临界点

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[[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 |

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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.

|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 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_c and a critical pressure p_c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

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Liquid–vapor critical point

Overview

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.

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

典型的聚合物溶液相行为图，包括两个临界点: a [ LCST 和 UCST ]

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

溶液的液液临界点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 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_c and critical pressure p_c. 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).

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 模板:Convert and 模板:Convert.

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.

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:

[math]\displaystyle{ \left(\frac{\partial p}{\partial V}\right)_T = 0, }[/math]

[math]\displaystyle{ \left(\frac{\partial^2p}{\partial V^2}\right)_T = 0. }[/math]

文件:Real Gas Isotherms.svg

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 Fisher and Widom, 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.

History

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 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.

Theory

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

[math]\displaystyle{ 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 laws.

| 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}

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

[math]\displaystyle{ T_\text{r} = \frac{T}{T_\text{c}}, Category:Condensed matter physics 类别: 凝聚态物理学 \quad p_\text{r} = \frac{p}{p_\text{c}}, Category:Conformal field theory 类别: 共形场论 \quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}. }[/math]

Category:Critical phenomena

范畴: 关键现象

Category:Phase transitions

类别: 阶段转变

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_r.

Category:Renormalization group

类别: 重整化群

Category:Threshold temperatures

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.

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