Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 33

G = H − T S (2.46)

It is thus important that, in all practical analyses, one should be aware of the effects
of temperature and pressure. The molecular forces that stabilize liquids will be
expected to decrease as temperature increases. Experiments also show that, in all
cases, surface tension decreases with increasing temperature.
The surface entropy of liquids is given by (−d γ/dT). This means that the entropy
is positive at higher temperatures. The rate of decrease of surface tension with tem-
perature is found to be different for different liquids (Appendix A), which supports
the foregoing description of liquids. This observation explains the molecular descrip-
tion of surface tension.
For example, the surface tension of water data is given as

At 5°C, γ = 75 mN/m
At 25°C, γ = 72 mN/m
At 90°C, γ = 60 mN/m

Extensive γ data for water was fitted to the following equation (Birdi, 2002):

γ = 75.69 − 0.1413 t C − 0.0002985 t C 2 (2.47)

where t C is in degree Centigrade. This equation gives the value of γ at 0°C as 75.69
mN/m. The value of γ at 50°C is found to be (75.69 − 0.1413 × 50 − 0.0002985 × 50
× 50) = 60 mN/m.
Further, these data show that γ of water decreases with temperature from 25°C to
60°C, (72 − 60)/(90 − 25) = 0.19 mN/mC. The differences in surface entropy yields
information on the structures of different liquids. It is also observed that the effect
of temperature will be lower for liquids with higher boiling point (such as Hg) than
for low-boiling liquids (such as n -hexane). Actually, a correlation exists between
and heat of vaporization (or boiling point). In fact, many systems even show big dif-
ferences when comparing winter or summer months (such as raindrops, sea waves,
foaming in natural environments, etc.).
Different thermodynamic relations have been derived that can be used to estimate
surface tension at different temperatures. In this regard, straight-chain alkanes have
been especially extensively analyzed. The data show that there exists a simple corre-
lation among surface tension, temperature, and n C , which allows one to estimate the
value of surface tension of a given alkane at any temperature. This observation has
many aspects in applied industry. It allows one to quickly estimate the magnitude of
surface tension of an alkane at the required temperature. Further, one has fairly good
quantitative analysis of how surface tension will change for a given alkane under a
given experimental condition. A detailed analysis is given in Appendix A.

2.7.2 d I f f e r e n T a S p e c T S of f l I q u I d S u r f a c e S
2.7.2.1 heat of Surface Formation and evaporation
In order to understand how liquids are stabilized, several attempts have been made to
relate the surface tension of a liquid to the latent heat of evaporation. It was argued a