153
个编辑
更改
无编辑摘要
此词条暂由Henry翻译
{{Other uses|Critical point (disambiguation){{!}}Critical point}}
{{Other uses|Critical point (disambiguation){{!}}Critical point}}
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，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-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。
== Liquid–vapor critical point ==
== Liquid–vapor critical point液-汽临界点 ==
=== Overview ===
=== Overview 总览===
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。]
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.
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。
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。
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 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.
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，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。
Near-critical behavior of aqueous systems.
Near-critical behavior of aqueous systems.
水体系的近临界行为
Chapter 2 in
Chapter 2 in
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:
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（临界等温线）中有一个固定的拐点。这意味着在临界点：
Aqueous System at Elevated Temperatures and Pressures
Aqueous System at Elevated Temperatures and Pressures
高温高压下的水体系
Palmer et al., eds.
Palmer et al., eds.
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）。
: <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，我们有一个隐藏的临界点，否则说我们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]]
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.
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 ===
=== History历史 ===
[[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.]]
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.
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 ===
=== Theory理论 ===
To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties
To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties
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pr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.
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。
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.
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).
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).
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）
==Mixtures: liquid–liquid critical point混合物：液体-液体临界点 ==
==Mixtures: liquid–liquid critical point==
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.
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.
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===
===Mathematical definition===
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).
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）。
==See also参见==
==See also==
* [[Conformal field theory]]
* [[Conformal field theory]]
共形场论
* [[Critical exponents]]
* [[Critical exponents]]
临界指数
* [[Critical phenomena]] (more advanced article)
* [[Critical phenomena]] (more advanced article)
临界现象
* [[Critical points of the elements (data page)]]
* [[Critical points of the elements (data page)]]
要素临界点
* [[Curie point]]
* [[Curie point]]
居里点
* [[Joback method]], [[Klincewicz method]], [[Lydersen method]] (estimation of critical temperature, pressure, and volume from molecular structure)
* [[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]]
* [[Liquid–liquid critical point]]
液体-液体临界点
* [[Lower critical solution temperature]]
* [[Lower critical solution temperature]]
较低临界溶液温度
* [[Néel point]]
* [[Néel point]]
Néel点
* [[Percolation thresholds]]
* [[Percolation thresholds]]
过滤阈值
* [[Phase transition]]
* [[Phase transition]]
相变
* [[Rushbrooke inequality]]
* [[Rushbrooke inequality]]
Rushbrooke不等式
* [[Scale invariance]]
* [[Scale invariance]]
比例不变性
* [[Self-organized criticality]]
* [[Self-organized criticality]]
自组织临界性
* [[Supercritical fluid]], [[Supercritical drying]], [[Supercritical water oxidation]], [[Supercritical fluid extraction]]
* [[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]]
* [[Tricritical point]]
三临界点
* [[Triple point]]
* [[Triple point]]
三重点
* [[Upper critical solution temperature]]
* [[Upper critical solution temperature]]
上临界溶液温度
* [[Widom scaling]]
* [[Widom scaling]]
Widom缩放
{{colend}}
{{colend}}
== Footnotes ==
== Footnotes脚注 ==
{{Reflist|38em}}
{{Reflist|38em}}
== References ==
== References参考 ==
*{{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 }}