factorize
3645:See also:
3425:10 Pa
2086:Foehn wind
2052:isothermal
1579:Nucleation
1423:Scientists
1227:Philosophy
940:Potentials
303:Heat pumps
260:Polytropic
245:Isentropic
235:Isothermal
9872:212731108
9856:0021-9606
9765:0008-4042
9585:Scott, R.
9310:Tisza, L.
9209:118230148
9025:adiabatic
8877:adiabatic
8870:adiabatic
8841:adiabatic
8836:adiabatic
8829:adiabatic
8714:adiabatic
8712:The term
8708:Etymology
8664:isotherms
8597:γ
8590:−
8587:γ
8499:−
8493:γ
8486:−
8483:γ
8438:−
8380:−
8374:γ
8367:−
8364:γ
8297:−
8250:−
8244:γ
8237:−
8234:γ
8174:α
8155:−
8133:α
8096:−
8090:γ
8083:−
8080:γ
8020:α
8017:−
7945:γ
7937:−
7872:γ
7869:−
7771:−
7766:γ
7763:−
7702:α
7699:−
7656:−
7651:γ
7648:−
7583:α
7580:−
7538:γ
7535:−
7519:−
7514:γ
7511:−
7488:γ
7465:α
7462:−
7397:γ
7394:−
7366:−
7334:γ
7331:−
7321:γ
7318:−
7302:−
7297:γ
7294:−
7273:γ
7209:γ
7144:∫
7106:γ
7019:γ
6983:γ
6919:Δ
6840:∫
6787:γ
6780:−
6777:γ
6689:−
6683:γ
6676:−
6673:γ
6628:−
6570:−
6564:γ
6557:−
6554:γ
6487:−
6440:−
6434:γ
6427:−
6424:γ
6364:α
6345:−
6323:α
6286:−
6280:γ
6273:−
6270:γ
6210:α
6207:−
6135:γ
6127:−
6062:γ
6059:−
5961:−
5956:γ
5953:−
5892:α
5889:−
5846:−
5841:γ
5838:−
5773:α
5770:−
5728:γ
5725:−
5709:−
5704:γ
5701:−
5678:γ
5655:α
5652:−
5587:γ
5584:−
5556:−
5524:γ
5521:−
5511:γ
5508:−
5492:−
5487:γ
5484:−
5463:γ
5399:γ
5334:∫
5296:γ
5209:γ
5173:γ
5109:Δ
5030:∫
4976:Δ
4967:α
4945:α
4942:−
4923:α
4914:Δ
4855:γ
4839:γ
4782:γ
4699:γ
4613:γ
4610:−
4472:
4464:α
4454:α
4448:−
4417:
4388:and from
4340:α
4310:α
4304:−
4259:α
4234:α
4228:−
4182:α
4166:α
4150:−
4049:α
4027:α
4008:α
3924:α
3909:α
3853:However,
3806:δ
3709:δ
3700:δ
3653:ideal gas
3583:−
3527:−
3519:×
3498:×
3388:−
3315:−
3307:×
3164:×
3135:×
3112:γ
2990:×
2908:γ
2782:−
2774:×
2768:×
2709:×
2650:γ
2540:−
2537:γ
2493:γ
2483:γ
2480:−
2285:γ
2224:γ
2205:equation
2199:ideal gas
2163:, or the
2106:lee waves
2020:isochoric
1925:isochoric
1674:adiábatos
1667:ἀδιάβατος
1658:from
1656:adiabatic
1560:Waterston
1510:von Mayer
1465:de Donder
1455:Clapeyron
1435:Boltzmann
1430:Bernoulli
1391:Education
1362:Timelines
1146:−
1091:−
879:Equations
846:∂
799:∂
750:α
714:∂
667:∂
621:−
615:β
579:∂
532:∂
240:Adiabatic
230:Isochoric
216:Processes
177:Ideal gas
60:Classical
9941:Archived
9864:32171229
9669:(1949).
9667:Born, M.
9649:(1907).
9587:(1940).
9560:(1871),
9538:(1949),
9404:Elsevier
9312:(1966).
9218:Archived
9183:(1909).
9059:See also
9029:diabatic
8896:Max Born
8766:Xenophon
6992:constant
5182:constant
4123:because
3632:with an
3419: =
2552:constant
2502:constant
2410:nitrogen
2233:constant
2078:air mass
2076:when an
1876:, where
1797:, where
1717:diabatic
1695:and its
1612:Category
1550:Thompson
1460:Clausius
1440:Bridgman
1294:Vis viva
1276:Theories
1210:Gas laws
1002:Enthalpy
410:Pressure
225:Isobaric
182:Real gas
70:Chemical
53:Branches
9995:Entropy
9904:General
9834:Bibcode
9792:Bibcode
9408:Bibcode
9402:(3–4).
9375:3 March
8856:Laidler
8848:Pippard
8774:Maxwell
8770:Rankine
8632:entropy
7442:
7425:
5632:
5615:
4535:
4518:
3973:is the
2611:
2599:
2435:
2423:
2405:
2393:
2360:is the
2270:is the
1929:viscous
1840:
1818:
1803:is the
1777:Laplace
1535:Smeaton
1530:Rankine
1520:Onsager
1505:Maxwell
1500:Massieu
1205:Entropy
1200:General
1191:History
1181:Culture
1178:History
402: (
399:Entropy
336:italics
137:Systems
9918:
9870:
9862:
9854:
9784:Nature
9763:
9722:
9697:
9493:
9456:
9347:
9253:
9207:
3961:where
3749:where
3600:
3555:
3535:
3511:
3360:
3343:
3323:
3299:
3221:) is:
3177:
3127:
2999:
2996:0.0001
2955:
2825:
2790:
2718:
2701:
2571:where
2414:oxygen
2252:where
2062:piston
2050:is an
2036:> 0
2022:work (
1991:> 0
1985:, and
1983:> 0
1960:< 0
1936:< 0
1911:> 0
1843:) and
1525:Planck
1515:Nernst
1490:Kelvin
1450:Carnot
740:
605:
473:
415:Volume
330:Note:
289:Cycles
118:Second
108:Zeroth
9868:S2CID
9205:S2CID
8797:Joule
8762:Greek
4538:with
3789:done
3552:0.333
3357:0.333
2715:0.001
2351:Here
2110:pilei
2088:, or
1728:flame
1662:
1573:Other
1540:Stahl
1495:Lewis
1485:Joule
1475:Gibbs
1470:Duhem
163:State
123:Third
113:First
9916:ISBN
9894:2020
9860:PMID
9852:ISSN
9761:ISSN
9720:ISBN
9695:ISBN
9491:ISBN
9454:ISBN
9427:2012
9377:2022
9345:ISBN
9296:2018
9251:ISBN
9215:here
8864:and
4808:and
4214:P dV
3977:and
3874:and
3495:2.51
3421:2.51
3161:2.51
2952:6.31
2822:6.31
2771:6.31
2461:as
2455:and
2412:and
2104:and
1705:work
1689:mass
1685:heat
1545:Tait
375:Heat
370:Work
100:Laws
9842:doi
9830:152
9800:doi
9788:119
9753:doi
9629:144
9607:144
9450:185
9416:doi
9400:286
9228:in
9197:doi
8852:not
7892:or
7431:+ 1
6082:or
5621:+ 1
4524:+ 1
4397:to
4382:to
3887:nRT
3676:= 0
3597:753
3340:300
3207:nRT
3124:000
3120:100
2698:000
2694:100
2592:so
2442:or
2142:.)
2112:or
2028:= 0
1973:= 0
1953:≠ 0
1946:= 0
1921:= 0
1904:= 0
1861:as
1770:= 0
1733:In
1687:or
1650:An
1388:Art
334:in
9981::
9866:.
9858:.
9850:.
9840:.
9828:.
9824:.
9798:.
9786:.
9782:.
9759:.
9749:72
9747:.
9743:.
9681:^
9627:.
9605:.
9583:,
9505:^
9452:.
9414:.
9398:.
9394:.
9368:.
9287:.
9265:^
9203:.
9193:67
9191:.
9187:.
9172:^
8683:).
8666:).
8644:PV
8000:,
7423:=
7043:c4
6953:c3
6934:0.
6897:c2
6190:,
5613:=
5233:b4
5143:b3
5124:0.
5087:b2
5001:b1
4469:ln
4414:ln
4293::
4290:PV
4217::
4136:.
4133:αR
4131:=
4120:dT
4116:nC
4114:=
4112:dU
4100:a4
3952:a3
3885:=
3883:PV
3877:dV
3871:dP
3865:.
3844:a2
3791:by
3786:δW
3780:δQ
3768:δW
3763:by
3758:δW
3752:dU
3740:a1
3674:δQ
3559:Pa
3523:10
3515:Pa
3502:10
3364:Pa
3311:10
3303:Pa
3290:10
3219:nR
3203:PV
3181:Pa
3168:10
3140:10
3131:Pa
2971:21
2959:Pa
2841:21
2829:Pa
2806:21
2794:Pa
2778:10
2759:10
2705:Pa
2597:=
2579:.
2446:.
2421:=
2391:=
2149:.
2123:.
2116:.
2084:,
1871:−
1867:=
1816:=
1794:γP
1792:=
1719:.
9947:.
9924:.
9896:.
9874:.
9844::
9836::
9808:.
9802::
9794::
9767:.
9755::
9728:.
9703:.
9636:.
9499:.
9475:.
9462:.
9429:.
9418::
9410::
9379:.
9353:.
9298:.
9259:.
9211:.
9199::
8997:,
8993:.
8990:.
8987:.
8983:,
8980:0
8977:=
8972:2
8967:3
8963:c
8957:,
8954:0
8951:=
8946:2
8941:2
8937:c
8931:,
8928:1
8925:=
8920:2
8915:1
8911:c
8756:/
8753:k
8750:ɪ
8747:t
8744:æ
8741:b
8738:ˈ
8735:ə
8732:i
8729:d
8726:æ
8723:ˌ
8720:/
8716:(
8693:V
8691:–
8689:P
8660:P
8656:V
8640:V
8638:–
8636:P
8603:.
8593:1
8580:)
8573:1
8569:P
8563:2
8559:P
8553:(
8546:1
8542:T
8538:=
8533:2
8529:T
8505:,
8502:1
8489:1
8476:)
8469:1
8465:P
8459:2
8455:P
8449:(
8444:=
8441:1
8431:1
8427:T
8421:2
8417:T
8391:,
8387:)
8383:1
8370:1
8357:)
8350:1
8346:P
8340:2
8336:P
8330:(
8324:(
8318:1
8314:T
8310:=
8305:1
8301:T
8292:2
8288:T
8261:.
8257:)
8253:1
8240:1
8227:)
8220:1
8216:P
8210:2
8206:P
8200:(
8194:(
8188:1
8184:T
8180:R
8177:n
8171:=
8168:)
8163:1
8159:T
8150:2
8146:T
8142:(
8139:R
8136:n
8107:.
8103:)
8099:1
8086:1
8073:)
8066:1
8062:P
8056:2
8052:P
8046:(
8040:(
8034:1
8030:T
8026:R
8023:n
8014:=
8011:W
7997:W
7979:.
7972:1
7968:V
7962:2
7958:V
7952:=
7942:1
7932:)
7925:1
7921:P
7915:2
7911:P
7905:(
7877:,
7864:)
7857:1
7853:V
7847:2
7843:V
7837:(
7832:=
7825:1
7821:P
7815:2
7811:P
7782:.
7778:)
7774:1
7760:1
7755:)
7748:1
7744:V
7738:2
7734:V
7728:(
7722:(
7716:1
7712:T
7708:R
7705:n
7696:=
7693:W
7667:.
7663:)
7659:1
7645:1
7640:)
7633:1
7629:V
7623:2
7619:V
7613:(
7607:(
7601:1
7597:V
7591:1
7587:P
7577:=
7574:W
7548:.
7544:)
7532:1
7527:1
7523:V
7508:1
7503:2
7499:V
7494:(
7483:1
7479:V
7473:1
7469:P
7459:=
7456:W
7438:α
7434:/
7429:α
7421:γ
7403:.
7391:1
7384:1
7380:V
7374:1
7370:P
7361:2
7357:V
7351:2
7347:P
7340:=
7328:1
7315:1
7310:1
7306:V
7291:1
7286:2
7282:V
7268:1
7264:V
7258:1
7254:P
7250:=
7247:W
7221:.
7218:V
7215:d
7204:)
7199:V
7194:1
7190:V
7184:(
7177:1
7173:P
7165:2
7161:V
7153:1
7149:V
7140:=
7137:W
7111:.
7101:)
7096:V
7091:1
7087:V
7081:(
7074:1
7070:P
7066:=
7063:P
7045:)
7041:(
7024:.
7014:1
7010:V
7004:1
7000:P
6996:=
6988:=
6979:V
6975:P
6955:)
6951:(
6931:=
6928:W
6925:+
6922:U
6899:)
6895:(
6878:.
6875:V
6872:d
6868:P
6861:2
6857:V
6849:1
6845:V
6836:=
6833:W
6793:.
6783:1
6770:)
6763:1
6759:P
6753:2
6749:P
6743:(
6736:1
6732:T
6728:=
6723:2
6719:T
6695:,
6692:1
6679:1
6666:)
6659:1
6655:P
6649:2
6645:P
6639:(
6634:=
6631:1
6621:1
6617:T
6611:2
6607:T
6581:,
6577:)
6573:1
6560:1
6547:)
6540:1
6536:P
6530:2
6526:P
6520:(
6514:(
6508:1
6504:T
6500:=
6495:1
6491:T
6482:2
6478:T
6451:.
6447:)
6443:1
6430:1
6417:)
6410:1
6406:P
6400:2
6396:P
6390:(
6384:(
6378:1
6374:T
6370:R
6367:n
6361:=
6358:)
6353:1
6349:T
6340:2
6336:T
6332:(
6329:R
6326:n
6297:.
6293:)
6289:1
6276:1
6263:)
6256:1
6252:P
6246:2
6242:P
6236:(
6230:(
6224:1
6220:T
6216:R
6213:n
6204:=
6201:W
6187:W
6169:.
6162:1
6158:V
6152:2
6148:V
6142:=
6132:1
6122:)
6115:1
6111:P
6105:2
6101:P
6095:(
6067:,
6054:)
6047:1
6043:V
6037:2
6033:V
6027:(
6022:=
6015:1
6011:P
6005:2
6001:P
5972:.
5968:)
5964:1
5950:1
5945:)
5938:1
5934:V
5928:2
5924:V
5918:(
5912:(
5906:1
5902:T
5898:R
5895:n
5886:=
5883:W
5857:.
5853:)
5849:1
5835:1
5830:)
5823:1
5819:V
5813:2
5809:V
5803:(
5797:(
5791:1
5787:V
5781:1
5777:P
5767:=
5764:W
5738:.
5734:)
5722:1
5717:1
5713:V
5698:1
5693:2
5689:V
5684:(
5673:1
5669:V
5663:1
5659:P
5649:=
5646:W
5628:α
5624:/
5619:α
5611:γ
5593:.
5581:1
5574:1
5570:V
5564:1
5560:P
5551:2
5547:V
5541:2
5537:P
5530:=
5518:1
5505:1
5500:1
5496:V
5481:1
5476:2
5472:V
5458:1
5454:V
5448:1
5444:P
5440:=
5437:W
5411:.
5408:V
5405:d
5394:)
5389:V
5384:1
5380:V
5374:(
5367:1
5363:P
5355:2
5351:V
5343:1
5339:V
5330:=
5327:W
5301:.
5291:)
5286:V
5281:1
5277:V
5271:(
5264:1
5260:P
5256:=
5253:P
5235:)
5231:(
5214:.
5204:1
5200:V
5194:1
5190:P
5186:=
5178:=
5169:V
5165:P
5145:)
5141:(
5121:=
5118:W
5115:+
5112:U
5089:)
5085:(
5068:.
5065:V
5062:d
5058:P
5051:2
5047:V
5039:1
5035:V
5026:=
5023:W
5003:)
4999:(
4982:.
4979:T
4973:n
4970:R
4964:=
4959:1
4955:T
4951:n
4948:R
4937:2
4933:T
4929:n
4926:R
4920:=
4917:U
4889:.
4885:t
4882:n
4879:a
4876:t
4873:s
4870:n
4867:o
4864:c
4860:=
4851:V
4847:P
4844:=
4834:0
4830:V
4824:0
4820:P
4793:,
4790:1
4787:=
4777:)
4770:0
4766:V
4762:V
4757:(
4751:)
4744:0
4740:P
4736:P
4731:(
4704:.
4694:)
4689:V
4684:0
4680:V
4674:(
4669:=
4665:)
4658:0
4654:P
4650:P
4645:(
4618:,
4605:)
4598:0
4594:V
4590:V
4585:(
4580:=
4576:)
4569:0
4565:P
4561:P
4556:(
4541:γ
4531:α
4527:/
4522:α
4500:.
4496:)
4489:0
4485:V
4481:V
4476:(
4460:1
4457:+
4445:=
4441:)
4434:0
4430:P
4426:P
4421:(
4400:P
4394:0
4391:P
4385:V
4379:0
4376:V
4358:.
4353:P
4349:P
4346:d
4337:=
4332:V
4328:V
4325:d
4319:)
4316:1
4313:+
4307:(
4272:,
4269:P
4266:d
4262:V
4256:=
4253:V
4250:d
4246:P
4243:)
4240:1
4237:+
4231:(
4212:−
4195:,
4192:P
4189:d
4185:V
4179:+
4176:V
4173:d
4169:P
4163:=
4160:V
4157:d
4153:P
4128:V
4126:C
4118:V
4102:)
4098:(
4081:.
4078:)
4075:P
4072:d
4068:V
4065:+
4062:V
4059:d
4055:P
4052:(
4046:=
4043:)
4040:V
4037:P
4034:(
4031:d
4024:=
4021:T
4018:d
4014:R
4011:n
4005:=
4002:U
3999:d
3980:n
3970:R
3964:α
3954:)
3950:(
3933:,
3930:V
3927:P
3921:=
3918:T
3915:R
3912:n
3906:=
3903:U
3862:V
3856:P
3846:)
3842:(
3825:.
3822:V
3819:d
3815:P
3812:=
3809:W
3774:U
3742:)
3738:(
3721:,
3718:0
3715:=
3712:Q
3706:=
3703:W
3697:+
3694:U
3691:d
3665:V
3663:–
3661:P
3608:.
3604:K
3594:=
3586:1
3578:K
3571:3
3566:m
3545:3
3540:m
3530:4
3506:6
3489:=
3482:2
3477:t
3474:n
3471:a
3468:t
3465:s
3462:n
3459:o
3456:c
3450:V
3447:P
3441:=
3438:T
3423:×
3417:P
3413:V
3396:.
3391:1
3383:K
3376:3
3371:m
3354:=
3347:K
3333:3
3328:m
3318:3
3294:5
3283:=
3278:2
3273:t
3270:n
3267:a
3264:t
3261:s
3258:n
3255:o
3252:c
3247:=
3242:T
3238:V
3235:P
3215:R
3211:n
3209:(
3172:6
3158:=
3153:5
3149:/
3145:7
3117:=
3107:)
3100:2
3096:V
3090:1
3086:V
3080:(
3073:1
3069:P
3065:=
3060:2
3056:P
3029:,
3023:5
3020:7
3015:)
3009:3
3004:m
2993:(
2987:P
2984:=
2979:5
2975:/
2966:m
2949:=
2944:1
2939:t
2936:n
2933:a
2930:t
2927:s
2924:n
2921:o
2918:c
2913:=
2903:2
2899:V
2893:2
2889:P
2854:,
2849:5
2845:/
2836:m
2819:=
2814:5
2810:/
2801:m
2785:5
2763:5
2755:=
2742:5
2739:7
2734:)
2728:3
2723:m
2712:(
2691:=
2686:1
2681:t
2678:n
2675:a
2672:t
2669:s
2666:n
2663:o
2660:c
2655:=
2645:1
2641:V
2635:1
2631:P
2608:5
2605:/
2602:7
2595:γ
2573:T
2556:.
2548:=
2543:1
2533:V
2529:T
2506:,
2498:=
2489:T
2477:1
2473:P
2458:V
2452:P
2432:5
2429:/
2426:7
2419:γ
2402:3
2399:/
2396:5
2389:γ
2376:f
2369:V
2367:C
2356:P
2354:C
2336:.
2331:f
2327:2
2324:+
2321:f
2315:=
2308:V
2304:C
2298:P
2294:C
2288:=
2267:γ
2261:V
2255:P
2237:,
2229:=
2220:V
2216:P
2034:S
2032:Δ
2026:V
2024:d
2012:V
2010:d
2008:P
1997:.
1989:S
1987:Δ
1981:Q
1971:S
1969:Δ
1958:W
1951:W
1944:Q
1934:W
1919:Q
1909:Q
1902:W
1892:W
1886:Q
1880:U
1878:Δ
1873:W
1869:Q
1865:U
1863:Δ
1846:P
1835:v
1833:C
1829:/
1824:p
1822:C
1814:γ
1811:(
1800:γ
1790:E
1783:(
1768:Q
1677:)
1671:(
1654:(
1639:e
1632:t
1625:v
1152:S
1149:T
1143:H
1140:=
1137:)
1134:p
1131:,
1128:T
1125:(
1122:G
1097:S
1094:T
1088:U
1085:=
1082:)
1079:V
1076:,
1073:T
1070:(
1067:A
1042:V
1039:p
1036:+
1033:U
1030:=
1027:)
1024:p
1021:,
1018:S
1015:(
1012:H
987:)
984:V
981:,
978:S
975:(
972:U
849:T
825:V
802:V
778:1
753:=
717:p
693:V
670:V
646:1
618:=
582:T
558:N
535:S
511:T
486:=
483:c
406:)
23:.
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