The surface of the liquid
1. Explain the physical concepts of “surface layer” and “capillarity”
Solution:
The surface and a drop of liquid, or a bubble, behave as if there were an elastic film on their surface – the “surface layer.” It has a thickness of about 10-9 m. It is formed by a layer of molecules. The surface and drop have one surface, a bubble has two surfaces.
Surface tension:
l = 2π.r S = π.r2
- Capillary elevation = rise of a wetting liquid in a capillary
- Capillary depression = lowering of a non-wetting liquid in a capillary
2.
What is the mass of a water drop (σ = 73.10-3 N.m-1) that dripped from a tube with a radius of 0.5 mm?
Solution:
Analysis:
R = 0.5·10-3 m, g = 10 m.s-2, σ = 73.10-3 N.m-1
The mass of the water drop is m = 22.9 mg.
3.
A capillary measured 100 drops of ethanol with a mass of 1.81 g. The same number of water drops from the same capillary and at the same temperature has a mass of 6.26 g. Determine the surface tension of ethanol σ1 if the surface tension of water is σ2(H2O) = 73.10-3 N.m-1.
Solution:
Analysis:
The surface tension of ethanol is σ1 = 21.1·10-3 N.m-1
4.
Water drips from a capillary with radius r = 0.9 mm. How many drops of water are in 1 cm3 of water? (σ = 73.10-3 N.m-1, ρ = 103 kg.m-3)
Solution:
r = 0.9 mm = 0.9·10-3 m, V0 = 1 cm3 = 10-6 m3, σ = 73.10-3 N.m-1, ρ = 103 kg.m-3
There are 24 drops in 1 cm3 of water.
5.
A movable rod with a length of 40 mm on a frame with a soap film is in equilibrium when loaded with a weight of 320 milligrams. What is the surface tension of the soap solution in water in contact with air? The film has two surfaces. (Neglect the mass of the rod)
Solution:
Analysis:
l = 40·10-3 m = 0.04 m, m = 320·10-6 kg, σ = ?
The surface tension of the soap solution in water is σ = 40 mN.m-1.
6. Determine the work (in an isothermal process) required to inflate a soap bubble with a diameter of 14 cm. The bubble has two surfaces. σ = 40·10-3 N.m-1
Solution:
Analysis:
The work required to inflate the soap bubble is W = 3.3 mJ.
7.
A soap bubble (σ = 40·10-3 N.m-1) has a radius of 2 cm. What work is done if we increase its radius by 1 cm?
Solution:
Analysis:
R1 = 2·10-2 m, R2 = 3·10-2 m, σ = 40·10-3 N.m-1, ΔW = ?
If we increase the bubble radius by 1 cm, the work done is 4.243·10-4 J.
8. Capillary rise – elevation – of ethanol in a narrow capillary is 12 mm. What is the inner diameter of the capillary? (ρ = 800 kg.m-3, σ = 21.4 mN.m-1)
Solution:
Analysis:
h = 12·10-3 m, ρ = 800 kg.m-3, σ = 21.4·10-3 N.m-1
The inner diameter of the capillary is about d = 0.9 mm.
9.
The capillary has an inner diameter of 0.2 mm. Calculate:
- a.) How high will benzene rise in the capillary (ρ = 870 kg.m-3, σ = 29.1·10-3 N.m-1)
- b.) How will the height change if we use a capillary with double the radius
- c.) How would the result of the experiment change on the Moon (gM = 0.167 g)
Solution:
Analysis:
R = 0.1 mm = 10-4 m, ρ = 870 kg.m-3, σ = 29.1·10-3 ```