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| {{Other uses|Critical point (disambiguation){{!}}Critical point}}
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| [[Image:Critical carbon dioxide.jpg|thumb|right|200px|critical carbon dioxide|[[Carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature]] In [[physical chemistry]], [[thermodynamics]], [[chemistry]] and [[condensed matter physics]], a '''critical point''', also known as a '''critical state''', occurs under conditions (such as specific values of temperature, pressure or composition) at which no [[phase (matter)|phase]] boundaries exist. There are multiple types of critical points, including vapor–liquid critical points and liquid–liquid critical points.
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| ==Pure substances: vapor–liquid critical point==
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| [[Image:CriticalPointMeasurementEthane.jpg|thumb|left|400px|3 states: subcricital, critical and supercritical ethane|
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| 1. Subcritical ethane, liquid and gas phase coexist<br />
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| 2. Critical point, opalescence<br />
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| 3. Supercritical [[ethane]], [[fluid]]<ref>Sven Horstmann, "Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung", Doktorarbeit, C.-v.-O. Universität Oldenburg, 2000</ref>]]
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| [[Image:phase-diag2.svg|thumb|350px|right|In a typical phase diagram, the boundary between gas and liquid runs from the triple point to the critical point.|The vapor–liquid 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.]]
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| The term [[critical point (thermodynamics)|critical point]] is sometimes used to specifically denote the vapor–liquid critical point of a material, above which distinct [[liquid]] and [[gas]] [[phases of matter|phases]] do not exist. As shown in the phase diagram to the right, this is the point at which the phase boundary between liquid and gas terminates. In water, the critical point occurs at around {{convert|647|K|abbr=on|lk=in}} and 22.064 [[Pascal (unit)|MPa]] (3200 PSIA or 218 [[Atmosphere (unit)|atm]]).<ref name="Steam 2007">International Association for the Properties of Water and Steam, 2007.</ref>
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| As the substance approaches critical temperature, the properties of its gas and liquid phases converge, resulting in only one phase at the critical point: a homogeneous [[supercritical fluid]]. The [[heat of vaporization]] is zero at and beyond this critical point, and so no distinction exists between the two phases. On the [[PT diagram]], the point at which critical temperature and critical pressure meet is called the critical point of the substance. Above the critical temperature, a liquid cannot be formed by an increase in [[pressure]], even though a solid may be formed under sufficient pressure. The critical pressure is the [[vapor pressure]] at the critical temperature. The critical [[molar volume]] is the volume of one mole of material at the critical temperature and pressure.
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| Critical properties vary from material to material, and for many pure substances are readily available in the literature. Nonetheless, obtaining critical properties for mixtures is more challenging.
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| ===Mathematical definition ===
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| [[Image:Real Gas Isotherms.svg|thumb|350px|right|The [[critical isotherm]] with the [[critical point (thermodynamics)|critical point]] K]]
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| For pure substances, there is an [[inflection point]] in the [[critical isotherm]] (constant temperature line) on a [[PV diagram]]. This means that at the critical point:<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W.H. Freeman 2006), p.21</ref><ref>K.J. Laidler and J.H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p.27</ref><ref>P.A. Rock, Chemical Thermodynamics (MacMillan 1969), p.123</ref>
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| :<math>\left(\frac{\partial p}{\partial V}\right)_T = \left(\frac{\partial^2p}{\partial V^2}\right)_T = 0</math>
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| That is, the first and second [[partial derivative]]s of the pressure ''p'' with respect to the volume ''V'' are both zero, with the partial derivatives evaluated at constant temperature ''T''. This relation can be used to evaluate two parameters for an [[equation of state]] in terms of the critical properties, such as the parameters a and b in the [[van der Waals equation]].<ref name=Atkins/>
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| Sometimes a set of [[reduced properties]] is defined in terms of the critical properties, i.e.:<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 0-07-121688-X | pages = 91–93}}</ref>
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| :<math>T_r = T/T_c\,</math>
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| :<math>p_r = p/p_c\,</math>
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| :<math>V_r = \frac{V}{RT_c/p_c}\,</math>
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| :<math>T_c = 8a/27Rb,</math>
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| :<math>V_c = 3nb\,</math>
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| :<math>P_c = a/27b^2,</math>
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| where <math>T_r</math> is the reduced temperature, <math>p_r</math> is the reduced pressure, <math>V_r</math> is the reduced volume, and <math>R</math> is the [[universal gas constant]].
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| ===Principle of corresponding states===
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| [[Critical variables]] are useful for writing a varied equation of state that applies to all materials, similar to [[normalization (statistics)|normalization]]. The [[theorem of corresponding states|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>''.
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| === Table of liquid–vapor critical temperature and pressure for selected substances ===
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| <center>
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| {| class="wikitable sortable" style="text-align: center;"
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| ! Substance<ref>{{cite book | last = Emsley | first = John | title = The Elements | edition = (Second Edition) | publisher = [[Oxford University Press]] | year = 1991 | isbn = 0-19-855818-X }}</ref><ref>{{cite book | first1 = Yunus A. | last1 = Cengel | first2 = Michael A. | last2 = Boles | title = Thermodynamics: An Engineering Approach |pages = 824 | edition = (Fourth Edition) | publisher = [[McGraw-Hill]] | year = 2002 | isbn = 0-07-238332-1 }}</ref>
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| ! Critical temperature
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| ! Critical pressure (absolute)
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| |-
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| | [[Argon]]
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| | {{sort|0150.8|{{convert|-122.4|C|K}}}}
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| | {{sort|0048.1|{{convert|48.1|atm|kPa|abbr=on}}}}
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| |-
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| | [[Ammonia]]<ref>http://www.engineeringtoolbox.com/ammonia-d_971.html</ref>
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| | {{sort|0405.6|{{convert|132.4|C|K}}}}
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| | {{sort|0111.3|{{convert|111.3|atm|kPa|abbr=on}}}}
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| |-
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| | [[Bromine]]
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| | {{sort|0584.0|{{convert|310.8|C|K}}}}
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| | {{sort|0102|{{convert|102|atm|kPa|abbr=on}}}}
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| |-
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| | [[Caesium]]
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| | {{sort|1938.00|{{convert|1664.85|C|K}}}}
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| | {{sort|0094|{{convert|94|atm|kPa|abbr=on}}}}
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| |-
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| | [[Chlorine]]
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| | {{sort|0417.0|{{convert|143.8|C|K}}}}
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| | {{sort|0076.0|{{convert|76.0|atm|kPa|abbr=on}}}}
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| |-
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| | [[Ethanol]]
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| | {{sort|0514.0|{{convert|241|C|K}}}}
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| | {{sort|0062.2|{{convert|62.18|atm|kPa|abbr=on}}}}
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| |-
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| | [[Fluorine]]
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| | {{sort|0144.30|{{convert|-128.85|C|K}}}}
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| | {{sort|0051.5|{{convert|51.5|atm|kPa|abbr=on}}}}
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| |-
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| | [[Helium]]
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| | {{sort|0005.19|{{convert|-267.96|C|K}}}}
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| | {{sort|0002.24|{{convert|2.24|atm|kPa|abbr=on}}}}
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| |-
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| | [[Hydrogen]]
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| | {{sort|0033.20|{{convert|-239.95|C|K}}}}
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| | {{sort|0012.8|{{convert|12.8|atm|kPa|abbr=on}}}}
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| |-
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| | [[Krypton]]
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| | {{sort|0209.4|{{convert|-63.8|C|K}}}}
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| | {{sort|0054.3|{{convert|54.3|atm|kPa|abbr=on}}}}
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| |-
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| | [[Methane|CH<sub>4</sub>]] (Methane)
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| | {{sort|0044.40|{{convert|-82.3|C|K}}}}
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| | {{sort|0027.2|{{convert|45.79|atm|kPa|abbr=on}}}}
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| |-
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| | [[Neon]]
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| | {{sort|0044.40|{{convert|-228.75|C|K}}}}
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| | {{sort|0027.2|{{convert|27.2|atm|kPa|abbr=on}}}}
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| |-
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| | [[Nitrogen]]
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| | {{sort|0126.3|{{convert|-146.9|C|K}}}}
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| | {{sort|0033.5|{{convert|33.5|atm|kPa|abbr=on}}}}
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| |-
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| | [[Oxygen]]
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| | {{sort|0154.6|{{convert|-118.6|C|K}}}}
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| | {{sort|0049.8|{{convert|49.8|atm|kPa|abbr=on}}}}
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| |-
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| | [[Carbon dioxide|CO<sub>2</sub>]]
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| | {{sort|0304.19|{{convert|31.04|C|K}}}}
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| | {{sort|0072.8|{{convert|72.8|atm|kPa|abbr=on}}}}
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| |-
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| | [[Nitrous oxide|N<sub>2</sub>O]]
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| | {{sort|0304.19|{{convert|36.4|C|K}}}}
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| | {{sort|0072.8|{{convert|71.5|atm|kPa|abbr=on}}}}
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| |-
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| | [[Sulfuric Acid|H<sub>2</sub>SO<sub>4</sub>]]
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| | {{sort|0927|{{convert|654|C|K}}}}
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| | {{sort|0045.4|{{convert|45.4|atm|kPa|abbr=on}}}}
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| |-
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| | [[Xenon]]
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| | {{sort|0289.8|{{convert|16.6|C|K}}}}
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| | {{sort|0057.6|{{convert|57.6|atm|kPa|abbr=on}}}}
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| |-
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| | [[Lithium]]
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| | {{sort|3223|{{convert|2950|C|K}}}}
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| | {{sort|0652|{{convert|652|atm|kPa|abbr=on}}}}
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| |-
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| | [[Mercury (element)|Mercury]]
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| | {{sort|1750.1|{{convert|1476.9|C|K}}}}
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| | {{sort|1720|{{convert|1720|atm|kPa|abbr=on}}}}
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| |-
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| | [[Sulfur]]
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| | {{sort|1314.00|{{convert|1040.85|C|K}}}}
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| | {{sort|0207|{{convert|207|atm|kPa|abbr=on}}}}
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| |-
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| | [[Iron]]
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| | {{sort|8500|{{convert|8227|C|K}}}}
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| |-
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| | [[Gold]]
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| | {{sort|7250|{{convert|6977|C|K}}}}
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| | {{sort|5000|{{convert|5000|atm|kPa|abbr=on}}}}
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| |-
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| | [[Aluminium]]
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| | {{sort|7850|{{convert|7577|C|K}}}}
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| |-
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| | [[Water]]<ref name="Steam 2007"/><ref>{{cite web | title = Critical Temperature and Pressure | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-19 }}</ref>
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| | {{sort|0647.096|{{convert|373.946|C|K}}}}
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| | {{sort|0217.7|{{convert|217.7|atm|MPa|abbr=on}}}}
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| |-
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| |}
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| </center>
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| ===History===
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| The existence of a critical point was first discovered by [[Charles Cagniard de la Tour]] in 1822<ref>Charles Cagniard de la Tour (1822) [http://books.google.com/books?id=rzNCAAAAcAAJ&vq=Cagniard&pg=PA127#v=onepage&q&f=false "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.</ref> <ref>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.</ref> and named by [[Thomas Andrews (scientist)|Thomas Andrews]] in 1869.<ref>Andrews, Thomas (1869) [http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html "The Bakerian lecture: On the continuity of the gaseous and liquid states of matter"] ''Philosophical Transactions of the Royal Society'' (London), '''159''', 575-590; the term "critical point" appears on page 588.</ref> He 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 3,000 atm.
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| ==Mixtures: liquid–liquid critical point==
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| [[Image:LCST-UCST plot.svg|thumb|350px|A plot of typical polymer solution phase behavior including two critical points: an [[LCST]] and a [[Upper critical solution temperature|UCST]].]]
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| 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) will lead 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 will induce phase separation, and the [[lower critical solution temperature]](LCST), which is the coldest point at which heating will induce phase separation.
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| ===Mathematical definition===
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| 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).
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| ==In renormalization group theory==
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| The critical point is described by a [[conformal field theory]]. According to the [[renormalization group]] theory, the defining property of criticality is that the characteristic [[length scale]] of the structure of the physical system, also known as the [[correlation length]] ''ξ'', becomes infinite. This can happen along ''critical lines'' in [[phase space]]. This effect is the cause of the [[critical opalescence]] that can be observed as binary fluid mixture approaches its liquid–liquid critical point.
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| In systems in equilibrium, the critical point is reached only by precisely tuning a control parameter. However, in some [[non-equilibrium thermodynamics|non-equilibrium]] systems, the critical point is an [[attractor]] of the dynamics in a manner that is robust with respect to system parameters, a phenomenon referred to as [[self-organized criticality]].
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| ==See also==
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| {{colbegin}}
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| *[[Conformal field theory]]
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| *[[Critical exponents]]
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| *[[Critical phenomena]]
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| *[[Joback method]], [[Klincewicz method]], [[Lydersen method]] (Estimation of critical temperature, pressure, and volume from molecular structure)
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| *[[Lower critical solution temperature]]
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| *[[Percolation thresholds]]
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| *[[Phase transition]]
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| *[[Rushbrooke inequality]]
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| *[[Scale invariance]]
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| *[[Self-organized criticality]]
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| *[[Supercritical fluid]], [[Supercritical drying]], [[Supercritical water oxidation]], [[Supercritical fluid extraction]]
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| *[[Tricritical point]]
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| *[[Triple point]]
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| *[[Upper critical solution temperature]]
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| *[[Widom scaling]]
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| {{colend}}
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| == Footnotes ==
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| {{Reflist}}
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| == References ==
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| *{{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 | format = [[PDF]] | accessdate = 2009-06-09 }}
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| ==External links==
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| * {{cite web |title=Critical points for some common solvents |url=http://www.proscitech.com.au/catalogue/notes/cpd.htm |archiveurl=http://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm |publisher=ProSciTech |archivedate=2008-01-31}}
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| *{{cite web | title = Critical Temperature and Pressure | work = Department of Chemistry
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| | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}
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| * [[Hagen Kleinert]] and Verena Schulte-Frohlinde, ''Critical Properties of φ<sup>4</sup>-Theories'', [http://www.worldscibooks.com/physics/4733.html World Scientific (Singapur, 2001)]; Paperback ISBN 981-02-4658-7'' (readable online [http://www.physik.fu-berlin.de/~kleinert/b8 here])''
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| {{Phase_of_matter}}
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| [[Category:Condensed matter physics]]
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| [[Category:Conformal field theory]]
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| [[Category:Critical phenomena]]
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| [[Category:Phase transitions]]
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| [[Category:Renormalization group]]
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| [[Category:Threshold temperatures]]
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