Editing Surface tension (section)

====Influence of temperature====
[[Image:Temperature dependence surface tension of water.svg|thumb|upright=1.3|Temperature dependence of the surface tension between the liquid and vapor phases of pure water]]
[[Image:SFT-benzene.png|thumb|upright=1.3|Temperature dependency of the surface tension of [[benzene]]]]

Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the [[critical temperature]]. For further details see [[Eötvös rule]]. There are only empirical equations to relate surface tension and temperature:
* Eötvös:<ref name="phywe">{{cite web|url=http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_4_05.pdf|title=Surface Tension by the Ring Method (Du Nouy Method)|access-date=2007-09-08|publisher=PHYWE|archive-date=2007-09-27|archive-url=https://web.archive.org/web/20070927010256/http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/1_4_05.pdf|url-status=live}}</ref><ref name="adam">{{Cite book|title=The Physics and Chemistry of Surfaces, 3rd ed|author=Adam, Neil Kensington|publisher=Oxford University Press|year=1941}}</ref><ref name="Physical Properties Sources Index (PPSI)">{{cite web|url=http://www.ppsi.ethz.ch/fmi/xsl/eqi/eqi_property_details_en.xsl?node_id=1113|title=Physical Properties Sources Index: Eötvös Constant|access-date=2008-11-16|url-status=dead|archive-url=https://web.archive.org/web/20110706231759/http://www.ppsi.ethz.ch/fmi/xsl/eqi/eqi_property_details_en.xsl?node_id=1113|archive-date=2011-07-06}}</ref> <math display="block">\gamma V^{2/3} = k(T_\mathrm{C}-T) .</math> Here {{mvar|V}} is the molar volume of a substance, {{math|''T''<sub>C</sub>}} is the [[critical temperature]] and {{mvar|k}} is a constant valid for almost all substances.<ref name="phywe"/> A typical value is {{mvar|k}} = {{val|2.1|e=-7|u=J K<sup>−1</sup> mol<sup>−{{2/3}}</sup>}}.<ref name="phywe"/><ref name="Physical Properties Sources Index (PPSI)"/> For water one can further use {{mvar|V}} = 18&nbsp;ml/mol and {{math|''T''<sub>C</sub>}} = 647&nbsp;K (374&nbsp;°C).<ref>{{cite journal|doi=10.1063/1.555688|url=https://www.nist.gov/data/PDFfiles/jpcrd231.pdf|title=International Tables of the Surface Tension of Water|journal=Journal of Physical and Chemical Reference Data|volume=12|issue=3|pages=817|year=1983|last1=Vargaftik|first1=N. B.|last2=Volkov|first2=B. N.|last3=Voljak|first3=L. D.|bibcode=1983JPCRD..12..817V|access-date=2017-07-13|archive-date=2016-12-21|archive-url=https://web.archive.org/web/20161221094427/http://nist.gov/data/PDFfiles/jpcrd231.pdf|url-status=dead}}</ref> A variant on Eötvös is described by Ramay and Shields:<ref name="moore">{{Cite book|title=Physical Chemistry, 3rd ed|author=Moore, Walter J.|publisher=Prentice Hall|year=1962}}</ref> <math display="block">\gamma V^{2/3} = k \left(T_\mathrm{C} - T - 6\,\mathrm{K}\right)</math> where the temperature offset of 6 K provides the formula with a better fit to reality at lower temperatures.
* Guggenheim–Katayama:<ref name="adam"/> <math display="block">\gamma = \gamma^\circ \left( 1-\frac{T}{T_\mathrm C} \right)^n </math> {{math|''γ''°}} is a constant for each liquid and {{mvar|n}} is an empirical factor, whose value is {{sfrac|11|9}} for organic liquids. This equation was also proposed by [[Johannes Diderik van der Waals|van der Waals]], who further proposed that {{math|''γ''°}} could be given by the expression <math display="block">K_2 T^{1/3}_\mathrm{C} P^{2/3}_\mathrm{C},</math> where {{math|''K''<sub>2</sub>}} is a universal constant for all liquids, and {{math|''P''<sub>C</sub>}} is the [[critical pressure]] of the liquid (although later experiments found {{math|''K''<sub>2</sub>}} to vary to some degree from one liquid to another).<ref name="adam"/>

Both Guggenheim–Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.