Inthermodynamics, acritical point (orcritical state) is the end point of a phaseequilibrium curve. One example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which aliquid and itsvapor can coexist. At higher temperatures, the gas comes into asupercritical phase, and so cannot be liquefied by pressure alone. At the critical point, defined by acritical temperatureTc and acritical pressurepc,phase boundaries vanish. Other examples include theliquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field.[2]
The liquid–vapor critical point in a pressure–temperaturephase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dashed green line shows the anomalous behavior of water.
The liquid–vapor critical point was the first critical point to be discovered, and it remains the best known and most studied one.
The figure shows the schematicP-T diagram of apure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly knownphasessolid,liquid andvapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At thetriple point, all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at somecritical temperatureTc andcritical pressurepc. This is thecritical point.
The critical point of water occurs at 647.096 K (373.946 °C; 705.103 °F) and 22.064 megapascals (3,200.1 psi; 217.75 atm; 220.64 bar).[3]
In thevicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming even more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a highdielectric 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 poordielectric, a bad solvent for electrolytes, and mixes more readily with nonpolar gases and organic molecules.[4]
Isotherms of a gas. The red line is the critical isotherm, with critical point K. The dashed lines represent parts of isotherms which are forbidden since the gradient would be positive, giving the gas in this region anegative compressibility.
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 calledsupercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged byFisher andWidom,[8] who identified ap–T line that separates states with different asymptotic statistical properties (Fisher–Widom line).
Sometimes[ambiguous] 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.[9]
Criticalcarbon dioxide exudingfog while cooling from supercritical to critical temperature.
The existence of a critical point was first discovered byCharles Cagniard de la Tour in 1822[10][11] and named byDmitri Mendeleev in 1860[12][13] andThomas Andrews in 1869.[14] 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.
However, the van der Waals equation, based on amean-field theory, does not hold near the critical point. In particular, it predicts wrongscaling laws.
To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties[15]
Theprinciple 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 ofpr.
For some gases, there is an additional correction factor, calledNewton'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.[16]
Table of liquid–vapor critical temperature and pressure for selected substances
A plot of typical polymer solution phase behavior including two critical points: aLCST and anUCST
Theliquid–liquid critical point of a solution, which occurs at thecritical 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 theupper critical solution temperature (UCST), which is the hottest point at which cooling induces phase separation, and thelower critical solution temperature (LCST), which is the coldest point at which heating induces phase separation.
From a theoretical standpoint, the liquid–liquid critical point represents the temperature–concentration extremum of thespinodal 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 (thesecond derivative of thefree energy with respect to concentration must equal zero), and the extremum condition (thethird 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).
^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 thePSRK group contribution equation of state] (Ph.D.) (in German). Oldenburg, Germany:Carl-von-Ossietzky Universität Oldenburg.ISBN3-8265-7829-5.OCLC76176158.
^Stanley, H. Eugene (1987).Introduction to phase transitions and critical phenomena. New York: Oxford University Press.ISBN0-19-505316-8.OCLC15696711.
^abWagner, 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.
^Anisimov,Sengers,Levelt Sengers (2004):Near-critical behavior of aqueous systems.Chapter 2 inAqueous System at Elevated Temperatures and PressuresPalmer et al., eds.Elsevier.
^abP. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.
^K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.
^P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.
^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.
^Mendeleev called the critical point the "absolute temperature of boiling" (Russian:абсолютная температура кипения;German:absolute Siedetemperatur).
Менделеев, Д. (1861). "О расширении жидкостей от нагревания выше температуры кипения" [On the expansion of liquids from heating above the temperature of boiling].Горный Журнал [Mining Journal] (in Russian).4:141–152. The "absolute temperature of boiling" is defined on p. 151. Available atWikimedia
German translation:Mendelejeff, D. (1861)."Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt" [On the expansion of fluids during heating above their boiling point].Annalen der Chemie und Pharmacie (in German).119:1–11.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 a2 = 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° anda2 = 0 [wherea2 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.)
^Cengel, Yunus A.; Boles, Michael A. (2002).Thermodynamics: an engineering approach. Boston: McGraw-Hill. pp. 91–93.ISBN978-0-07-121688-3.
^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.
