Liquid Surface Tension Variation by Temperature

As we know (dy/dT). = -(3Ss/dA)T n., from Equation (213), the temperature variation of surface tension can be related to the differential surface excess entropy, and since the left-hand side of the equation is almost always negative, there is an increase in the interfacial entropy with the increase in surface area. For a constant unit area of As = 1 m2, if we want to compare the surface excess entropy of a one-component pure liquid, with the entropy of its bulk liquid, we have to use Equation (219), SsdTs + dy + -TfdJuf =0 

If we further increase the temperature towards the critical temperature, Tc, the restraining force on the surface molecules diminishes, and the vapor pressure increases, and when Tc is reached, the surface tension vanishes altogether (y= 0). There are several empirical approaches using critical properties and molar volume to predict the surface tension of pure liquids. By comparing the surfaces on the basis of the number of similarly shaped and symmetrically packed molecules per unit area, Eotvos derived an equation in 1886, 

Katayama replaced the density of the liquid by the difference in density between the liquid and saturated vapor in the Eotvos equation  

Simple expressions were offered for the nearly linear variation of surface tension with temperature, such as y= y°(l - bT), where, y°, is a constant for every liquid. Since y= 0 at T by denoting b= 1ITC, this linear plot may be expressed as 

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