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- Critical point (thermodynamics)

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.

For simplicity and clarity, the generic notion of *critical point* is best introduced by discussing a specific example, the vapor-liquid 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*.

In water, the critical point occurs at 647.096K and 22.064MPa.^{[1]}

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.^{[2]}

*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:^{[3]} ^{[4]} ^{[5]}

\left( | \partialp |

\partialV |

*\right)*_{T}=0*,*

\left( | \partial^{2p} |

\partialV^{2} |

*\right)*_{T}=0*.*

*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,^{[6]} who identified a *p*–*T* line that separates states with different asymptotic statistical properties (Fisher–Widom line).

Sometimes 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.^{[7]}

The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822^{[8]} ^{[9]} and named by Dmitri Mendeleev in 1860^{[10]} ^{[11]} and Thomas Andrews in 1869.^{[12]} Cagniard showed that CO_{2} 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.

Solving the above condition

*(\partial**p**/**\partial**V)*_{T}=0

*T*_{c}=

8a | |

27Rb |

*,
* *V*_{c}=3*nb,
* *p*_{c}=

a | |

27b^{2} |

*.*

To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties^{[13]}

*T*_{r}=

T | |

T_{c} |

*,
* *p*_{r}=

p | |

p_{c} |

*,
* *V*_{r}=

V | |

RT_{c}/p_{c} |

*.*

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}.

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.^{[14]}

See also: Critical points of the elements (data page).

Substance^{[15]} ^{[16]} | Critical temperature | Critical pressure (absolute) |
---|---|---|

Argon | ||

Ammonia (NH_{3})^{[17]} | ||

Bromine | ||

Caesium | ||

Chlorine | ||

Ethanol (C_{2}H_{5}OH) | ||

Fluorine | ||

Helium | ||

Hydrogen | ||

Krypton | ||

Methane (CH_{4}) | ||

Neon | ||

Nitrogen | ||

Oxygen (O_{2}) | ||

Carbon dioxide (CO_{2}) | ||

Nitrous oxide (N_{2}O) | ||

Sulfuric acid (H_{2}SO_{4}) | ||

Xenon | ||

Lithium | ||

Mercury | ||

Sulfur | ||

Iron | ||

Gold | ||

Aluminium | ||

Water (H_{2}O)^{[18]} | ||

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.

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).

- 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)
- Liquid–liquid critical point
- 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

- Web site: Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam . International Association for the Properties of Water and Steam . August 2007 . 2009-06-09 .

- Web site: Critical points for some common solvents . https://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm . ProSciTech . 2008-01-31.
- Web site: Critical Temperature and Pressure . Department of Chemistry. Purdue University . 2006-12-03 .

- Wagner . W. . Pruß . A. . The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use . Journal of Physical and Chemical Reference Data . June 2002 . 31 . 2 . 398 . 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.
- P. 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.
- Fisher, Widom:
*Decay of Correlations in Linear Systems*, J. Chem. Phys. 50, 3756 (1969). - Das . Tamoghna . Ganguly . Saswati . Sengupta . Surajit . Rao . Madan . Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals . Scientific Reports . 3 June 2015 . 5 . 1 . 10644 . 10.1038/srep10644 . 26039380 . 4454149 . 2015NatSR...510644D . free .
- 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 . 21 . 127–132 . fr.
- 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. . О расширении жидкостей от нагревания выше температуры кипения . Горный Журнал [Mining Journal] . 1861 . 4 . 141–152 . On the expansion of liquids from heating above the temperature of boiling . ru. The "absolute temperature of boiling" is defined on p. 151. Available at Wikimedia
- German translation: Mendelejeff . D. . Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt . Annalen der Chemie und Pharmacie . 1861 . 119 . 1–11 . On the expansion of fluids during heating above their boiling point . de . 10.1002/jlac.18611190102 . The "absolute temperature of boiling" is defined on p. 11: "German:
*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*^{2}= 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: Mendelejeff . D. . Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure . Annalen der Physik . 1870 . 141 . 618–626 . 10.1002/andp.18702171218 . 2nd series . Comments on Andrews' investigations into the compressibility of carbon dioxide . de.

- Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].
- 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 . 10.1098/rstl.1869.0021 . free . The term "critical point" appears on page 588.
- Book: Cengel . Yunus A. . Boles . Michael A. . Thermodynamics: an engineering approach . 2002 . McGraw-Hill . Boston . 978-0-07-121688-3 . 91–93.
- Compressibility Chart for Hydrogen and Inert Gases . Frank D. . Maslan . Theodore M. . Littman . Ind. Eng. Chem. . 1953 . 45 . 7 . 1566–1568 . 10.1021/ie50523a054 .
- Book: Emsley, John . The Elements . Second . . 1991 . 978-0-19-855818-7 .
- Book: Yunus A. . Cengel . Michael A. . Boles . Thermodynamics: An Engineering Approach . 824 . Fourth . . 2002 . 978-0-07-238332-4 . registration .
- Web site: Ammonia - NH3 - Thermodynamic Properties. www.engineeringtoolbox.com. 2017-04-07.
- Web site: Critical Temperature and Pressure . Purdue University . 2006-12-19 .