perspective—to be in the form of one body rather than multiple smaller bodies.
This is indeed the case.
The relationship of surface tension to free energy also explains another phe-
nomenon. According to equation 22.5,
G A
In words, this equation says that the change in the Gibbs energy is directly
proportional to the change in area of a liquid. If we consider an isothermal,
isobaric process (that is,dp0 and dT0; these conditions are necessary
when you consider the natural variable expression in equation 22.7), the
process is spontaneous if Gis negative. Since surface tension must be a pos-
itive number, this implies that Afor a spontaneous process must be nega-
tive: a spontaneous process must occur with a corresponding decreasein sur-
face area.
It has long been known that a sphere is the most compact solid object: it
has the minimum surface area for any given volume. Therefore, the effects of
surface tension require that liquids assume a spherical shape if no additional
forces are acting on them. In the absence of gravity, this is indeed what hap-
pens (see Figure 22.4), and it is ultimately caused by the surface tension of the
liquid. In many instances, liquid amounts are large enough that effects due to
gravity distort the ideal spherical shape of liquids. However, for small
amounts—like small drops of water on a plastic surface—the tendency to-
ward a spherical shape can be obvious. Figure 22.5 shows an example of a
phenomenon that is probably familiar—and whose ultimate origin is surface
tension.
Finally, surface tension explains why certain phenomena occur, like insects
walking on water or a needle or razor blade floating on water. It takes work—
energy—to change the area of a surface; it takes work—energy—to pass through
a surface. (In passing through a surface, distortion of the surface must occur.)
If a process occurs without enough work to overcome the surface tension, the
process will not break the surface. Insects typically experience a very tiny area
of contact with a surface, so they float on water. Needles and razor blades can
be placed so lightly that the force due to their gravity does not overcome the
surface tension, so that they too will float on water.Example 22.3
Show that a razor blade can float on water (which can be demonstrated ex-
perimentally if the system is set up carefully enough). Do this by calculating
the work needed to move a razor blade by a distance equal to its thickness,
and comparing it to the work needed to increase the surface area of water by
the area of the razor blade. A typical double-edged razor blade has dimen-
sions of 19.9 mm by 38.9 mm, a thickness of 0.250 mm, and a mass of
1.1240 g (and therefore experiences a gravitational force of 1.1462 10 ^4
N). Water has a surface tension of 72.75 erg/cm^2. Ignore buoyancy effects and
other interactions (although in reality they can have a significant impact).Solution
We need to show that to make a “hole” in the surface of the water large
enough to pass the razor blade through requires more energy than is gener-
ated by moving the razor blade down by a distance of one thickness. First, we
will calculate the decrease in gravitational potential energy as a 1.1240-g770 CHAPTER 22 SurfacesFigure 22.5 Even though the effects of gravity
can alter the ideal shape of liquid droplets, the
tendency of small liquid droplets toward a spher-
ical shape is obvious. This tendency is caused by
surface tension.Figure 22.4 Because of surface tension effects,
liquid droplets that do not experience other ef-
fects adopt a spherical shape.© John Harwood/Science Photo Library/Photo Researchers, Inc.
© Paul Silverman/Fundamental Photographs