Empirical relations between surface tension and temperature

Empirical relations between surface tension and temperature. Although no simple equation can be constructed which will accurately express the variation of the surface tension of all liquids with temperature, yet in many cases formulae can be found w hich are sufficiently accurate to be used for interpolation purposes. 

The simplest of these is the expression of the nearly linear variation of surface tension with temperature 

Since the surface tension vanishes at the critical temperature, this may be approximately written 

The accuracy of (5) is within the limits of experimental error for many liquids. As the linear relation does not usually hold near the critical temperature, (6) is less accurate, though it is preferable theoretically as containing one less arbitrary constant. Refinements of the linear equation have usually been made along one of two lines the first is to follow Eotvos s plan of introducing the twro-thirds power of the molecular volume, as in equation (1) of Ramsay and Shields, or Katayama s modification2 

Equation (8) was first proposed by van der Waals1 as a result of thermodynamical theory, the constant y0 having the value K2T p, where K2 is a universal constant for all liquids, pc is the critical pressure, and n also should have the same value for all liquids. In practice, van der Waals universal constants are not accurately the same for all liquids. Ferguson2 has tested the power equation (8) with experimental data, finding a mean value for 14 common organic liquids, for n, of 1 21, with variations of a few per cent. only. 

---