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dx
l
FIGure 2.2
Surface film of a liquid (see text for details).
a liquid, while H
2
S is a gas. This means that H
2
O molecules interact with different
forces to form a liquid phase. On the other hand, H
2
S molecules exhibit much lower
interactions and thus are in a gas phase at room temperature and pressure.
2.2.1
S
u r f a c e
e
n e r g y
The state of
surface energy
has also been described by the following classic example
(Adamson and Gast, 1997; Chattoraj and Birdi, 1984; Birdi, 1989; Birdi, 1997, 2002).
Consider the area of a liquid film that is stretched in a wire frame by an increment
d
A
, whereby the surface energy changes by (γ d
A
) (Figure 2.2). Under this process,
the opposing force is
f
. From these data on dimensions, we find that
Surface tension = γ
Change in area = d
A
=
l
d
x
Change in
x
-direction = d
x
f
d
x
= γ d
A
(2.1)
or
γ =
f
(d
x
/dA)
=
f
/2
l
(2.2)
where d
x
is the change in displacement, and
l
is the length of the thin film. The
quantity γ represents the force per unit length of the surface (mN/m = dyn/cm), and
this force is defined as surface tension or interfacial tension. The
surface tension
,
γ, is the differential change of free energy with change of surface area at constant
temperature, pressure, and composition.
One may consider another example to describe surface energy. Let us imagine that
a liquid fills a container of the shape of a funnel. In the funnel, if one moves the liquid
upwards, then there will be an increase in
surface area
. This requires that some mole-
cules from the bulk phase have to move into the surface area and create extra surface A
s
.
The work required to do so will be (force × area) γ A
S
. This work is reversible at constant
temperature and pressure, and thus gives the increase in free energy of the system:
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