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[[Image:SFT-benzene.png|thumb|Temperature dependence of the surface tension of [[benzene]]]]

The '''Eötvös rule''', named after the Hungarian physicist [[Loránd Eötvös|Loránd (Roland) Eötvös]] (1848–1919) enables the prediction of the [[surface tension]] of an arbitrary [[liquid]] pure substance at all [[temperature]]s. The [[density]], [[molar mass]] and the [[critical temperature]] of the liquid have to be known. At the [[critical point (thermodynamics)|critical point]] the surface tension is zero.

The first assumption of the Eötvös rule is:

1. The surface tension is a linear function of the temperature.
:This assumption is approximately fulfilled for most known liquids. When plotting the surface tension versus the temperature a fairly straight line can be seen which has a surface tension of zero at the critical temperature.

The Eötvös rule also gives a relation of the surface tension behaviour of different liquids in respect to each other:

2. The temperature dependence of the surface tension can be plotted for all liquids in a way that the data collapses to a single master curve. To do so either the molar mass, the density, or the molar volume of the corresponding liquid has to be known.

== The Eötvös rule ==

If ''V'' is the molar volume and ''T''<sub>c</sub> the critical temperature of a liquid the [[surface tension]] γ is given by<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)|accessdate=2007-09-08|publisher=PHYWE|format=pdf}}</ref>
:<math>\gamma V^{2/3} = k(T_c - T)\,</math>
where ''k'' is a constant valid for all liquids. The Eötvös constant has a value of 2.1×10<sup>−7</sup> [[Joule|J]]/(K·[[mole (unit)|mol]]<sup>2/3</sup>).

More precise values can be gained when considering that the line normally passes the temperature axis 6 [[Kelvin|K]] before the critical point:

:<math>\gamma V^{2/3} = k(T_c - 6 \ \mathrm{K} - T)\,</math>

The molar volume ''V'' is given by the molar mass ''M'' and the density ρ

:<math>V = M / \rho\,</math>

The term <math>\gamma V^{2/3}</math> is also referred to as the "molar surface tension" γ<sub>mol</sub> :
:<math>\gamma_{mol} = \gamma V^{2/3}\,</math>

A useful representation that prevents the use of the unit mol<sup>−2/3</sup> is given by the [[Avogadro constant]] N<sub>A</sub> :
:<math>\gamma = k' \left( \frac{M}{\rho N_A} \right)^{-2/3}(T_c - 6 \ \mathrm{K} - T) = k' \left( \frac{N_A}{V} \right)^{2/3}(T_c - 6 \ \mathrm{K} - T)</math>

As [[John Lennard-Jones]] and Corner showed in 1940 by means of the [[statistical mechanics]] the constant ''k''&prime; is nearly equal to the [[Boltzmann constant]].

=== Water ===
For water, the following equation is valid between 0 and 100 °C.
:<math>\gamma = 0.07275 \ \mathrm{ N/m} \cdot (1-0.002 \cdot (T - 291 \ \mathrm{K}))</math>

== Historical ==

As a student, Eötvös started to research surface tension and developed a new method for its determination. The Eötvös rule was first found phenomenologically and published in 1886.<ref>{{cite journal|first=L. |last=Eötvös |journal=[[Annalen der Physik]] |year=1886 |volume=27 |page=448}} Cited in: {{cite journal|last=Palit|first=Santi R.|title=Thermodynamic Interpretation of the Eötvös Constant|journal=Nature|year=1956|volume=177|issue=4521|pages=1180–1180|doi=10.1038/1771180a0|bibcode = 1956Natur.177.1180P }}</ref> In 1893 [[William Ramsay]] and Shields showed an improved version considering that the line normally passes the temperature axis 6 [[Kelvin|K]] before the critical point. [[John Lennard-Jones]] and Corner published (1940) a derivation of the equation by means of [[statistical mechanics]]. In 1945 [[E. A. Guggenheim]] gave a further improved variant of the equation.

==References==
<references/>

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[[Category:Physical chemistry]]
[[Category:Thermodynamic equations]]