10.3 Solutions
425
10.2.7 Surface Tension
10.62 If the surface tension of the liquid–gas interface is 0.072 N/m, the density is
1 kg/L and the radius of the capillary is 1 mm, to what height will the liquid
rise up the capillary?
[University of Manchester 2007]
10.63 A mole of gaseous molecules in a bubble obeys the ideal gas law. What is the
volume of the bubble at a 100 m depth of water if the temperature is 293 K,
the atmospheric pressure is 101 kPa, density of water is 1000 kg/m
3 and the
ideal gas constant is 8.314 J/mol/K.
[University of Manchester 2008]
10.64 Let n droplets each of radius r coalesce to form a large drop of radius R.
Assuming that the droplets are incompressible and S is the surface tension
calculate the rise in temperature if c is the specific heat and ρ is the density.
10.65 A soap bubble of surface tension 0.03 N/m is blown from 1 cm radius to 5 cm
radius. Find the work done.
10.66 A small hollow vessel which has a small hole in it is immersed in water to
a depth of 45 cm before any water penetrates into the vessel. If the surface
tension of water is 0.073 N/m, what should be the radius of the hole?
10.67 What will be the depth of water at which an air bubble of radius 0.3×10 −3 m
may remain in equilibrium (surface tension of water = 0.072 N/m and g =
9.8 m/s 2 )?
10.68 A capillary tube of radius 0.2 mm and of length 6 cm is barely dipped
in water. Will the water overflow through the capillary? If not what happens to the meniscus (surface tension of water = 0.073 N/m and angle of
contact = 0 ◦ )?
10.69 A soap bubble of radius 2.0 cm is charged so that the excess of pressure due
to surface tension is neutralized. If the surface tension is 0.03 N/m, what is
the charge on the bubble?
10.70 Two soap bubbles with radii r 1 and r 2 coalesce to form a bigger bubble of
radius r . Show that r =
r 2
1 + r 2
2 .
10.3 Solutions
10.3.1 Kinetic Theory of Gases
10.1 The mean free path λ of a gas molecule is the average distance travelled by
the molecule between successive collisions.
λ = x/N
(1)
425
10.2.7 Surface Tension
10.62 If the surface tension of the liquid–gas interface is 0.072 N/m, the density is
1 kg/L and the radius of the capillary is 1 mm, to what height will the liquid
rise up the capillary?
[University of Manchester 2007]
10.63 A mole of gaseous molecules in a bubble obeys the ideal gas law. What is the
volume of the bubble at a 100 m depth of water if the temperature is 293 K,
the atmospheric pressure is 101 kPa, density of water is 1000 kg/m
3 and the
ideal gas constant is 8.314 J/mol/K.
[University of Manchester 2008]
10.64 Let n droplets each of radius r coalesce to form a large drop of radius R.
Assuming that the droplets are incompressible and S is the surface tension
calculate the rise in temperature if c is the specific heat and ρ is the density.
10.65 A soap bubble of surface tension 0.03 N/m is blown from 1 cm radius to 5 cm
radius. Find the work done.
10.66 A small hollow vessel which has a small hole in it is immersed in water to
a depth of 45 cm before any water penetrates into the vessel. If the surface
tension of water is 0.073 N/m, what should be the radius of the hole?
10.67 What will be the depth of water at which an air bubble of radius 0.3×10 −3 m
may remain in equilibrium (surface tension of water = 0.072 N/m and g =
9.8 m/s 2 )?
10.68 A capillary tube of radius 0.2 mm and of length 6 cm is barely dipped
in water. Will the water overflow through the capillary? If not what happens to the meniscus (surface tension of water = 0.073 N/m and angle of
contact = 0 ◦ )?
10.69 A soap bubble of radius 2.0 cm is charged so that the excess of pressure due
to surface tension is neutralized. If the surface tension is 0.03 N/m, what is
the charge on the bubble?
10.70 Two soap bubbles with radii r 1 and r 2 coalesce to form a bigger bubble of
radius r . Show that r =
r 2
1 + r 2
2 .
10.3 Solutions
10.3.1 Kinetic Theory of Gases
10.1 The mean free path λ of a gas molecule is the average distance travelled by
the molecule between successive collisions.
λ = x/N
(1)