On the temperature dependence of surface tension: Historical perspective on the Eötvös equation of capillarity, celebrating his 175th anniversary

The Hungarian baron Roland Eötvös (Eötvös Loránd, 1848–1919) lived in the difficult period between two revolutions in Hungary, but nevertheless he achieved revolutionary results in two fields of science: capillarity (1875–1886) and gravity (after 1886). This paper describes his famous capillary equation published in 1886 in the world-language of the time (German) and in one of the most famous scientific journals of the time (Annalen der Physik und Chemie). In his paper he showed a simple equation for the temperature dependence of surface tension of one-component liquids and more importantly he showed that this quantity approaches zero as temperature tends towards the critical temperature. This result was achieved by measuring the surface tension of 160 (!) different liquids along their boiling lines as function of temperature, in a home-made high-pressure high-temperature equipment, probably the first one of this kind. In this way he extended the meaning of the critical point previously introduced by van der Waals. In this paper, also a modern model of surface tension of one-component liquids is discussed, simplified and compared to the Eötvös equation. It is also shown, how the Avogadro number and the molecular sizes can be determined from the experimental results of Eötvös (note: the Avogadro number was estimated with reasonable accuracy for the first time by Einstein in 1905 from the kinetic theory of liquids). Apparently, it was not that easy to do back in 1886: this becomes obvious from the 1911-paper by Einstein, who gave a wrong estimate for the diameter of Hg atoms (5.19 nm) using the data of Eötvös (the correct value is around 0.3 nm). The Appendix to this paper contains the summary of 1543 handwritten pages on surface tension by Eötvös, including the on-line availability of all pdf files. Note also, that Eötvös used g = 10.0 m/s² for acceleration due gravity and so he over-estimated his surface tension values and also his Eötvös constant by about 2.0%. The corrected Eötvös constant using his measured values but the correct g-value would be “0.222” vs his published value of “0.227”. Probably this uncertainty in the value of g was one of the motives that pushed Eötvös to study gravity after 1886.