22.2 Surface Tension
22.1.Using the explanation of unbalanced forces as the source
of surface tension, justify why it requiresenergy to increase the
surface area of a liquid. Is there any circumstance in which
energy is given off when increasing a liquid’s surface area?
22.2.The surface tension of liquid mercury from Table 22.1
is 435.5 N/m. What is the value of (Hg) in units of dyn/cm?
22.3.The surface tension of chloroform, CHCl 3 , is 27.1 dyn/cm.
(a)How many joules does it take to increase the surface area
of a pool of chloroform by 50.0 cm^2? (b)How many joules
does it take to make a film of chloroform that has an area of
0.010 m^2?
22.4.Equation 22.6 defines surface tension in terms of Gibbs
free energy. Borrowing an analogy from chemical potential,
we submit that surface tension can also be defined in terms of
enthalpy, internal energy, or Helmholtz energy. Write partial
derivatives for those definitions.
22.5.In early chapters of this book, we considered expan-
sions and contractions of gases and calculated changes in
thermodynamic quantities for those changes. However, we did
not consider changes in surface energies, as those gases
changed their surface areas. Why not?
22.6.Since energy is given off as small droplets coalesce into
larger ones, maybe we can use that coalescence to perform
useful work. Let’s try a test case.
How much does the temperature change if two 1.00-nm-ra-
dius water droplets at 20.0°C coalesce into a single droplet?
The surface tension of water is 72.75 erg/cm^2.
22.7.Approximate the surface tension of a liquid that a razor
blade will notfloat on. Use the data in Example 22.3 to make
your estimates.
22.8.A spherical soap bubble slowly decreases in size. Is work
done on the bubble or by the bubble? Explain your answer.
22.9. (a)As a first approximation, raindrops can be thought
of as small amounts of water in free fall, experiencing no net
gravitational force. What should be their expected shape, and
why?
(b)In reality, falling raindrops are distorted somewhat from
their ideal shape because they are usually falling at some ter-
minal velocity. Just considering that fact, can you predict a
shape of a distorted raindrop?
22.3 Interface Effects
22.10.Explain how equation 22.9 does not violate the first
law of thermodynamics.
22.11.The Laplace-Young equation can be derived in a dif-
ferent and incorrect way by writing the area of a sphere in
terms of volume and then evaluating A/ V. Why do you not
get the same expression?
22.12.Show that the right side of equation 22.13, the
Laplace-Young equation, has units of pressure (as required by
the mathematics).
22.13.Can the evaporation of droplets be minimized by in-
creasing the external pressure, like by pressuring region II of a
system (refer to Figure 22.6) with an inert gas? Why or why
not? Assume ideal behavior.
22.14.Researchers in nuclear fusion try to create tiny mi-
crospheres of gold containing deuterium-tritium mixes that
they can heat to very high temperatures and pressures using
focused lasers. Under such conditions, fusion of the nuclei can
occur. Does the Laplace-Young equation suggest that smaller
or larger microspheres would be better targets? Comment on
whether this supports or detracts from the possibility of sus-
tained fusion under these conditions.
22.15.Determine the pressure difference on a droplet of
mercury with a surface tension of 480 dyn/cm if its radius is
(a)1.00 mm or (b)0.001 mm.
22.16.Although the text did not address the effect of tem-
perature on the Laplace-Young equation, what is the expected
effect on pas Tincreases? Does this expected effect agree
with equations 22.14 and 22.15 and the behavior of with
increasing temperature?
22.17.Redraw Figure 22.8 and draw the three surface-
tension vectors that contribute to equation 22.16. Using this
diagram, rationalize the form of equation 22.16 and show
how the costerm arises.
22.18.The Kelvin equationis used to calculate the equilibrium
vapor pressure of a droplet of radius r:ln pp°v
va
ap
po
or
r^2 rRTV
where pvaporis the vapor pressure of the droplet, p°vaporis the
vapor pressure of the bulk liquid at standard conditions (that
is, 25°C), and Vis the molar volume of the liquid. The vari-
ables R, T, and have their usual meaning.
(a)Argue that the vapor pressure of a liquid increases as the
radius of the droplet decreases. What implications does this
have for condensation processes (that is, a vapor forming a liq-
uid) and for atmospheric processes like raindrop formation?
(b)Calculate the vapor of a droplet of water having a radius
of 20.0 nm at 298 K. The vapor pressure of bulk water at this
temperature is 23.77 mmHg.
22.19.Why are capillary rises and depressions not seen for
cylinders with large radii?
22.20.What is the expected contact angle if a capillary of
bore radius 0.200 mm, immersed in water at 25°, shows a
capillary rise of 4.78 cm?22.4 & 22.5 Surface Films; Solid Surfaces790 Exercises for Chapter 22
EXERCISES FOR CHAPTER 22