Eötvös rule

If V is the molar volume and T_c the critical temperature of a liquid the surface tension γ is given by[1]

${\displaystyle \gamma V^{2/3}=k(T_{c}-T)\,}$

where k is a constant valid for all liquids. The Eötvös constant has a value of 2.1×10⁻⁷ J/(K·mol^2/3).

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

${\displaystyle \gamma V^{2/3}=k(T_{c}-6\ \mathrm {K} -T)\,}$

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

${\displaystyle V=M/\rho \,}$

The term ${\displaystyle \gamma V^{2/3}}$ is also referred to as the "molar surface tension" γ_mol :

${\displaystyle \gamma _{mol}=\gamma V^{2/3}\,}$

A useful representation that prevents the use of the unit mol^−2/3 is given by the Avogadro constant N_A :

${\displaystyle \gamma =k'\left({\frac {M}{\rho N_{A}}}\right)^{-2/3}(T_{c}-6\ \mathrm {K} -T)=k'\left({\frac {N_{A}}{V}}\right)^{2/3}(T_{c}-6\ \mathrm {K} -T)}$

As John Lennard-Jones and Corner showed in 1940 by means of the statistical mechanics the constant k′ is nearly equal to the Boltzmann constant.

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.[2] In 1893 William Ramsay and Shields showed an improved version considering that the line normally passes the temperature axis 6 K before the critical point.[3] John Lennard-Jones and Corner published (1940)[4] a derivation of the equation by means of statistical mechanics. In 1945 E. A. Guggenheim gave a further improved variant of the equation.[5]