Chemistry Reference
In-Depth Information
Appendix A: Effect of
Temperature and Pressure on
Surface Tension of Liquids
(Corresponding States Theory)
Both in industry and research, large data are manipulated that could be systemized.
Understanding the chemistry and physics of liquid surfaces is important so as to
describe interfacial forces as a function of temperature and pressure. The magnitude
of surface tension, γ, decreases almost linearly with temperature (
t
) within a narrow
range (Birdi, 2002, 2008; Defay et al., 1966):
γt = ko (1 − k1
t
)
(A.1)
where ko is a constant. It was found that coefficient k1 is approximately equal to the
rate of decrease of density (ρ), with rise in temperature:
ρt = ρo (1 − k1
t
)
(A.2)
Where ρo is the value of density at t = 0°C, and values of constant k1 were found
to be different for different liquids. Further, the value of γ was related to the critical
temperature (TC).
The following equation relates surface tension of a liquid to the density of liquid,
ρl, and vapor, ρv (Partington, 1951; Birdi, 1989):
γ/(ρl − ρv )
4
= C
(A.3)
where the value of the constant C is nonvariable only for organic liquids, while it is
not constant for liquid metals.
At the critical temperature, Tc, and critical pressure, Pc, a liquid and its vapor
are identical, and the surface tension, γ, and total surface energy, as in the case of
the energy of vaporization, must be zero (Birdi, 1997). At temperatures below the
boiling point, which is 2/3 Tc, the total surface energy and the energy of evaporation
are nearly constant. The variation in surface tension, γ, with temperature is given in
Figure A.1 for different liquids.
These data clearly show that the variation of γ with temperature is a very charac-
teristic physical property. This observation becomes even more important when it is
considered that the sensitivity of γ measurements can be as high as approximately
0.001 dyn/cm(= mN/m; as described in detail in the following text). The change
in γ with temperature in the case of mixtures would thus be dependent on their
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