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第1行： − 此词条暂由Henry翻译+ + + + − 此词条暂由Miyasaki审校 − {{Other uses|Critical point (disambiguation){{!}}Critical point}}+ − [[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5| − [[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|+ − + − [图片: 临界点测量乙烷 jpg | thumb | right | upright = 1.5 | − − {{ordered list − − {{ordered list − − {有序列表 − − |Subcritical [[ethane]], liquid and gas phase coexist. − − |Subcritical ethane, liquid and gas phase coexist. − − 亚临界乙烷，液态和气态共存。 − − |Critical point (32.17 °C, 48.72 bar), opalescence. − − |Critical point (32.17 °C, 48.72 bar), opalescence. − − 临界点(32.17 °C，48.72 bar) ，乳白色。 − − |Supercritical [[ethane]], [[fluid]].<ref>{{cite thesis |first=Sven |last=Horstmann |title=Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung |language=de |trans-title=Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the [[PSRK]] group contribution equation of state |type=Ph.D. |location=Oldenburg, Germany |publisher=[[University of Oldenburg|Carl-von-Ossietzky Universität Oldenburg]] |year=2000 |isbn=3-8265-7829-5|oclc=76176158}}</ref> − − |Supercritical ethane, fluid. − − 超临界乙烷，流体。<ref>{{cite thesis |first=Sven |last=Horstmann |title=Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung |language=de |trans-title=Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the [[PSRK]] group contribution equation of state |type=Ph.D. |location=Oldenburg, Germany |publisher=[[University of Oldenburg|Carl-von-Ossietzky Universität Oldenburg]] |year=2000 |isbn=3-8265-7829-5|oclc=76176158}}</ref> − − }}]] − − }}]] − − }}]] − − − − In [[thermodynamics]], a '''critical point''' (or '''critical state''') is the end point of a phase [[Equilibrium (thermodynamics)|equilibrium]] curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a [[liquid]] and its [[vapor]] can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''<sub>c</sub> and a ''critical pressure'' ''p''<sub>c</sub>, [[phase (matter)|phase]] boundaries vanish. Other examples include the liquid–liquid critical points in mixtures. − − In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature T<sub>c</sub> and a critical pressure p<sub>c</sub>, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures. − − 在热力学中，一个<font color="#ff8000"> 临界点Critical point </font>（或临界状态）就是相平衡曲线的终点。最突出的例子是液-汽临界点，即压力-温度曲线的终点，它指明了液体和其蒸汽可以共存的条件。温度再高，气体就不能单靠压力液化。在由临界温度T<sub>c</sub>和临界压力p<sub>c</sub>定义的临界点，相边界消失。其他例子包括混合物中的液-液临界点。 − − − − − − − − − − − − [[Image:phase-diag2.svg|thumb|upright=1.5|In a typical phase diagram, the boundary between gas and liquid runs from the triple point to the critical point.|The liquid–vapor critical point in a pressure–temperature [[phase diagram]] is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.]] − − The liquid–vapor critical point in a pressure–temperature [[phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.]] − − 在压力-温度[[相图]中，液-汽临界点位于液-气相界面的高温极端处。绿色虚线显示了水的反常行为。] − − − − For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one. − − For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one. + − − − The figure to the right shows the schematic [[PT diagram]] of a ''pure substance'' (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known [[phase (matter)|phases]] ''solid'', ''liquid'' and ''vapor'' are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At the [[triple point]], all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at some ''critical temperature'' ''T''<sub>c</sub> and ''critical pressure'' ''p''<sub>c</sub>. This is the ''critical point''. − − The figure to the right shows the schematic PT diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid, liquid and vapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At the triple point, all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at some critical temperature T<sub>c</sub> and critical pressure p<sub>c</sub>. This is the critical point. + − In water, the critical point occurs at {{convert|647.096|K|C F}} and {{convert|22.064|MPa|psi atm}}.<ref name=IAPWS95>{{cite journal |last1=Wagner |first1=W. |last2=Pruß |first2=A. |title=The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use |journal=Journal of Physical and Chemical Reference Data |date=June 2002 |volume=31 |issue=2 |page=398 |doi=10.1063/1.1461829}}</ref> − In water, the critical point occurs at and .+ + − 在水中，临界点发生在647.096K 和22.064MPa下。<ref name=IAPWS95>{{cite journal |last1=Wagner |first1=W. |last2=Pruß |first2=A. |title=The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use |journal=Journal of Physical and Chemical Reference Data |date=June 2002 |volume=31 |issue=2 |page=398 |doi=10.1063/1.1461829}}</ref> − + − − In the ''vicinity'' of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high [[dielectric constant]], and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor [[dielectric]], a bad solvent for electrolytes, and prefers to mix with nonpolar gases and organic molecules.<ref>Anisimov, Sengers, [[Anneke Levelt Sengers|Levelt Sengers]] (2004):Near-critical behavior of aqueous systems. − 水体系的近临界行为 − Chapter 2 inAqueous System at Elevated Temperatures and Pressures − 高温高压下的水体系 − Palmer et al., eds. − − <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math> − − 左(frac { partial p }{ partial v } right) _ t = 0, − − Elsevier.</ref> − − − − In the vicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high dielectric constant, and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor dielectric, a bad solvent for electrolytes, and prefers to mix with nonpolar gases and organic molecules. − − 在临界点附近，液体和蒸汽的物理性质发生了巨大的变化，两个相变得越来越相似。例如，因为液态水在正常条件下几乎不可压缩，热膨胀系数低，介电常数高，所以它是电解液的优良溶剂。在临界点附近，所有这些性质都会发生完全相反的变化：水变得可压缩、可膨胀、介电性差、电解质溶剂性差，更容易与非极性气体和有机分子混合。 − − − − − − ''At'' the critical point, only one phase exists. The [[heat of vaporization]] is zero. There is a [[stationary point|stationary]] [[inflection point]] in the constant-temperature line (''critical isotherm'') on a [[PV diagram]]. This means that at the critical point:<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.</ref><ref>K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.</ref><ref>P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.</ref> − − At the critical point, only one phase exists. The heat of vaporization is zero. There is a stationary inflection point in the constant-temperature line (critical isotherm) on a PV diagram. This means that at the critical point: − − 在临界点，只有一个相存在。汽化热为零。在PV图上的恒温线（<font color="#ff8000"> 临界等温线Critical isotherm</font>）中有一个固定的拐点。这意味着在临界点：<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.</ref><ref>K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.</ref><ref>P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.</ref> − − − The critical isotherm with the critical point K − − 临界点 k 的临界等温线 − − − − − ''Above'' the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called [[supercritical fluid]]. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by [[Michael Fisher|Fisher]] and [[Benjamin Widom|Widom]],<ref>Fisher, Widom: ''Decay of Correlations in Linear Systems'', J. Chem. Phys. 50, 3756 (1969).</ref> who identified a ''p''–''T'' line that separates states with different asymptotic statistical properties ([[Fisher–Widom line]]). − − Above the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called supercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by Fisher and Widom, who identified a p–T line that separates states with different asymptotic statistical properties (Fisher–Widom line). − − 在临界点以上存在一种物质状态，它与液态和气态连续相连（无相变即可转化）。它被称为超临界流体。关于液体和蒸汽之间的所有区别都在临界点之外消失的共同教科书知识受到了费舍尔和威登的质疑，他们确定了一条p-T线，它分开了具有不同渐近统计性质的状态（Fisher-Widom线）。 − + − Some times the critical point does not manifest in most thermodynamic or mechanical properties, but is hidden and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. In those cases we have a hidden critical point, otherwise we have an exposed critical point. − + − + − + − + − + − − Some times the critical point does not manifest in most thermodynamic or mechanical properties, but is ''hidden'' and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. In those cases we have a [[hidden critical point]], otherwise we have an [[exposed critical point]].<ref>{{cite journal |last1=Das |first1=Tamoghna |last2=Ganguly |first2=Saswati |last3=Sengupta |first3=Surajit |last4=Rao |first4=Madan |title=Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals |journal=Scientific Reports |date=3 June 2015 |volume=5 |issue=1 |pages=10644 |doi=10.1038/srep10644 |pmid=26039380 |pmc=4454149 |bibcode=2015NatSR...510644D |doi-access=free }}</ref> − − − − === History历史 === − − Critical [[carbon dioxide exuding fog while cooling from supercritical to critical temperature.]] − − 在从超临界温度冷却到临界温度时，临界二氧化碳释放出雾。 − − − − − − Solving the above condition <math>(\partial p / \partial V)_T = 0</math> for the van der Waals equation, one can compute the critical point as − − 解决上述条件(∂p/∂V)T=0，对于范德华方程，可以计算临界点为 − − The existence of a critical point was first discovered by [[Charles Cagniard de la Tour]] in 1822<ref>{{cite journal |author=Charles Cagniard de la Tour |date=1822 |url=https://books.google.com/books?id=rzNCAAAAcAAJ&q=Cagniard&pg=PA127 |title=Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée |trans-title=Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether (i.e., diethyl ether), and distilled petroleum spirit |journal=Annales de Chimie et de Physique |volume=21 |pages=127–132 |language=fr}}</ref><ref>Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1–3001-4.</ref> and named by [[Dmitri Mendeleev]] in 1860<ref>Mendeleev called the critical point the "absolute temperature of boiling" ({{lang-ru|абсолютная температура кипения}}; {{lang-de|absolute Siedetemperatur}}). − − <math>T_\text{c} = \frac{8a}{27Rb}, − − 8 a }{27Rb } , − − − \quad V_\text{c} = 3nb, − − 3nb, − + − \quad p_\text{c} = \frac{a}{27b^2}.</math> − 27b ^ 2} . </math > + − * In 1870, Mendeleev asserted, against Thomas Andrews, his priority regarding the definition of the critical point: {{cite journal |last1=Mendelejeff |first1=D. |title=Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure |journal=Annalen der Physik |date=1870 |volume=141 |pages=618–626 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352249;view=1up;seq=648 |series=2nd series |trans-title=Comments on Andrews' investigations into the compressibility of carbon dioxide |language=de}}</ref><ref>Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].</ref> and [[Thomas Andrews (scientist)|Thomas Andrews]] in 1869.<ref>{{cite journal |author=Andrews, Thomas |date=1869 |url=http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html |title=The Bakerian lecture: On the continuity of the gaseous and liquid states of matter |journal=Philosophical Transactions of the Royal Society |location=London |volume=159 |pages=575–590 |doi=10.1098/rstl.1869.0021 |doi-access=free }} The term "critical point" appears on page 588.</ref> Cagniard showed that CO<sub>2</sub> could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3000 atm.+ − − The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860 and Thomas Andrews in 1869. Cagniard showed that CO<sub>2</sub> could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3000 atm. − − 临界点的存在于1822年<ref>{{cite journal |author=Charles Cagniard de la Tour |date=1822 |url=https://books.google.com/books?id=rzNCAAAAcAAJ&q=Cagniard&pg=PA127 |title=Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée |trans-title=Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether (i.e., diethyl ether), and distilled petroleum spirit |journal=Annales de Chimie et de Physique |volume=21 |pages=127–132 |language=fr}}</ref><ref>Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1–3001-4.</ref> 由Charles Cagniard de la Tour首次发现，1860年<ref>Mendeleev called the critical point the "absolute temperature of boiling" ({{lang-ru|абсолютная температура кипения}}; {{lang-de|absolute Siedetemperatur}}). − − <math>T_\text{c} = \frac{8a}{27Rb}, − − 8 a }{27Rb } , − − * {{cite journal |last1=Менделеев |first1=Д. |title=О расширении жидкостей от нагревания выше температуры кипения |journal=Горный Журнал [Mining Journal] |date=1861 |volume=4 |pages=141–152 |trans-title=On the expansion of liquids from heating above the temperature of boiling |language=ru}} The "absolute temperature of boiling" is defined on p. 151. Available at [https://upload.wikimedia.org/wikipedia/commons/e/e6/%D0%93%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%2C_1861%2C_%E2%84%9604_%28%D0%B0%D0%BF%D1%80%D0%B5%D0%BB%D1%8C%29.pdf Wikimedia] + − − 3nb, − − * German translation: {{cite journal |last1=Mendelejeff |first1=D. |title=Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt |journal=Annalen der Chemie und Pharmacie |date=1861 |volume=119 |pages=1–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.c036497486;view=1up;seq=13 |trans-title=On the expansion of fluids during heating above their boiling point |language=de |doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: "{{lang|de|2=Als absolute Siedetemperatur müssen wir den Punkt betrachten, bei welchem 1) die Cohäsion der Flüssigkeit = 0° ist und a<sup>2</sup> = 0, bei welcher 2) die latente Verdamfungswärme auch = 0 ist und bei welcher sich 3) die Flüssigkeit in Dampf verwandelt, unabhängig von Druck und Volum."}} (As the "absolute temperature of boiling" we must regard the point at which (1) the cohesion of the liquid equals 0° and ''a''<sup>2</sup> = 0 [where ''a''<sup>2</sup> is the coefficient of capillarity, p. 6], at which (2) the latent heat of vaporization also equals zero, and at which (3) the liquid is transformed into vapor, independently of the pressure and the volume.) − − 27b ^ 2} . </math > − * In 1870, Mendeleev asserted, against Thomas Andrews, his priority regarding the definition of the critical point: {{cite journal |last1=Mendelejeff |first1=D. |title=Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure |journal=Annalen der Physik |date=1870 |volume=141 |pages=618–626 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352249;view=1up;seq=648 |series=2nd series |trans-title=Comments on Andrews' investigations into the compressibility of carbon dioxide |language=de}}</ref><ref>Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].</ref> Dmitri mendelev和Thomas Andrews于1869年<ref>{{cite journal |author=Andrews, Thomas |date=1869 |url=http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html |title=The Bakerian lecture: On the continuity of the gaseous and liquid states of matter |journal=Philosophical Transactions of the Royal Society |location=London |volume=159 |pages=575–590 |doi=10.1098/rstl.1869.0021 |doi-access=free }} The term "critical point" appears on page 588.</ref> 分别命名。Cagniard表明， CO<sub>2</sub>在31°C的压力下可以液化，但在更高一点的温度下，即使在高达3000 atm的压力下也不能液化。+ − + − However, the van der Waals equation, based on a mean-field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws. − − 然而，基于平均场理论的van der Waals方程在临界点附近并不成立。尤其是，它预测了错误的标度定律 − − === Theory理论 === − − To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties − − 为了分析临界点附近的流体性质，有时需要定义相对于临界性质的简化状态变量 − − − − Solving the above condition <math>(\partial p / \partial V)_T = 0</math> for the [[van der Waals equation]], one can compute the critical point as − − 解对于van der Waals方程的上述条件<math>(\partial p / \partial V)_T = 0</math>，就能将临界点计算为 − − <math>T_\text{r} = \frac{T}{T_\text{c}}, − − 如果你想知道更多的信息，请访问我的网站, − − : <math>T_\text{c} = \frac{8a}{27Rb}, − − − 4.1.1.1.2.2.2.2.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3 − − \quad V_\text{c} = 3nb, − − 4 v _ text { r } = frac { v }{ RT _ text { c }/p _ text { c } . </math > − − \quad p_\text{c} = \frac{a}{27b^2}.</math> − − --[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）这里内容有待整理 − − However, the van der Waals equation, based on a [[mean-field theory]], does not hold near the critical point. In particular, it predicts wrong [[scaling law]]s. − − 但是，基于一个平均场理论的van der Waals方程，不能在近临界点成立。尤其是，它会得出错误的标度律。 − − The principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of p<sub>r</sub>. − − To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 978-0-07-121688-3 | pages = 91–93}}</ref> − − 为分析接近临界点的液体的性质，还原态变量有时会被相对于临界性质定义。<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 978-0-07-121688-3 | pages = 91–93}}</ref> − − For some gases, there is an additional correction factor, called ''Newton's correction'', added to the critical temperature and critical pressure calculated in this manner. These are empirically derived values and vary with the pressure range of interest.<ref>{{cite journal |title= Compressibility Chart for Hydrogen and Inert Gases |first1= Frank D. |last1= Maslan |first2= Theodore M. |last2= Littman |journal= Ind. Eng. Chem. |year= 1953 |volume= 45 |issue= 7 |pages= 1566–1568 |doi= 10.1021/ie50523a054 }}</ref> − − For some gases, there is an additional correction factor, called Newton's correction, added to the critical temperature and critical pressure calculated in this manner. These are empirically derived values and vary with the pressure range of interest. − − − : <math>T_\text{r} = \frac{T}{T_\text{c}}, − − \quad p_\text{r} = \frac{p}{p_\text{c}}, − − \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math> − − <center> − − < 中心 > − − − − {| class="wikitable sortable" style="text-align: center;" − − { | class = “ wikitable sortable” style = “ text-align: center; ” − − The [[theorem of corresponding states|principle of corresponding states]] indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of ''p''<sub>r</sub>. − − |- − − |- − − − − ! Substance − − !物质 − − − ! Critical temperature − − !临界温度 − − − − ! Critical pressure (absolute) − − !临界压力(绝对值) − − |- − − |- − − {{see also|Critical points of the elements (data page)}} − − | Argon − − | 氩气 − − − | }} − − | }} − − − | }} − − | }} − − |- − − |- − − − − | Ammonia (NH<sub>3</sub>) − − | 氨(NH < sub > 3 </sub >) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Argon]] − − − | R-134a − − | R-134a − − − | }} − − | }} − − + − − − | }} − − | [[Ammonia]] (NH<sub>3</sub>)<ref>{{Cite web|url=http://www.engineeringtoolbox.com/ammonia-d_971.html|title=Ammonia - NH3 - Thermodynamic Properties|website=www.engineeringtoolbox.com|access-date=2017-04-07}}</ref> − − |- − − |- − − − − | R-410A − − | R-410A − − |- − − | }} − − | }} − − − − | }} − − | }} − − | [[R-134a]] − − |- − + − − − | Bromine − − | 溴 − − |- − − | }} − − | }} − − − − | }} − − | }} − − | [[R-410A]] − − |- − + − − | Caesium − − 铯 − − − | }} − − | }} − − + − − | }} − − − − |- − − |- − − | [[Bromine]] − − | Chlorine − − | 氯气 − − − | }} − − | }} − − − | }} − − | }} − − |- − − |- − − + − − − | Ethanol (C<sub>2</sub>H<sub>5</sub>OH) − − | 乙醇(c < sub > 2 </sub > h < sub > 5 </sub > OH) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Chlorine]] − − | Fluorine − − | 氟 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Ethanol]] (C<sub>2</sub>H<sub>5</sub>OH) − − | Helium − − | 氦气 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Fluorine]] − − | Hydrogen − − | 氢气 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Helium]] − − | Krypton − − 氪星 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Hydrogen]] − − | Methane (CH<sub>4</sub>) − − | 甲烷(CH < sub > 4 </sub >) − − − | }} − − | }} − − − | }} − − | }} − − |- − − |- − − + − − − | Neon − − 霓虹灯 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Methane]] (CH<sub>4</sub>) − − | Nitrogen − − | 氮气 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Neon]] − − | Oxygen (O<sub>2</sub>) − − | 氧气(o < sub > 2 </sub >) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Nitrogen]] − − | Carbon dioxide (CO<sub>2</sub>) − − | 二氧化碳(CO < sub > 2 </sub >) − − − | }} − − | }} − − − | }} − − | }} − − |- − − |- − − + − − − | Nitrous oxide (N<sub>2</sub>O) − − | 氧化亚氮(n < sub > 2 </sub > o) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Carbon dioxide]] (CO<sub>2</sub>) − − | Sulfuric acid (H<sub>2</sub>SO<sub>4</sub>) − − | 硫酸(h < sub > 2 </sub > SO < sub > 4 </sub >) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Nitrous oxide]] (N<sub>2</sub>O) − − | Xenon − − | 氙气 − − − | }} − − | }} − − − | }} − − | }} − − |- − − |- − − + − − − | Lithium − − | Lithium − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Xenon]] − − | Mercury − − 水星 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Lithium]] − − | Sulfur − − 硫磺 − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Mercury (element)|Mercury]] − − | Iron − − 铁 − − − | }} − − | }} − − − | − − | − − |- − − + − − − | [[Sulfur]] − − | Gold − − | 黄金 − − − | }} − − | }} − − − | }} − − | }} − − |- − − + − − − | [[Iron]] − − | Aluminium − − | 铝 − − − | }} − − | }} − − − | − − | − − |- − − |- − − + − − − | Water (H<sub>2</sub>O) − − | 水(h < sub > 2 </sub > o) − − − | }} − − | }} − − − | }} − − | }} − − + − − − |- − − | [[Aluminium]] − − |} − − |} − − − </center> − − </center > − − − + − − − − A plot of typical polymer solution phase behavior including two critical points: a [[LCST and an UCST]] − − 典型的聚合物溶液相行为图，包括两个临界点: a [ LCST 和 UCST ] − − − The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) leads to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature (UCST), which is the hottest point at which cooling induces phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating induces phase separation. − − 溶液的液-液临界点出现在临界溶液温度下，出现在相图两相区的极限处。换言之，它是某个热力学变量（如温度或压力）的微小变化导致混合物分离为两个不同的液相的点，如右侧的聚合物-溶剂相图所示。两种类型的液-液临界点是上临界溶液温度（UCST），这是冷却导致相分离的最热点，而下临界溶液温度（LCST）是加热导致相分离的最冷点。 − − − − − − From a theoretical standpoint, the liquid–liquid critical point represents the temperature–concentration extremum of the spinodal curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the second derivative of the free energy with respect to concentration must equal zero), and the extremum condition (the third derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero). − ==Mixtures: liquid–liquid critical point混合物：液体-液体临界点 == + − + − The [[liquid–liquid critical point]] of a solution, which occurs at the ''critical solution temperature'', occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) leads to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the [[upper critical solution temperature]] (UCST), which is the hottest point at which cooling induces phase separation, and the [[lower critical solution temperature]] (LCST), which is the coldest point at which heating induces phase separation.+ − − + + − From a theoretical standpoint, the liquid–liquid critical point represents the temperature–concentration extremum of the [[spinodal]] curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the ''second'' derivative of the [[Gibbs free energy|free energy]] with respect to concentration must equal zero), and the extremum condition (the ''third'' derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero).+ − 从理论上看，从液体的临界点（从理论上看，是指液体的临界温度）。因此，双组分体系中的液-液临界点必须满足两个条件：旋节曲线的条件（[[Gibbs自由能|自由能]]相对于浓度的“二阶”导数必须等于零）和极值条件（自由能相对于浓度的“第三”导数）也必须等于零，或者旋节温度对浓度的导数必须等于零）。+ − − − − − − {{colbegin}}+ + + + + + + + + + + + + − * [[Conformal field theory]] − 共形场论 − * [[Critical exponents]] − 临界指数 − * [[Critical phenomena]] (more advanced article) − 临界现象 − * [[Critical points of the elements (data page)]] − 要素临界点 − * [[Curie point]] − 居里点 − * [[Joback method]], [[Klincewicz method]], [[Lydersen method]] (estimation of critical temperature, pressure, and volume from molecular structure) − Joback 方法 Klingewicz方法 Lydersen 方法（从分子结构估算临界温度、压力和体积） − * [[Liquid–liquid critical point]] − 液体-液体临界点 − * [[Lower critical solution temperature]] − 较低临界溶液温度 − * [[Néel point]] − Néel点 − * [[Percolation thresholds]] − 过滤阈值 − * [[Phase transition]] − 相变 − * [[Rushbrooke inequality]] − Rushbrooke不等式 − * [[Scale invariance]] − 比例不变性 − * [[Self-organized criticality]] − 自组织临界性 − * [[Supercritical fluid]], [[Supercritical drying]], [[Supercritical water oxidation]], [[Supercritical fluid extraction]] − 超临界流体 超临界干燥 超临界水氧化 超临界流体萃取 − * [[Tricritical point]] − 三临界点 − * [[Triple point]] − 三重点 − * [[Upper critical solution temperature]] − 上临界溶液温度 − * [[Widom scaling]] − Widom缩放 − + − + − − {{Reflist|38em}} − − | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }} − − | publisher = 普渡大学 | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03} − − − − == References参考 == − − Category:Condensed matter physics − 类别: 凝聚态物理学+ − + − + − Category:Conformal field theory − − 类别: 共形场论 − * {{cite web |title=Critical points for some common solvents |url=http://www.proscitech.com.au/catalogue/notes/cpd.htm |archiveurl=https://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm |publisher=ProSciTech |archivedate=2008-01-31}} − Category:Critical phenomena+ + + + − 范畴: 关键现象+ + + + + − *{{cite web | title = Critical Temperature and Pressure | work = Department of Chemistry − Category:Phase transitions+ + − 类别: 阶段转变+ + + + + − | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }} − Category:Renormalization group+ + − 类别: 重整化群 + + + + + − Category:Threshold temperatures − 类别: 临界温度 − {{Phase_of_matter}}+ + − Category:Gases − 分类: 气体 − <noinclude>+ − <small>This page was moved from [[wikipedia:en:Critical point (thermodynamics)]]. Its edit history can be viewed at [[临界点（热力学）/edithistory]]</small></noinclude> − + + + + + + +
无编辑摘要
{{#seo:
|keywords=热力学,液-汽临界点,液-液临界点
|description=热力学中的相平衡曲线的终点
}}
在热力学中，一个'''临界点 Critical point'''（或临界状态）就是相平衡曲线的终点。最突出的例子是液-汽临界点，即压力-温度曲线的终点，它指明了液体和其蒸汽可以共存的条件。温度再高，气体就不能单靠压力液化。在由临界温度T<sub>c</sub>和临界压力p<sub>c</sub>定义的临界点，相边界消失。其他例子包括混合物中的液-液临界点。
== 液-汽临界点 ==
=== 总览===
== Liquid–vapor critical point液-汽临界点 ==
=== Overview 总览===
[[Image:phase-diag2.svg.png|thumb|upright=1.5|在压力-温度[[相图]中，液-汽临界点位于液-气相界面的高温极端处。绿色虚线显示了水的反常行为。]]
为使表述简单明晰，临界点的一般概念最好通过讨论一个具体的例子，液体-蒸汽临界点，来介绍。这是第一个被发现的临界点，也仍然是最著名和被研究最多的一个。
为使表述简单明晰，临界点的一般概念最好通过讨论一个具体的例子，液体-蒸汽临界点，来介绍。这是第一个被发现的临界点，也仍然是最著名和被研究最多的一个。
右图显示了纯物质的PT示意图（与混合物相反，混合物具有额外的状态变量和更丰富的相图，如下所述）。众所周知的固相、液相和汽相通过相边界分离，即两相可以共存的压力-温度组合。在三相点，所有三个相可以共存。然而，在临界温度T<sub>c</sub>和临界压力 p<sub>c</sub>时，液-汽边界终止于一个端点。这便是临界点。
右图显示了纯物质的PT示意图（与混合物相反，混合物具有额外的状态变量和更丰富的相图，如下所述）。众所周知的固相、液相和汽相通过相边界分离，即两相可以共存的压力-温度组合。在三相点，所有三个相可以共存。然而，在临界温度T<sub>c</sub>和临界压力 p<sub>c</sub>时，液-汽边界终止于一个端点。这便是临界点。
在水中，临界点出现在 647.096 K（373.946 °C；705.103 °F）和 22.064 兆帕（3,200.1 psi；217.75 atm）。.<ref name=IAPWS95>{{cite journal |last1=Wagner |first1=W. |last2=Pruß |first2=A. |title=The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use |journal=Journal of Physical and Chemical Reference Data |date=June 2002 |volume=31 |issue=2 |page=398 |doi=10.1063/1.1461829}}</ref>
在临界点附近，液体和蒸汽的物理性质发生了巨大变化，两相变得越来越相似。例如，液态水在正常条件下几乎不可压缩，热膨胀系数低，介电常数高，是电解质的优良溶剂。在临界点附近，所有这些特性都变成完全相反的：水变得可压缩、可膨胀、介电性差、电解质的不良溶剂，并且更喜欢与非极性气体和有机分子混合。<ref>Anisimov, Sengers, [[Anneke Levelt Sengers|Levelt Sengers]] (2004):Near-critical behavior of aqueous systems.
Chapter 2 in Aqueous System at Elevated Temperatures and Pressures Palmer et al., eds. Elsevier.</ref>
在临界点，只有一个相存在。汽化热为零。在PV图上的恒温线（临界等温线 Critical isotherm）中有一个固定的拐点。这意味着在临界点：<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.</ref><ref>K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.</ref><ref>P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.</ref>
: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>
: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>
: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>
: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>
在临界点以上存在一种物质状态，它与液态和气态连续相连（无相变即可转化）。它被称为'''超临界流体 supercritical fluid'''。关于液体和蒸汽之间的所有区别都在临界点之外消失的共同教科书知识受到了Michael Fisher和Benjamin Widom的质疑，<ref>Fisher, Widom: ''Decay of Correlations in Linear Systems'', J. Chem. Phys. 50, 3756 (1969).</ref>他们确定了一条p-T线，它分开了具有不同渐近统计性质的状态（Fisher-Widom线）。
有时，临界点并不表现在大多数热力学或机械性质上，而是隐藏在弹性模量的不均匀性开始、非仿射液滴的外观和局部特性的显著变化以及缺陷对浓度的突然增强中。在这些情况下，我们会有一个隐藏的临界点，否则我们就有一个暴露的临界点。
有时，临界点并不表现在大多数热力学或机械性质上，而是隐藏在弹性模量的不均匀性开始、非仿射液滴的外观和局部特性的显著变化以及缺陷对浓度的突然增强中。在这些情况下，我们会有一个隐藏的临界点，否则我们就有一个暴露的临界点。 <ref>{{cite journal |last1=Das |first1=Tamoghna |last2=Ganguly |first2=Saswati |last3=Sengupta |first3=Surajit |last4=Rao |first4=Madan |title=Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals |journal=Scientific Reports |date=3 June 2015 |volume=5 |issue=1 |pages=10644 |doi=10.1038/srep10644 |pmid=26039380 |pmc=4454149 |bibcode=2015NatSR...510644D |doi-access=free }}</ref>
[[Image:Real Gas Isotherms.svg|thumb|upright=1.5|The ''critical isotherm'' with the critical point K]]
[[Image:Real Gas Isotherms.svg.png|thumb|upright=1.5|临界点 k 的临界等温线]]
=== 历史 ===
[[Image:Critical carbon dioxide.jpg|thumb|在从超临界温度冷却到临界温度时，临界二氧化碳释放出雾。]]
临界点的存在于 1822 年由Charles Cagniard de la Tour <ref>{{cite journal |author=Charles Cagniard de la Tour |date=1822 |url=https://books.google.com/books?id=rzNCAAAAcAAJ&q=Cagniard&pg=PA127 |title=Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée|journal=Annales de Chimie et de Physique |volume=21 |pages=127–132 |language=fr}}</ref><ref>Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1–3001-4.</ref>首次发现，并由Dmitri Mendeleev在 1860 年<ref>Mendeleev called the critical point the "absolute temperature of boiling" ({{lang-ru|абсолютная температура кипения}}; {{lang-de|absolute Siedetemperatur}}).
[[Image:Critical carbon dioxide.jpg|thumb|Critical [[carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature.]]
* {{cite journal |last1=Менделеев |first1=Д. |title=О расширении жидкостей от нагревания выше температуры кипения |journal=Горный Журнал [Mining Journal] |date=1861 |volume=4 |pages=141–152 |trans-title=On the expansion of liquids from heating above the temperature of boiling |language=ru}} The "absolute temperature of boiling" is defined on p. 151. Available at [https://upload.wikimedia.org/wikipedia/commons/e/e6/%D0%93%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%2C_1861%2C_%E2%84%9604_%28%D0%B0%D0%BF%D1%80%D0%B5%D0%BB%D1%8C%29.pdf Wikimedia]
* {{cite journal |last1=Менделеев |first1=Д. |title=О расширении жидкостей от нагревания выше температуры кипения |journal=Горный Журнал [Mining Journal] |date=1861 |volume=4 |pages=141–152 |trans-title=On the expansion of liquids from heating above the temperature of boiling |language=ru}} The "absolute temperature of boiling" is defined on p. 151. Available at [https://upload.wikimedia.org/wikipedia/commons/e/e6/%D0%93%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%2C_1861%2C_%E2%84%9604_%28%D0%B0%D0%BF%D1%80%D0%B5%D0%BB%D1%8C%29.pdf Wikimedia]
* German translation: {{cite journal |last1=Mendelejeff |first1=D. |title=Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt |journal=Annalen der Chemie und Pharmacie |date=1861 |volume=119 |pages=1–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.c036497486;view=1up;seq=13 |trans-title=On the expansion of fluids during heating above their boiling point |language=de |doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: "{{lang|de|2=Als absolute Siedetemperatur müssen wir den Punkt betrachten, bei welchem 1) die Cohäsion der Flüssigkeit = 0° ist und a<sup>2</sup> = 0, bei welcher 2) die latente Verdamfungswärme auch = 0 ist und bei welcher sich 3) die Flüssigkeit in Dampf verwandelt, unabhängig von Druck und Volum."}} (As the "absolute temperature of boiling" we must regard the point at which (1) the cohesion of the liquid equals 0° and ''a''<sup>2</sup> = 0 [where ''a''<sup>2</sup> is the coefficient of capillarity, p. 6], at which (2) the latent heat of vaporization also equals zero, and at which (3) the liquid is transformed into vapor, independently of the pressure and the volume.)
* German translation: {{cite journal |last1=Mendelejeff |first1=D. |title=Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt |journal=Annalen der Chemie und Pharmacie |date=1861 |volume=119 |pages=1–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.c036497486;view=1up;seq=13 |trans-title=On the expansion of fluids during heating above their boiling point |language=de |doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: "{{lang|de|2=Als absolute Siedetemperatur müssen wir den Punkt betrachten, bei welchem 1) die Cohäsion der Flüssigkeit = 0° ist und a<sup>2</sup> = 0, bei welcher 2) die latente Verdamfungswärme auch = 0 ist und bei welcher sich 3) die Flüssigkeit in Dampf verwandelt, unabhängig von Druck und Volum."}} (As the "absolute temperature of boiling" we must regard the point at which (1) the cohesion of the liquid equals 0° and ''a''<sup>2</sup> = 0 [where ''a''<sup>2</sup> is the coefficient of capillarity, p. 6], at which (2) the latent heat of vaporization also equals zero, and at which (3) the liquid is transformed into vapor, independently of the pressure and the volume.)
* In 1870, Mendeleev asserted, against Thomas Andrews, his priority regarding the definition of the critical point: {{cite journal |last1=Mendelejeff |first1=D. |title=Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure |journal=Annalen der Physik |date=1870 |volume=141 |pages=618–626 |doi=10.1002/andp.18702171218 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352249;view=1up;seq=648 |series=2nd series |trans-title=Comments on Andrews' investigations into the compressibility of carbon dioxide |language=de}}</ref><ref>Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].</ref>和Thomas Andrews在 1869年命名。<ref>{{cite journal |author=Andrews, Thomas |date=1869 |url=http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html |title=The Bakerian lecture: On the continuity of the gaseous and liquid states of matter |journal=Philosophical Transactions of the Royal Society |location=London |volume=159 |pages=575–590 |doi=10.1098/rstl.1869.0021 |doi-access=free }} The term "critical point" appears on page 588.</ref>Cagniard 表明 CO 2可以在 31 °C 和 73 atm 的压力下液化，但不能在稍高的温度下液化，即使在高达 3000 atm 的压力下也是如此。
=== 理论 ===
解决对于van der Waals方程的上述条件<math>(\partial p / \partial V)_T = 0</math>，就能将临界点计算为
: <math>T_\text{c} = \frac{8a}{27Rb},
\quad V_\text{c} = 3nb,
\quad V_\text{c} = 3nb,
\quad p_\text{c} = \frac{a}{27b^2}.</math>
\quad p_\text{c} = \frac{a}{27b^2}.</math>
然而，基于平均场理论的van der Waals方程在临界点附近不成立。特别是，它预测了错误的标度定律。为分析接近临界点的液体的性质，还原态变量有时会被相对于临界性质定义：<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 978-0-07-121688-3 | pages = 91–93}}</ref>
: <math>T_\text{r} = \frac{T}{T_\text{c}},
\quad p_\text{r} = \frac{p}{p_\text{c}},
\quad p_\text{r} = \frac{p}{p_\text{c}},
\quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math>
\quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math>
对应态原理表明，在相同的减压和温度下，物质具有相等的还原体积。这种关系对于许多物质来说几乎是正确的，但是对于p<sub>r</sub>的大值，这种关系变得越来越不准确。
对应态原理表明，在相同的减压和温度下，物质具有相等的还原体积。这种关系对于许多物质来说几乎是正确的，但是对于p<sub>r</sub>的大值，这种关系变得越来越不准确。
对于某些气体，在以这种方式计算的临界温度和临界压力上，还有一个额外的修正系数，叫做牛顿修正。这些是根据经验得出的值，并随感兴趣的压力范围而变化。<ref>{{cite journal |title= Compressibility Chart for Hydrogen and Inert Gases |first1= Frank D. |last1= Maslan |first2= Theodore M. |last2= Littman |journal= Ind. Eng. Chem. |year= 1953 |volume= 45 |issue= 7 |pages= 1566–1568 |doi= 10.1021/ie50523a054 }}</ref>
对于某些气体，在以这种方式计算的临界温度和临界压力上，还有一个额外的修正系数，叫做牛顿修正。这些是根据经验得出的值，并随感兴趣的压力范围而变化。<ref>{{cite journal |title= Compressibility Chart for Hydrogen and Inert Gases |first1= Frank D. |last1= Maslan |first2= Theodore M. |last2= Littman |journal= Ind. Eng. Chem. |year= 1953 |volume= 45 |issue= 7 |pages= 1566–1568 |doi= 10.1021/ie50523a054 }}</ref>
=== Table of liquid–vapor critical temperature and pressure for selected substances ===
=== Table of liquid–vapor critical temperature and pressure for selected substances ===
<center>
<center>
{| class="wikitable sortable" style="text-align: center;"
{| class="wikitable sortable" style="text-align: center;"
|-
|-
! Substance<ref>{{cite book |last= Emsley |first= John |title= The Elements |edition= Second |publisher= [[Oxford University Press]] |year= 1991 |isbn= 978-0-19-855818-7 }}</ref><ref>{{cite book |first1= Yunus A. |last1= Cengel |first2= Michael A. |last2= Boles |title= Thermodynamics: An Engineering Approach |pages= [https://archive.org/details/thermodynamicsen00ceng_0/page/824 824] |edition= Fourth |publisher= [[McGraw-Hill]] |year= 2002 |isbn= 978-0-07-238332-4 |url-access= registration |url= https://archive.org/details/thermodynamicsen00ceng_0/page/824 }}</ref>
! Substance<ref>{{cite book |last= Emsley |first= John |title= The Elements |edition= Second |publisher= [[Oxford University Press]] |year= 1991 |isbn= 978-0-19-855818-7 }}</ref><ref>{{cite book |first1= Yunus A. |last1= Cengel |first2= Michael A. |last2= Boles |title= Thermodynamics: An Engineering Approach |pages= [https://archive.org/details/thermodynamicsen00ceng_0/page/824 824] |edition= Fourth |publisher= [[McGraw-Hill]] |year= 2002 |isbn= 978-0-07-238332-4 |url-access= registration |url= https://archive.org/details/thermodynamicsen00ceng_0/page/824 }}</ref>
! Critical temperature
! Critical temperature
! Critical pressure (absolute)
! Critical pressure (absolute)
|-
|-
| 氩气
|-
| {{sort|0150.8|{{convert|-122.4|C|K}}}}
| {{sort|0150.8|{{convert|-122.4|C|K}}}}
| {{sort|0048.1|{{convert|48.1|atm|kPa|abbr=on}}}}
| {{sort|0048.1|{{convert|48.1|atm|kPa|abbr=on}}}}
|-
|-
| 氨(NH<sub>3</sub><ref>{{Cite web|url=http://www.engineeringtoolbox.com/ammonia-d_971.html|title=Ammonia - NH3 - Thermodynamic Properties|website=www.engineeringtoolbox.com|access-date=2017-04-07}}</ref>
| }}
| {{sort|0405.6|{{convert|132.4|C|K}}}}
| {{sort|0405.6|{{convert|132.4|C|K}}}}
| {{sort|0111.3|{{convert|111.3|atm|kPa|abbr=on}}}}
| {{sort|0111.3|{{convert|111.3|atm|kPa|abbr=on}}}}
|-
|-
| R-134a
| {{sort|0374|{{convert|101.06|C|K}}}}
| {{sort|0374|{{convert|101.06|C|K}}}}
| {{sort|0040|{{convert|40.06|atm|kPa|abbr=on}}}}
| {{sort|0040|{{convert|40.06|atm|kPa|abbr=on}}}}
|-
|-
| R-410A
| {{sort|0346|{{convert|72.8|C|K}}}}
| {{sort|0346|{{convert|72.8|C|K}}}}
| {{sort|0047|{{convert|47.08|atm|kPa|abbr=on}}}}
| {{sort|0047|{{convert|47.08|atm|kPa|abbr=on}}}}
|-
|-
| }}
| 溴
| {{sort|0584.0|{{convert|310.8|C|K}}}}
| {{sort|0584.0|{{convert|310.8|C|K}}}}
| {{sort|0102|{{convert|102|atm|kPa|abbr=on}}}}
| {{sort|0102|{{convert|102|atm|kPa|abbr=on}}}}
|-
|-
| 铯
| [[Caesium]]
| {{sort|1938.00|{{convert|1664.85|C|K}}}}
| {{sort|1938.00|{{convert|1664.85|C|K}}}}
| {{sort|0094|{{convert|94|atm|kPa|abbr=on}}}}
| {{sort|0094|{{convert|94|atm|kPa|abbr=on}}}}
|-
|-
| 氯气
|-
| {{sort|0417.0|{{convert|143.8|C|K}}}}
| {{sort|0417.0|{{convert|143.8|C|K}}}}
| {{sort|0076.0|{{convert|76.0|atm|kPa|abbr=on}}}}
| {{sort|0076.0|{{convert|76.0|atm|kPa|abbr=on}}}}
|-
|-
| 乙醇 (C<sub>2</sub>H<sub>5</sub>OH)
|-
| {{sort|0514.0|{{convert|241|C|K}}}}
| {{sort|0514.0|{{convert|241|C|K}}}}
| {{sort|0062.2|{{convert|62.18|atm|kPa|abbr=on}}}}
| {{sort|0062.2|{{convert|62.18|atm|kPa|abbr=on}}}}
|-
|-
| 氟
|-
| {{sort|0144.30|{{convert|-128.85|C|K}}}}
| {{sort|0144.30|{{convert|-128.85|C|K}}}}
| {{sort|0051.5|{{convert|51.5|atm|kPa|abbr=on}}}}
| {{sort|0051.5|{{convert|51.5|atm|kPa|abbr=on}}}}
|-
|-
| 氦气
|-
| {{sort|0005.19|{{convert|-267.96|C|K}}}}
| {{sort|0005.19|{{convert|-267.96|C|K}}}}
| {{sort|0002.24|{{convert|2.24|atm|kPa|abbr=on}}}}
| {{sort|0002.24|{{convert|2.24|atm|kPa|abbr=on}}}}
|-
|-
| 氢气
|-
| {{sort|0033.20|{{convert|-239.95|C|K}}}}
| {{sort|0033.20|{{convert|-239.95|C|K}}}}
| {{sort|0012.8|{{convert|12.8|atm|kPa|abbr=on}}}}
| {{sort|0012.8|{{convert|12.8|atm|kPa|abbr=on}}}}
|-
|-
| 氪星
| [[Krypton]]
| {{sort|0209.4|{{convert|-63.8|C|K}}}}
| {{sort|0209.4|{{convert|-63.8|C|K}}}}
| {{sort|0054.3|{{convert|54.3|atm|kPa|abbr=on}}}}
| {{sort|0054.3|{{convert|54.3|atm|kPa|abbr=on}}}}
|-
|-
| 甲烷(CH<sub>4</sub>)
|-
| {{sort|0190.8|{{convert|-82.3|C|K}}}}
| {{sort|0190.8|{{convert|-82.3|C|K}}}}
| {{sort|0045.79|{{convert|45.79|atm|kPa|abbr=on}}}}
| {{sort|0045.79|{{convert|45.79|atm|kPa|abbr=on}}}}
|-
|-
| 氖
|-
| {{sort|0044.40|{{convert|-228.75|C|K}}}}
| {{sort|0044.40|{{convert|-228.75|C|K}}}}
| {{sort|0027.2|{{convert|27.2|atm|kPa|abbr=on}}}}
| {{sort|0027.2|{{convert|27.2|atm|kPa|abbr=on}}}}
|-
|-
| 氮气
|-
| {{sort|0126.3|{{convert|-146.9|C|K}}}}
| {{sort|0126.3|{{convert|-146.9|C|K}}}}
| {{sort|0033.5|{{convert|33.5|atm|kPa|abbr=on}}}}
| {{sort|0033.5|{{convert|33.5|atm|kPa|abbr=on}}}}
|-
|-
| 氧气(O<sub>2</sub>)
| [[Oxygen]] (O<sub>2</sub>)
| {{sort|0154.6|{{convert|-118.6|C|K}}}}
| {{sort|0154.6|{{convert|-118.6|C|K}}}}
| {{sort|0049.8|{{convert|49.8|atm|kPa|abbr=on}}}}
| {{sort|0049.8|{{convert|49.8|atm|kPa|abbr=on}}}}
|-
|-
| 二氧化碳 (CO<sub>2</sub>)
|-
| {{sort|0304.19|{{convert|31.04|C|K}}}}
| {{sort|0304.19|{{convert|31.04|C|K}}}}
| {{sort|0072.8|{{convert|72.8|atm|kPa|abbr=on}}}}
| {{sort|0072.8|{{convert|72.8|atm|kPa|abbr=on}}}}
|-
|-
| 氧化亚氮(N<sub>2</sub>O)
|-
| {{sort|0304.19|{{convert|36.4|C|K}}}}
| {{sort|0304.19|{{convert|36.4|C|K}}}}
| {{sort|0072.8|{{convert|71.5|atm|kPa|abbr=on}}}}
| {{sort|0072.8|{{convert|71.5|atm|kPa|abbr=on}}}}
|-
|-
| 硫酸(H<sub>2</sub>SO<sub>4</sub>)
| [[Sulfuric acid]] (H<sub>2</sub>SO<sub>4</sub>)
| {{sort|0927|{{convert|654|C|K}}}}
| {{sort|0927|{{convert|654|C|K}}}}
| {{sort|0045.4|{{convert|45.4|atm|kPa|abbr=on}}}}
| {{sort|0045.4|{{convert|45.4|atm|kPa|abbr=on}}}}
|-
|-
| 氙气
|-
| {{sort|0289.8|{{convert|16.6|C|K}}}}
| {{sort|0289.8|{{convert|16.6|C|K}}}}
| {{sort|0057.6|{{convert|57.6|atm|kPa|abbr=on}}}}
| {{sort|0057.6|{{convert|57.6|atm|kPa|abbr=on}}}}
|-
|-
| 锂
|-
| {{sort|3223|{{convert|2950|C|K}}}}
| {{sort|3223|{{convert|2950|C|K}}}}
| {{sort|0652|{{convert|652|atm|kPa|abbr=on}}}}
| {{sort|0652|{{convert|652|atm|kPa|abbr=on}}}}
|-
|-
| 汞
|-
| {{sort|1750.1|{{convert|1476.9|C|K}}}}
| {{sort|1750.1|{{convert|1476.9|C|K}}}}
| {{sort|1720|{{convert|1720|atm|kPa|abbr=on}}}}
| {{sort|1720|{{convert|1720|atm|kPa|abbr=on}}}}
|-
|-
| 硫
|-
| {{sort|1314.00|{{convert|1040.85|C|K}}}}
| {{sort|1314.00|{{convert|1040.85|C|K}}}}
| {{sort|0207|{{convert|207|atm|kPa|abbr=on}}}}
| {{sort|0207|{{convert|207|atm|kPa|abbr=on}}}}
|-
|-
| 铁
|-
| {{sort|8500|{{convert|8227|C|K}}}}
| {{sort|8500|{{convert|8227|C|K}}}}
|
|
|-
|-
| 金
| [[Gold]]
| {{sort|7250|{{convert|6977|C|K}}}}
| {{sort|7250|{{convert|6977|C|K}}}}
| {{sort|5000|{{convert|5000|atm|kPa|abbr=on}}}}
| {{sort|5000|{{convert|5000|atm|kPa|abbr=on}}}}
|-
|-
| 铝
|-
| {{sort|7850|{{convert|7577|C|K}}}}
| {{sort|7850|{{convert|7577|C|K}}}}
|
|
|-
|-
| 水 (H<sub>2</sub>O)<ref name=IAPWS95/><ref>{{cite web | title = Critical Temperature and Pressure | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | access-date = 2006-12-19 }}</ref>
| [[Water]] (H<sub>2</sub>O)<ref name=IAPWS95/><ref>{{cite web | title = Critical Temperature and Pressure | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-19 }}</ref>
| {{sort|0647.096|{{convert|373.946|C|K}}}}
| {{sort|0647.096|{{convert|373.946|C|K}}}}
| {{sort|0217.7|{{convert|217.7|atm|kPa|abbr=on}}}}
| {{sort|0217.7|{{convert|217.7|atm|kPa|abbr=on}}}}
|-
|-
|}
|}
</center>
</center>
从理论上讲，液-液临界点代表旋节曲线的温度-浓度极值（如右图所示）。因此，双组分体系的液-液临界点必须满足两个条件：旋节曲线的条件（自由能对浓度的二阶导数必须等于零），以及极值条件（自由能对浓度的三阶导数也必须等于零，或者旋节温度对浓度的导数必须等于零）
从理论上讲，液-液临界点代表旋节曲线的温度-浓度极值（如右图所示）。因此，双组分体系的液-液临界点必须满足两个条件：旋节曲线的条件（自由能对浓度的二阶导数必须等于零），以及极值条件（自由能对浓度的三阶导数也必须等于零，或者旋节温度对浓度的导数必须等于零）
==混合物：液体-液体临界点 ==
[[Image:LCST-UCST plot.svg|thumb|upright=1.5|A plot of typical polymer solution phase behavior including two critical points: a [[LCST]] and an [[Upper critical solution temperature|UCST]]]]
[[Image:LCST-UCST plot.svg.png|thumb|upright=1.5|典型的聚合物溶液相行为图，包括两个临界点:下临界溶液温度和上临界溶液温度]]
在“临界溶液温度”下，溶液的[[液-液临界点]]出现在相图两相区的极限处。换言之，它是某个热力学变量（如温度或压力）的微小变化导致混合物分离为两个不同的液相的点，如右侧的聚合物-溶剂相图所示。两种类型的液-液临界点是[[上临界溶液温度]] upper critical solution temperature（UCST），这是冷却导致相分离的最热点，和[[下临界溶液温度]] lower critical solution temperature（LCST），这是加热导致相分离的最冷点。
在“临界溶液温度”下，溶液的[[液-液临界点]]出现在相图两相区的极限处。换言之，它是某个热力学变量（如温度或压力）的微小变化导致混合物分离为两个不同的液相的点，如右侧的聚合物-溶剂相图所示。两种类型的液-液临界点是[[上临界溶液温度]]（UCST），这是冷却导致相分离的最热点，和[[下临界溶液温度]]（LCST），这是加热导致相分离的最冷点。
===Mathematical definition数学定义===
===数学定义===
从理论上看，从液体的临界点（从理论上看，是指液体的临界温度）。因此，双组分体系中的液-液临界点必须满足两个条件：旋节曲线的条件（[[Gibbs自由能]]相对于浓度的“二阶”导数必须等于零）和极值条件（自由能相对于浓度的“第三”导数）也必须等于零，或者旋节温度对浓度的导数必须等于零）。
==参见==
{{colbegin}}
==See also参见==
* [[共形场论 Conformal field theory]]
* [[临界指数 Critical exponents]]
* [[临界现象 Critical phenomena]]
* [[要素临界点 Critical points of the elements (data page)]]
* [[居里点 Curie point]]
* [[液体-液体临界点 Liquid–liquid critical point]]
* [[Néel点 Néel point]]
* [[过滤阈值 Percolation thresholds]]
* [[相变 Phase transition]]
* [[Rushbrooke不等式 Rushbrooke inequality]]
* [[比例不变性 Scale invariance]]
* [[自组织临界性]]
* [[Widom缩放 Widom scaling]]
{{colend}}
{{colend}}
==参考文献 ==
== Footnotes脚注 ==
<references/>
*{{cite web | title = Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam | publisher = International Association for the Properties of Water and Steam | date = August 2007 | url = http://www.iapws.org/relguide/IF97-Rev.pdf | accessdate = 2009-06-09 }}
*{{cite web | title = Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam | publisher = International Association for the Properties of Water and Steam | date = August 2007 | url = http://www.iapws.org/relguide/IF97-Rev.pdf | accessdate = 2009-06-09 }}
==外部链接==
==External links外部链接==
* {{cite web |title=Critical points for some common solvents |url=http://www.proscitech.com.au/catalogue/notes/cpd.htm |archiveurl=https://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm |publisher=ProSciTech |archivedate=2008-01-31}}
*{{cite web | title = Critical Temperature and Pressure | work = Department of Chemistry| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}
== 编者推荐==
===集智课程===
====[https://campus.swarma.org/course/1131 复杂性与临界现象 2020]====
该课程为北京师范大学系统科学学院陈晓松教授开设的研究生课程《复杂性与临界现象》课程回放。
主要讲解内容：
*复杂系统与复杂性简介
*统计系统理论
*平衡态系统临界现象
*非平衡与复杂系统临界现象
====[https://campus.swarma.org/course/1378 平衡态系统相变临界现象]====
目前临界在平衡态系统的研究比较成熟，本节课程将对过去一百多年的关于相变临界现象的研究进行介绍，其研究思想、方法、观点、概念，对其他非平衡态系统、动力系统的研究也有借鉴意义。
主要讲解内容：
*平衡态临界现象的根本特征是长程关联
*系统的宏观性质具有标度性和普适性
*描述系统宏观性质的临界指数只依赖系统维数和序参量的维数
*在平均场近似下，不同空间维数系统的临界指数相同
====[https://campus.swarma.org/course/1525 临界现象的标度性与超标度关系]====
在物理学中，精确解具有重要的意义。该课程将从与临界涨落相关的热力学量自由能，其奇异部分满足齐次性要求下，求解推出临界现象的标度性与超标度关系，得出一般性规律。
主要讲解内容：
*由自由能奇异部分的齐次性，可将所有临界指数用关联长度的临界指数表示
*关联长度有对温度和外场两个临界指数
*各热力学量的临界指数并不独立，满足超标度（hyperscaling）关系
*临界现象理论得到了微重力、高精度实验的证实
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[[Category: 凝聚态物理学]]
[[Category:共形场论]]
[[Category:关键现象]]
[[Category:阶段转变]]
[[Category:重整化群]]
[[Category:临界温度]]
[[Category:气体]]