临界点(热力学)

来自集智百科
跳到导航 跳到搜索

此词条暂由Henry翻译

此词条暂由Miyasaki审校

模板:Other uses

[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|

[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|

[图片: 临界点测量乙烷 jpg | thumb | right | upright = 1.5 |

{{ordered list

{{ordered list

{有序列表

|Subcritical ethane, liquid and gas phase coexist.

|Subcritical ethane, liquid and gas phase coexist.

亚临界乙烷,液态和气态共存。

|Critical point (32.17 °C, 48.72 bar), opalescence.

|Critical point (32.17 °C, 48.72 bar), opalescence.

临界点(32.17 °C,48.72 bar) ,乳白色。

|Supercritical ethane, fluid.[1]

|Supercritical ethane, fluid.

超临界乙烷,流体。[2]

}}]]

}}]]

}}]]


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 Tc and a critical pressure pc, 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 Tc and a critical pressure pc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

在热力学中,一个 临界点Critical point (或临界状态)就是相平衡曲线的终点。最突出的例子是液-汽临界点,即压力-温度曲线的终点,它指明了液体和其蒸汽可以共存的条件。温度再高,气体就不能单靠压力液化。在由临界温度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液-汽临界点

Overview 总览

文件:Phase-diag2.svg
The liquid–vapor critical point in a pressure–temperature phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.

The liquid–vapor critical point in a pressure–temperature phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.

在压力-温度[[相图]中,液-汽临界点位于液-气相界面的高温极端处。绿色虚线显示了水的反常行为。]


For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.

For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.

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 Tc and critical pressure pc. 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 Tc and critical pressure pc. 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 模板:Convert and 模板:Convert.[3]

In water, the critical point occurs at and .

在水中,临界点发生在647.096K 和22.064MPa下。[3]


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.[4]


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:[5][6][7]

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Critical isotherm)中有一个固定的拐点。这意味着在临界点:[5][8][9]



The critical isotherm with the critical point K

临界点 k 的临界等温线


[math]\displaystyle{ \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 Fisher and Widom,[10] who identified a pT 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]\displaystyle{ \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.

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。

文件:Real Gas Isotherms.svg
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.[11]


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。

文件:Critical carbon dioxide.jpg
Critical carbon dioxide exuding fog while cooling from supercritical to critical temperature.


Solving the above condition [math]\displaystyle{ (\partial p / \partial V)_T = 0 }[/math] for the van der Waals equation, one can compute the critical point as

解决上述条件(∂p/∂V)T=0,对于范德华方程,可以计算临界点为

The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822[12][13] and named by Dmitri Mendeleev in 1860[14][15] and Thomas Andrews in 1869.[16] Cagniard showed that CO2 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 CO2 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[17][18] 由Charles Cagniard de la Tour首次发现,1860年[19][20] Dmitri mendelev和Thomas Andrews于1869年[21] 分别命名。Cagniard表明, CO2在31°C的压力下可以液化,但在更高一点的温度下,即使在高达3000 atm的压力下也不能液化。


However, the van der Waals equation, based on a mean-field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws.

然而,基于平均场理论的van der Waals方程在临界点附近并不成立。尤其是,它预测了错误的标度定律

Theory理论

To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties

为了分析临界点附近的流体性质,有时需要定义相对于临界性质的简化状态变量


Solving the above condition [math]\displaystyle{ (\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]\displaystyle{ (\partial p / \partial V)_T = 0 }[/math],就能将临界点计算为

[math]\displaystyle{ T_\text{r} = \frac{T}{T_\text{c}},

如果你想知道更多的信息,请访问我的网站,

: \lt math\gt T_\text{c} = \frac{8a}{27Rb},

  \quad p_\text{r} = \frac{p}{p_\text{c}},

4.1.1.1.2.2.2.2.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3

  \quad V_\text{c} = 3nb,

  \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}. }[/math]

4 v _ text { r } = frac { v }{ RT _ text { c }/p _ text { c } . </math >

 \quad p_\text{c} = \frac{a}{27b^2}.</math>
 --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 laws.

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 pr.

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。


To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties[22]

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。[23]

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.[24]

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。[25]



[math]\displaystyle{ T_\text{r} = \frac{T}{T_\text{c}}, \quad p_\text{r} = \frac{p}{p_\text{c}}, \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}. }[/math]

< 中心 >


{ | class = “ wikitable sortable” style = “ text-align: center; ” 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 pr.
Substance 物质


Critical temperature 临界温度


Critical pressure (absolute) 临界压力(绝对值)

Table of liquid–vapor critical temperature and pressure for selected substances

Argon 氩气
}} }}
}} }}
Substance[26][27] Ammonia (NH3) 氨(NH < sub > 3 ) Critical temperature }} }} Critical pressure (absolute) }} }}
Argon 模板:Sort R-134a R-134a 模板:Sort }} }}
}} }} Ammonia (NH3)[28]
模板:Sort 模板:Sort R-410A R-410A
}} }}


}} }} R-134a
模板:Sort 模板:Sort Bromine
}} }}


}} }} R-410A
模板:Sort Caesium

模板:Sort }} }}
}} }}


Bromine Chlorine 氯气 模板:Sort }} }} 模板:Sort }} }}
Caesium Ethanol (C2H5OH) 乙醇(c < sub > 2 h < sub > 5 OH) 模板:Sort }} }} 模板:Sort }} }}
Chlorine Fluorine 模板:Sort }} }} 模板:Sort }} }}
Ethanol (C2H5OH) Helium 氦气 模板:Sort }} }} 模板:Sort }} }}
Fluorine Hydrogen 氢气 模板:Sort }} }} 模板:Sort }} }}
Helium Krypton

氪星

模板:Sort }} }} 模板:Sort }} }}
Hydrogen Methane (CH4) 甲烷(CH < sub > 4 ) 模板:Sort }} }} 模板:Sort }} }}
Krypton Neon

霓虹灯

模板:Sort }} }} 模板:Sort }} }}
Methane (CH4) Nitrogen 氮气 模板:Sort }} }} 模板:Sort }} }}
Neon Oxygen (O2) 氧气(o < sub > 2 ) 模板:Sort }} }} 模板:Sort }} }}
Nitrogen Carbon dioxide (CO2) 二氧化碳(CO < sub > 2 ) 模板:Sort }} }} 模板:Sort }} }}
Oxygen (O2) Nitrous oxide (N2O) 氧化亚氮(n < sub > 2 o) 模板:Sort }} }} 模板:Sort }} }}
Carbon dioxide (CO2) Sulfuric acid (H2SO4) 硫酸(h < sub > 2 SO < sub > 4 ) 模板:Sort }} }} 模板:Sort }} }}
Nitrous oxide (N2O) Xenon 氙气 模板:Sort }} }} 模板:Sort }} }}
Sulfuric acid (H2SO4) Lithium Lithium 模板:Sort }} }} 模板:Sort }} }}
Xenon Mercury

水星

模板:Sort }} }} 模板:Sort }} }}
Lithium Sulfur

硫磺

模板:Sort }} }} 模板:Sort }} }}
Mercury Iron

模板:Sort }} }} 模板:Sort
Sulfur Gold 黄金 模板:Sort }} }} 模板:Sort }} }}
Iron Aluminium 模板:Sort }} }}
Gold Water (H2O) 水(h < sub > 2 o) 模板:Sort }} }} 模板:Sort }} }}
Aluminium

| 模板:Sort

|

|-

| Water (H2O)[3][29]

| 模板:Sort

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 ]

| 模板:Sort

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).

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

文件:LCST-UCST plot.svg
A plot of typical polymer solution phase behavior including two critical points: a LCST and an UCST

The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) leads to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature (UCST), which is the hottest point at which cooling induces phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating induces phase separation. 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

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(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

模板:Colbegin

共形场论

临界指数

临界现象

要素临界点

居里点

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)

液体-液体临界点

较低临界溶液温度

Néel点

过滤阈值

相变

Rushbrooke不等式

比例不变性

自组织临界性

超临界流体 超临界干燥 超临界水氧化 超临界流体萃取

三临界点

三重点

上临界溶液温度

Widom缩放 模板:Colend


Footnotes脚注

  1. Horstmann, Sven (2000). Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung [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] (Ph.D.) (in Deutsch). Oldenburg, Germany: Carl-von-Ossietzky Universität Oldenburg. ISBN 3-8265-7829-5. OCLC 76176158.
  2. Horstmann, Sven (2000). Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung [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] (Ph.D.) (in Deutsch). Oldenburg, Germany: Carl-von-Ossietzky Universität Oldenburg. ISBN 3-8265-7829-5. OCLC 76176158.
  3. 3.0 3.1 3.2 Wagner, W.; Pruß, A. (June 2002). "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use". Journal of Physical and Chemical Reference Data. 31 (2): 398. doi:10.1063/1.1461829.
  4. Anisimov, Sengers, Levelt Sengers (2004):Near-critical behavior of aqueous systems. 水体系的近临界行为 Chapter 2 inAqueous System at Elevated Temperatures and Pressures 高温高压下的水体系 Palmer et al., eds. [math]\displaystyle{ \left(\frac{\partial p}{\partial V}\right)_T = 0, }[/math] 左(frac { partial p }{ partial v } right) _ t = 0, Elsevier.
  5. 5.0 5.1 P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.
  6. K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.
  7. P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.
  8. K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.
  9. P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.
  10. Fisher, Widom: Decay of Correlations in Linear Systems, J. Chem. Phys. 50, 3756 (1969).
  11. Das, Tamoghna; Ganguly, Saswati; Sengupta, Surajit; Rao, Madan (3 June 2015). "Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals". Scientific Reports. 5 (1): 10644. Bibcode:2015NatSR...510644D. doi:10.1038/srep10644. PMC 4454149. PMID 26039380.
  12. Charles Cagniard de la Tour (1822). "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" [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]. Annales de Chimie et de Physique (in français). 21: 127–132.
  13. 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.
  14. Mendeleev called the critical point the "absolute temperature of boiling" (模板:Lang-ru; 模板:Lang-de). [math]\displaystyle{ 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\lt sup\gt 2\lt /sup\gt = 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''\lt sup\gt 2\lt /sup\gt = 0 [where ''a''\lt sup\gt 2\lt /sup\gt 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 >
  15. Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].
  16. Andrews, Thomas (1869). "The Bakerian lecture: On the continuity of the gaseous and liquid states of matter". Philosophical Transactions of the Royal Society. London. 159: 575–590. doi:10.1098/rstl.1869.0021. The term "critical point" appears on page 588.
  17. Charles Cagniard de la Tour (1822). "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" [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]. Annales de Chimie et de Physique (in français). 21: 127–132.
  18. 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.
  19. Mendeleev called the critical point the "absolute temperature of boiling" (模板:Lang-ru; 模板:Lang-de). [math]\displaystyle{ 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\lt sup\gt 2\lt /sup\gt = 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''\lt sup\gt 2\lt /sup\gt = 0 [where ''a''\lt sup\gt 2\lt /sup\gt 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 >
  20. Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].
  21. Andrews, Thomas (1869). "The Bakerian lecture: On the continuity of the gaseous and liquid states of matter". Philosophical Transactions of the Royal Society. London. 159: 575–590. doi:10.1098/rstl.1869.0021. The term "critical point" appears on page 588.
  22. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93. ISBN 978-0-07-121688-3. 
  23. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93. ISBN 978-0-07-121688-3. 
  24. Maslan, Frank D.; Littman, Theodore M. (1953). "Compressibility Chart for Hydrogen and Inert Gases". Ind. Eng. Chem. 45 (7): 1566–1568. doi:10.1021/ie50523a054.
  25. Maslan, Frank D.; Littman, Theodore M. (1953). "Compressibility Chart for Hydrogen and Inert Gases". Ind. Eng. Chem. 45 (7): 1566–1568. doi:10.1021/ie50523a054.
  26. Emsley, John (1991). The Elements (Second ed.). Oxford University Press. ISBN 978-0-19-855818-7. 
  27. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: An Engineering Approach (Fourth ed.). McGraw-Hill. pp. 824. ISBN 978-0-07-238332-4. https://archive.org/details/thermodynamicsen00ceng_0/page/824. 
  28. "Ammonia - NH3 - Thermodynamic Properties". www.engineeringtoolbox.com. Retrieved 2017-04-07.
  29. "Critical Temperature and Pressure". Purdue University. Retrieved 2006-12-19.

| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}

| publisher = 普渡大学 | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03}


References参考


Category:Condensed matter physics

类别: 凝聚态物理学

External links外部链接

Category:Conformal field theory

类别: 共形场论

Category:Critical phenomena

范畴: 关键现象

  • "Critical Temperature and Pressure". Department of Chemistry Category:Phase transitions 类别: 阶段转变. Purdue University. Retrieved 2006-12-03. line feed character in |work= at position 24 (help)

Category:Renormalization group

类别: 重整化群


Category:Threshold temperatures

类别: 临界温度

模板:Phase of matter

Category:Gases

分类: 气体


This page was moved from wikipedia:en:Critical point (thermodynamics). Its edit history can be viewed at 临界点(热力学)/edithistory