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第1行： − 此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。{{Other uses|Critical point (disambiguation){{!}}Critical point}}+ − − − − − + 第11行：
第7行： − + − − 1. Subcritical [[ethane]], liquid and gas phase coexist<br /> − − 1. Subcritical ethane, liquid and gas phase coexist<br /> − − 1.亚临界乙烷、液相和气相共存 − − 2. Critical point (32.17 °C, 48.72 bar), opalescence<br /> − − 2. Critical point (32.17 °C, 48.72 bar), opalescence<br /> − − 2.临界点(32.17 c，48.72 bar) ，乳白比 / − − 3. 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. |publisher=Carl-von-Ossietzky Universität Oldenburg |year=2000 |isbn=3-8265-7829-5}}</ref>]] − − 3. Supercritical ethane, fluid]] − − 3.[超临界乙烷]] − − − − − − 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，临界点(或临界状态)是相平衡曲线的终点。最突出的例子是液体-蒸汽临界点，即指定液体和蒸汽共存条件的压力-温度曲线的终点。在较高的温度下，气体不能单靠压力液化。在临界点，由临界温度 t 子 c / sub 和临界压力 p 子 c / sub 定义，相界消失。其他例子包括混合物中的液-液临界点。 − − − − − − == Liquid-vapor critical point == − − == Liquid-vapor critical point == − − 液-气临界点 − − − − − − === Overview === − − === Overview === − − 概览 − − − − − − [[Image:phase-diag2.svg|thumb|upright=1.5|right|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。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. − − 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，这个例子就是液体-蒸汽临界点。这是第一个被发现的临界点，而且它仍然是最著名和研究最多的一个。 − − − − − − 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 [[phase (matter)|phase]]s ''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. − − 右边的图显示了纯物质的 PT 示意图(相对于混合物，混合物有额外的状态变量和更丰富的相图，下面将讨论)。通常所知的固相、液相和蒸汽由相界分开，即:。两个阶段可以共存的压力-温度组合。在三相点上，所有三个阶段都可以共存。然而，液-汽边界终止于某一临界温度 t 低于 c / 亚临界压力 p 低于 c / 亚临界压力的终点。这是临界点。 − − − − − − 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，临界点发生在和。 − − − − − − 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.<ref>Anisimov, Sengers, Levelt Sengers (2004): − − 在临界点附近，液相和蒸汽的物理性质发生了剧烈的变化，两相变得越来越相似。例如，液态水在正常情况下几乎是不可压缩的，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、介电性能差、是电解质的糟糕溶剂，而且更喜欢与非极性气体和有机分子混合。 参考 Anisimov，Sengers，Levelt Sengers (2004) : − − Near-critical behavior of aqueous systems. − − Near-critical behavior of aqueous systems. − − 水系统的近临界行为。 − − Chapter 2 in − − Chapter 2 in − − 第二章 − − Aqueous System at Elevated Temperatures and Pressures − − Aqueous System at Elevated Temperatures and Pressures − − 高温高压下的水系统 − − Palmer et al, eds. − − Palmer et al, eds. − − 帕尔默等人。 − − Elsevier.</ref> − − Elsevier.</ref> − − 爱思唯尔 / 裁判 − − − − − − ''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，只有一个阶段存在。汽化热为零。在 PV 图的恒温线(临界等温线)上有一个稳定的拐点。这意味着在关键时刻: − − − − − − :<math>\left(\frac{\partial p}{\partial V}\right)_T = 0</math> − − <math>\left(\frac{\partial p}{\partial V}\right)_T = 0</math> − − 左(部分 p)右) 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> − − 左(部分 v ^ 2)右) t 0 / math − − + + − [[Image:Real Gas Isotherms.svg|thumb|upright=1.5|right|The ''critical isotherm'' with the critical point K]]+ − 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，这种状态连续地连接着液态和气态(可以不经过相变而转化为液态和气态)。它被称为超临界流体。一般教科书认为，在临界点以外，液体和蒸汽之间的所有区别都会消失，这一认识受到了 Fisher 和 Widom 的挑战，他们确定了一个 p，t 线，它可以分离具有不同渐近统计性质的状态(Fisher-Widom 线)。+ − + − − − − === History === − − === History === − − 历史 − − − − − − [[Image:Critical carbon dioxide.jpg|thumb|right|critical carbon dioxide|[[Carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature]] − − [[Carbon dioxide exuding fog while cooling from supercritical to critical temperature]] − − [二氧化碳在从超临界温度冷却到临界温度时产生雾] − − − − − − 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&vq=Cagniard&pg=PA127#v=onepage&q&f=false |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" (Russian: абсолютная температура кипения ; German: ''absolute Siedetemperatur'' ). − − The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860<ref>Mendeleev called the critical point the "absolute temperature of boiling" (Russian: абсолютная температура кипения ; German: absolute Siedetemperatur ). − − 临界点的存在最早是由卡尼亚尔·德·拉·图尔于1822年发现的，并由 Dmitri Mendeleev 于1860年命名为，参考 Mendeleev 称临界点为“沸腾的绝对温度”(俄语: ; 德语: 绝对 sietemperatur)。 − − * {{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=Russian}} 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=German|doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: ''"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 |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=German}}</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 3,000 atm. − − − − − − − − === Theory === − − === Theory === − − 理论 − − − − − − 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 − − 解决上述条件数学(部分 p / 部分 v) t 0 / 数学的范德华方程，可以计算临界点为 − − :<math>T_c = \frac{8a}{27Rb},\ V_c = 3nb,\ p_c = \frac a {27b^2}</math>. − − <math>T_c = \frac{8a}{27Rb},\ V_c = 3nb,\ p_c = \frac a {27b^2}</math>. − − 27Rb， v c 3nb， p c frac a {27b ^ 2} / math. − − 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 laws. − − 然而，基于平均场理论的范德华方程，在临界点附近并不成立。特别是，它预测了错误的比例定律。 − − − − − − 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 − − 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 − − − − − − :<math>T_r = \frac T {T_c},\ p_r = \frac p {p_c},\ V_r = \frac{V}{RT_c/p_c}</math>. − − <math>T_r = \frac T {T_c},\ p_r = \frac p {p_c},\ V_r = \frac{V}{RT_c/p_c}</math>. − − 数学 t r frac { tc } ， p r frac { p c } ， v r frac { v }{ RT c / p c } / math。 − − − − − − 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>''. − − 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>. − − 相应状态原理表明，物质在相同减少的压力和温度下有相同减少的体积。对于许多物质来说，这种关系近似正确，但对于 p sub r / sub 的大值，这种关系变得越来越不准确。 − − − − − − 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. − − 对于某些气体，在用这种方法计算的临界温度和临界压力之外，还有一个额外的修正因子，称为牛顿修正。这些都是经验得出的价值和变化的压力范围的利息。 − − − − − − === Table of liquid–vapor critical temperature and pressure for selected substances === − − === Table of liquid–vapor critical temperature and pressure for selected substances === − − 选定物质的液体-蒸气临界温度和压力表 − − {{see also|Critical points of the elements (data page)}} − − − − <center> − − <center> − − 中心 − − {| class="wikitable sortable" style="text-align: center;" − − {| class="wikitable sortable" style="text-align: center;" − − { | 类“ wikitable sortable”样式“ 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 − − !物质 − − ! Critical temperature − − ! Critical temperature − − !临界温度 − − ! Critical pressure (absolute) − − ! Critical pressure (absolute) − − !临界压力(绝对值) − − |- − − |- − − |- − − | [[Argon]] − − | Argon − − | 氩气 − − | {{sort|0150.8|{{convert|-122.4|C|K}}}} − − | }} − − | {{sort|0048.1|{{convert|48.1|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[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> − − | Ammonia (NH<sub>3</sub>) − − | 氨(NH 分3 / sub) − − | {{sort|0405.6|{{convert|132.4|C|K}}}} − | }} − | {{sort|0111.3|{{convert|111.3|atm|kPa|abbr=on}}}} 第399行：
第45行： − + − + − − − − | [[R-134a]] − − | R-134a − − | R-134a − − | {{sort|0374|{{convert|101.06|C|K}}}} − − | }} − − | }} − − | {{sort|0040|{{convert|40.06|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − − − − − | [[R-410A]] − − | R-410A − − | R-410A − − | {{sort|0346|{{convert|72.8|C|K}}}} − − | }} − − | }} − − | {{sort|0047|{{convert|47.08|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − − − − − | [[Bromine]] − − | Bromine − − | 溴 − − | {{sort|0584.0|{{convert|310.8|C|K}}}} − − | }} − − | }} − − | {{sort|0102|{{convert|102|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Caesium]] − − | Caesium − − 铯 − − | {{sort|1938.00|{{convert|1664.85|C|K}}}} − − | }} − − | }} − − | {{sort|0094|{{convert|94|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Chlorine]] − − | Chlorine − − | 氯气 − − | {{sort|0417.0|{{convert|143.8|C|K}}}} − − | }} − − | }} − − | {{sort|0076.0|{{convert|76.0|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Ethanol]] (C<sub>2</sub>H<sub>5</sub>OH) − − | Ethanol (C<sub>2</sub>H<sub>5</sub>OH) − − 乙醇(c sub 2 / sub h sub 5 / sub OH) − − | {{sort|0514.0|{{convert|241|C|K}}}} − − | }} − − | }} − − | {{sort|0062.2|{{convert|62.18|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Fluorine]] − − | Fluorine − − | 氟 − − | {{sort|0144.30|{{convert|-128.85|C|K}}}} − − | }} − − | }} − − | {{sort|0051.5|{{convert|51.5|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Helium]] − − | Helium − − | 氦气 − − | {{sort|0005.19|{{convert|-267.96|C|K}}}} − − | }} − − | }} − − | {{sort|0002.24|{{convert|2.24|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Hydrogen]] − − | Hydrogen − − | 氢 − − | {{sort|0033.20|{{convert|-239.95|C|K}}}} − − | }} − − | }} − − | {{sort|0012.8|{{convert|12.8|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Krypton]] − − | Krypton − − 氪星 − − | {{sort|0209.4|{{convert|-63.8|C|K}}}} − − | }} − − | }} − − | {{sort|0054.3|{{convert|54.3|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Methane]] (CH<sub>4</sub>) − − | Methane (CH<sub>4</sub>) − − | 甲烷(ch4 / sub) − − | {{sort|0190.8|{{convert|-82.3|C|K}}}} − − | }} − − | }} − − | {{sort|0045.79|{{convert|45.79|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Neon]] − − | Neon − − 霓虹灯 − − | {{sort|0044.40|{{convert|-228.75|C|K}}}} − − | }} − − | }} − − | {{sort|0027.2|{{convert|27.2|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Nitrogen]] − − | Nitrogen − − | 氮气 − − | {{sort|0126.3|{{convert|-146.9|C|K}}}} − − | }} − − | }} − − | {{sort|0033.5|{{convert|33.5|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Oxygen]] (O<sub>2</sub>) − − | Oxygen (O<sub>2</sub>) − − | 氧气(o 亚2 / 亚) − − | {{sort|0154.6|{{convert|-118.6|C|K}}}} − − | }} − − | }} − − | {{sort|0049.8|{{convert|49.8|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Carbon dioxide]] (CO<sub>2</sub>) − − | Carbon dioxide (CO<sub>2</sub>) − − | 二氧化碳(co2 / sub) − − | {{sort|0304.19|{{convert|31.04|C|K}}}} − − | }} − − | }} − − | {{sort|0072.8|{{convert|72.8|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Nitrous oxide]] (N<sub>2</sub>O) − − | Nitrous oxide (N<sub>2</sub>O) − − | 氧化亚氮(n2 / sub o) − − | {{sort|0304.19|{{convert|36.4|C|K}}}} − − | }} − − | }} − − | {{sort|0072.8|{{convert|71.5|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Sulfuric acid]] (H<sub>2</sub>SO<sub>4</sub>) − − | Sulfuric acid (H<sub>2</sub>SO<sub>4</sub>) − − | 硫酸(h 亚2 / 亚 SO 亚4 / 亚) − − | {{sort|0927|{{convert|654|C|K}}}} − − | }} − − | }} − − | {{sort|0045.4|{{convert|45.4|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Xenon]] − − | Xenon − − 氙气 − − | {{sort|0289.8|{{convert|16.6|C|K}}}} − − | }} − − | }} − − | {{sort|0057.6|{{convert|57.6|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Lithium]] − − | Lithium − − | Lithium − − | {{sort|3223|{{convert|2950|C|K}}}} − − | }} − − | }} − − | {{sort|0652|{{convert|652|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Mercury (element)|Mercury]] − − | Mercury − − 水星 − − | {{sort|1750.1|{{convert|1476.9|C|K}}}} − − | }} − − | }} − − | {{sort|1720|{{convert|1720|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Sulfur]] − − | Sulfur − − 硫磺 − − | {{sort|1314.00|{{convert|1040.85|C|K}}}} − − | }} − − | }} − − | {{sort|0207|{{convert|207|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Iron]] − − | Iron − − 铁 − − | {{sort|8500|{{convert|8227|C|K}}}} − − | }} − − | }} − − | − − | − − | − − |- − − |- − − |- − − | [[Gold]] − − | Gold − − | 黄金 − − | {{sort|7250|{{convert|6977|C|K}}}} − − | }} − − | }} − − | {{sort|5000|{{convert|5000|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − | [[Aluminium]] − − | Aluminium − − | 铝 − − | {{sort|7850|{{convert|7577|C|K}}}} − − | }} − − | }} − − | − − | − − | − − |- − − |- − − |- − − | [[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> − − | Water (H<sub>2</sub>O) − − | 水(h 分2 / sub o) − − | {{sort|0647.096|{{convert|373.946|C|K}}}} − − | }} − − | }} − − | {{sort|0217.7|{{convert|217.7|atm|kPa|abbr=on}}}} − − | }} − − | }} − − |- − − |- − − |- − − |} 第1,023行：
第57行： − </center>+ − + − + − − − − − − 混合物: 液-液临界点 + + − [[Image:LCST-UCST plot.svg|thumb|upright=1.5|A plot of typical polymer solution phase behavior including two critical points: an [[LCST]] and a [[Upper critical solution temperature|UCST]].]]+ − A plot of typical polymer solution phase behavior including two critical points: an [[LCST and a UCST.]] − 典型的聚合物溶液相行为图，包括两个临界点: [ 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) will lead 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 will induce phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating will induce phase separation.+ − 溶液的液-液临界点出现在临界溶液温度，出现在相图的两相区极限处。换句话说，正如右边的聚合物-溶剂相图所示，在某些热力学变量(如温度或压力)中的无限小的变化将导致混合物分离成两种不同的液相。液液两相临界点分别为上临界溶液温度(UCST)和下临界溶液温度(LCST)。上临界溶液温度是导致相分离的最热点，下临界溶液温度是导致相分离的最冷点。+ + − ===Mathematical definition=== − ===Mathematical definition===+ − − 数学定义 − − − − − − − − 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). + + − ==See also==+ − ==See also==+ − 参见+ + + − {{colbegin}}+ − *[[Conformal field theory]]+ + − *[[Critical exponents]] + − *[[Critical phenomena]] (more advanced article) + − *[[Critical points of the elements (data page)]] + − *[[Curie point]] + + − *[[Joback method]], [[Klincewicz method]], [[Lydersen method]] (Estimation of critical temperature, pressure, and volume from molecular structure) + − + + + − *[[Lower critical solution temperature]] + − *[[Néel point]] − − − − *[[Percolation thresholds]] − − − − *[[Phase transition]] − − − − *[[Rushbrooke inequality]] − − − − *[[Scale invariance]] − − − − *[[Self-organized criticality]] − − − − *[[Supercritical fluid]], [[Supercritical drying]], [[Supercritical water oxidation]], [[Supercritical fluid extraction]] − − − − *[[Tricritical point]] − − − − *[[Triple point]] − − − − *[[Upper critical solution temperature]] − − − − *[[Widom scaling]] − − − − {{colend}} − − − − − − − − == Footnotes == − − == Footnotes == − − 脚注 − − {{Reflist|38em}} − − − − − − − − == References == − − == References == − − 参考资料 − − *{{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 }} − − − − − − − − ==External links== − − ==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 }}+ − + + − {{Phase_of_matter}} − + − − − − − − [[Category:Condensed matter physics]] 第1,243行：
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Moved page from wikipedia:en:Critical point (thermodynamics) (history)
此词条暂由彩云小译翻译，翻译字数共273，未经人工整理和审校，带来阅读不便，请见谅。
{{Other uses|Critical point (disambiguation){{!}}Critical point}}
[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|
[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|
[[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 |
[图片: 临界点测量乙烷 jpg | thumb | right | upright = 1.5 |
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|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。
}}]]
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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.
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== Liquid–vapor critical point ==
</center>
</center>
/ 中心
</center >
=== Overview ===
==Mixtures: liquid–liquid critical point==
==Mixtures: liquid–liquid critical point==
[[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.]]
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|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) will lead 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 will induce phase separation, and the [[lower critical solution temperature]] (LCST), which is the coldest point at which heating will induce phase separation.
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.
溶液的液液临界点发生在临界溶液温度，出现在相图的两相区极限处。换句话说，它是一些热力学变量(如温度或压力)的无限小的变化导致混合物分离成两个不同的液相的点，如右边的聚合物-溶剂相图所示。液-液两相临界点分别为上临界溶液温度(UCST)和下临界溶液温度(LCST) ，前者是诱发相分离的最热点，后者是诱发相分离的最冷点。
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.
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''.
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).
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).
从理论角度来看，液-液临界点表示调节曲线的温度-浓度极值(如右图所示)。因此，双组分体系中的液-液临界点必须满足两个条件: 自由能对浓度的二阶导数必须等于零的条件和极值条件(自由能对浓度的三阶导数也必须等于零或自由能对浓度的三阶导数必须等于零)。
从理论角度来看，液-液临界点表示调节曲线的温度-浓度极值(如右图所示)。因此，双组分体系中的液-液临界点必须满足两个条件: 自由能对浓度的二阶导数必须等于零的条件和极值条件(自由能对浓度的三阶导数也必须等于零或自由能对浓度的三阶导数必须等于零)。
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 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.
Chapter 2 in
Aqueous System at Elevated Temperatures and Pressures
Palmer et al., eds.
Elsevier.</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>
: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>
: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>
[[Image:Real Gas Isotherms.svg|thumb|upright=1.5|The ''critical isotherm'' with the critical point K]]
''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]]).
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 ===
[[Image:Critical carbon dioxide.jpg|thumb|Critical [[carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature.]]
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}}).
*[[Liquid-liquid critical point]]
* {{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.)
* 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.
=== Theory ===
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
: <math>T_\text{c} = \frac{8a}{27Rb},
\quad V_\text{c} = 3nb,
\quad p_\text{c} = \frac{a}{27b^2}.</math>
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.
| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}
| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}
| 出版商普渡大学 | 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}
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>
: <math>T_\text{r} = \frac{T}{T_\text{c}},
Category:Condensed matter physics
Category:Condensed matter physics
类别: 凝聚态物理学
类别: 凝聚态物理学
\quad p_\text{r} = \frac{p}{p_\text{c}},
Category:Conformal field theory
Category:Conformal field theory
类别: 共形场论
类别: 共形场论
\quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math>
Category:Critical phenomena
Category:Critical phenomena
范畴: 关键现象
范畴: 关键现象
Category:Phase transitions
Category:Phase transitions
类别: 阶段转变
类别: 阶段转变
[[Category:Renormalization group]]
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>.
Category:Renormalization group
Category:Renormalization group
类别: 重整化群
类别: 重整化群
Category:Threshold temperatures
Category:Threshold temperatures
类别: 临界温度
类别: 临界温度
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>
Category:Gases
Category:Gases