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第27行： − | 临界点(32.17 ° c，48.72 bar) ，乳白色。+ 第31行：
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第47行： − 在热力学中，<font color="#ff8000"> 临界点Critical point </font>（或临界状态）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。在较高的温度下，气体不能单靠压力液化。在由临界温度Tc和临界压力Pc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。 + 第69行：
第71行： − 为了简单明了，临界点的一般概念最好通过讨论一个具体的例子来介绍，例如液体-蒸汽临界点。这是第一个被发现的临界点，也仍然是最著名和研究最多的一个。+ 第77行：
第79行： − + 第85行：
第87行： − + − − − − 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): − 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 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： − − Aqueous System at Elevated Temperatures and Pressures 第113行：
第103行： − <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math> − 左(frac { partial ^ 2p }{ partial v ^ 2} right) _ t = 0+ + + + + + + + + + + + + 第128行：
第129行： + + − 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挑战，他们确定了一条p-T线，它将具有不同渐近统计性质的状态分开（Fisher-Widom线）。 + 第139行：
第142行： − 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，我们有一个隐藏的临界点，否则说我们有一个暴露的临界点。 + − ''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]]). − − Critical [[carbon dioxide exuding fog while cooling from supercritical to critical temperature.]] − − 临界温度[在从超临界温度冷却到临界温度时，二氧化碳释放出雾] 第154行：
第152行： − 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年由查尔斯 卡尼亚 德拉图尔（Charles Cagniard de la Tour）首次发现，1860年由德米特里·门捷列夫（Dmitri mendelev）和托马斯·安德鲁斯（Thomas Andrews）于1869年分别命名。Cagniard表明，CO2在31°C的压力下可以液化，但在稍高的温度下，即使在高达3000 atm的压力下也不能液化。 + + − === History历史 ===+ 第189行：
第187行： + + + + + + + + + + + + + + + + + + + + + + + + 第203行：
第225行： + + 第221行：
第245行： + + + + − 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pr的大值，这种关系变得越来越不准确。+ + + + + − + + + 第265行：
第299行： − 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>
无编辑摘要
此词条暂由Henry翻译
此词条暂由Henry翻译
此词条暂由Miyasaki审校
{{Other uses|Critical point (disambiguation){{!}}Critical point}}
{{Other uses|Critical point (disambiguation){{!}}Critical point}}
|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]].<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.
|Supercritical ethane, fluid.
超临界乙烷，流体。
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 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.
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。
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.
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。
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.
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.
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Tc和临界压力Pc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。
In water, the critical point occurs at and .
In water, the critical point occurs at and .
在水中，临界点发生在647.096K 和22.064MPa下。
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>
Near-critical behavior of aqueous systems.
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
水体系的近临界行为
Chapter 2 in
Chapter 2 inAqueous System at Elevated Temperatures and Pressures
高温高压下的水体系
高温高压下的水体系
Palmer et al., eds.
Palmer et al., eds.
Elsevier.</ref>
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 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
The critical isotherm with the critical point K
: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>
: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>
''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).
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）。
: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>
: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>
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.
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。
[[Image:Real Gas Isotherms.svg|thumb|upright=1.5|The ''critical isotherm'' with the critical point K]]
[[Image:Real Gas Isotherms.svg|thumb|upright=1.5|The ''critical isotherm'' with the critical point K]]
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>
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。
[[Image:Critical carbon dioxide.jpg|thumb|Critical [[carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature.]]
[[Image:Critical carbon dioxide.jpg|thumb|Critical [[carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature.]]
* 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.
* 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]
\quad V_\text{c} = 3nb,
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.)
\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> 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.
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.
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
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}},
<math>T_\text{r} = \frac{T}{T_\text{c}},
\quad p_\text{c} = \frac{a}{27b^2}.</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.
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>.
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>.
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。
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>
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.
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.
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。
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>
!物质
!物质
! Critical temperature
! Critical temperature