1. The properties of a surface are quite different from the properties of the bulk material.
2. A molecule well inside a body is surrounded by similar particles from all sides. But a molecule on the surface has particles of one type on one side and of different type on the other side.
3. The attractive forces between the molecules of a substance are called cohesive forces.
4. The attractive forces between the molecules of a different substances are called adhesive forces.
5. A molecule of water well inside the bulk experiences cohesive forces but a molecule at the surface experiences both cohesive and adhesive forces. This asymmetric force distribution is responsible for surface tension.
6. The maximum distance upto which the cohesive force between two molecules exists is called the molecular range and of the order 10-9 m or 1 nm.
7. An imaginary sphere drawn around a molecule with a radius of molecular range is called the sphere of influence of that molecule.
8. Intermolecular force of attraction varies inversely as the eighth power of the intermolecular distance.surface has particles of one type on one side and of different type on the other side.
9. The surface of the liquid behaves like a stretched rubber sheet. Surface tension is due to cohesion between the molecules of the liquid.
10. Surface tension is the force per unit length of a line drawn on the liquid surface and acting perpendicular to it.
11. A molecule in the surface has greater potential energy than a molecule well inside the liquid. The extra energy that a surface layer has is called the surface energy.
12. Surface tension of a liquid is also equal to the surface energy per unit surface area. Unit is J/m.
13. Surface energy is defined as the quantity of work done in increasing the surface area of the liquid through unity (also equal to the surface tension of liquid)
14. Work done = surface tension × increase in surface area.
15. At constant temperature, liquid surface does not obey Hooke’s law, and surface tension is independent of the surface area.
16. The free liquid surface tries to attain minimum surface area. This is the reason for a free liquid drop (like rain drop) to attain a spherical shape.
17. The work done (W) in blowing a soap bubble of radius r is W = 8ππr2T.
18. Work done in increasing the area of circular soap film from radius r1 to r2;
19. Work done in increasing the radius of a bubble from r1 to r2 is given by
20. When a number of small liquid drops coalesce to form a large drop, energy is released (since surface area decreases).
21. Energy is required to break a liquid drop into smaller drops (since surface area increases).
22. The work done by an agent to split a liquid drop of radius R into ‘n’ identical drops is W = 4πR2T(n1/3 – 1) where T is surface tension.
23. The amount of energy evolved when ‘n’ droplets of a liquid of radius ‘r’ combine to form a large drop is E = 4πr2T(n – n2/3).
24. ‘n’ drops each of radius ‘r’ combine to form a big drop of radius ‘R’. Then the work done (or) the energy expended is 4ππT(nr2 - R2).
25. Factors which influence surface tension of a liquid:
1) depends upon the medium in contact with its surface.
2) decreases with increase of temperature.
3) decreases when an organic substance is dissolved eg: Soap solution: 32 dyne/cm
4) increases when an inorganic substance is dissolved eg: NaCl solution: 84 dynes/cm
26. Of all liquids, mercury has maximum surface tension.
27. Angle of contact: It is the angle between the tangent drawn at the point of contact of a solid and liquid and the surface of solid within the liquid.
28. The angle of contact may assume any value between 0o and 180o.
29. The angle of contact depends on solid-liquid pair, temperature and impurities.
30. The angle of contact is not altered by the amount of inclination of solid object in the liquid.
31. θ is independent of manner of contact i.e. glass plate in a liquid or liquid drop on a plate or liquid in a solid vessel.
32. Angle of contact increases with increase in temperature.
33. For pure water and glass, the angle of contact is zero.
34. Angle of contact decreases on adding soluble impurity, detergent and wetting agent to a liquid.
35. For mercury and glass, angle of contact is about 140o
36. (a) For Ag and H2O angle of contact is 90o.
(b) For ordinary water θ lies between 8o and 18o.
(c) Angle of contact of chromium with water is as high as 160o.
37. If a liquid wets the solid, then the angle of contact is less than 90o and if the liquid doesn’t wet the solid, then the angle of contact is greater than 90o.
38. Angle of contact in case of solid, liquid and air in contact:
Let T1 is surface tension for air-liquid surface, T2 for air-solid and T3 for liquid-solid surfaces respectively. If θ be the angle of contact of the liquid with the solid, then
a) If T2 is greater than T3, cosθ will be positive i.e., θ will be less than 90o.
b) If T2 is less than T3, cosθ will be negative i.e., θ will be between 90o and 180o.
c) If T2 > T1 + T3, there will be no equilibrium, and the liquid will spread over the solid.
39. Capillarity: The property of rise or depression of the liquid due to surface tension in a tube is known as capillarity.
40. Oil ascends in a wick due to capillarity.
41. Flow of ink through a nib is due to capillarity.
42. A painter’s brush under water has its hair spread but on withdrawal from water they adhere to each other due to surface tension.
43. Ploughing of land brings moisture to the top by capillary action.
44. The addition of a detergent decreases the surface tension and angle of contact.
45. Wetting agents are used in detergents in order to clean clothes.
46. The addition of a water proofing agent like waxy substance to a liquid increases angle of contact.
47. If the angle of contact () is acute (
48. If the angle of contact () is obtuse ( > 90o), there will be capillary depression. e.g.: mercury in capillary.
49. If the angle of contact is 90o, there will be neither rise nor fall. e.g.: water in silver capillary.
50. Rise of liquid in tubes of insufficient length: If a liquid can rise upto a height ‘h’ in the tube but its total length outside the water surface is less than ‘h’ the liquid will not overflow out of the tube. Instead of it, the liquid will rise to the top of the tube.
51. Excess pressure in a drop of liquid of radius r is given by P = 2T/r.
52. Excess pressure in a soap bubble of radius r is given by P = 4T/r.
53. Excess pressure inside a soap bubble present in a liquid P = 2T/r, where r is radius and T is surface tension.
54. If the surface be curved in two directions and radii of the two curvatures be r1 and r2 respectively the total difference of pressure on the two sides of the surface will
55. Pressure difference across a surface film:
a) When free surface of the liquid is plane (fig a), the surface tension acts horizontally and its normal component is zero, thus no extra pressure is communicated to the inside or outside.
b) When free surface is convex, the forces due to surface tension acting on both sides of a line on the surface have components acting downwards which gives excess pressure inside the liquid.
c) Similarly when free surface is concave, the pressure inside the liquid is decreased.
d) Thus there is always an excess pressure on the concave side.
56. In case of concave meniscus the pressure below the meniscus is lesser than above it by
57. In case of convex meniscus the pressure below the meniscus more than above it by
58. The spherical surface of the liquid in the liquid is called meniscus.
59. If the adhesive force is large compared with cohesive force, the liquid has concave meniscus upwards. e.g.: water and glass tube.
60. If the adhesive force is less than cohesive force, the liquid has a convex meniscus. e.g.: mercury and glass tube.
61. Shape of liquid meniscus in a capillary tube:
For a liquid molecule at P, force of adhesion Fa acts at right angles to the tube at the point P, force of cohesion Fc acts at an angle of 45o to the vertical. The resultant force on it will be the resultant of these two forces of adhesion and cohesion.
a) When i.e., the cohesive force is times the adhesive force the molecules of the liquid are neither raised nor lowered and the liquid surface remains flat or plane (fig a)
b) When i.e., the cohesive force is less than
c) When i.e., the cohesive force is greater than times the adhesive force, the liquid molecules near the walls of the tube are depressed making the surface convex upwards as in case of mercury. (fig c)
62. When a charge either positive or negative is given to a soap bubble, it expands due to repulsions among the charges.
63. Surface tension by capillary rise method.
64. In capillary rise the force due to surface tension in upward direction is equal to the weight of liquid column 2ππrT cos
65. Jurin’s law: According to Jurin’s law, inversely the height of the liquid (h) risen in capillary tube is proportional to the radius (r) rh = constant
66. A graph between h and r is a rectangular hyperbola.
67. If a liquid rises to a height ‘h’ in a capillary tube and the tube is inclined at an angle ‘α’ to the vertical, the length of the liquid column inside the tube increases but the vertical height to which the liquid rises remains the same.
where L = length of the liquid column inside the tube.
68. If a capillary tube is dipped in water in a satellite, the water level will rise to the full length of the tube.
69. For the liquids of low surface tension wetting property is more.
70. Critical temperature: The temperature at which surface tension of the liquid becomes zero is known as critical temperature.
71. In case of molten copper and molten cadmium T increases with increase of temperature.
72. Surface tension of liquid metals is very very high.
73. ST of a liquid is zero at its boiling point.
74. Over small ranges of temperature, the surface tension of a liquid decreases linearly with the rise of temperature.
75. T=To(1 - α t) where T is surface tension at toC, To is the surface tension at 0oC and α is the coefficient of surface tension.
76. When two soap bubbles of radii a and b coalesce under isothermal condition, the resultant bubble has a radius R such that
77. If two soap bubbles of radii a and b coalesce (a > b), then the radius of curvature of the interface between the two bubbles will be
78. A spherical soap bubble of radius r1 is formed inside another of radius r2. The radius of the single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is
79. A slide is suspended from one arm of a balance and is counter balanced. Now the slide is lowered into a beaker of water until it just touches the surface of water. If m is the additional mass to keep the balance beam horizontal, then Where l is length and t is thickness of slide.
80. If a small drop of water is squeezed between two plates so that a thin layer of large area is formed, then the pressure inside the water layer is less than the pressure on the plates. The force pushing the two plates together is given by F = excess pressure × area of the layer.
where d = thickness of layer.
81. When two soap bubbles of different sizes are in communication with each other, the air passes from the smaller one to the larger one and the larger one grows at the expense of the smaller one. i.e., size of smaller bubble decreases and that of larger bubble increases. This is because excess pressure inside the smaller bubble (smaller radius) is greater than that in the larger bubble (greater radius).
82. Energy required to raise a liquid in a capillary tube:
When a capillary tube is depressed vertically into a liquid which wets the walls of the tube, there is a rise of the liquid inside the tube. The energy required to raise the liquid in the capillary tube is obtained from the surface energy of the air glass surface.
83. Force required to pull a circular ring of radius r from the surface of water of surface tension T is F = 4πrT.
84. Force required to pull a rectangular plate of length ‘l’ and thickness ‘t’ from the surface of water of surface tension T is F = 2(l + t)T.
85. Force required to pull a circular disc of radius R with hole of radius r from the surface of water of surface tension T is F = 2π(R + r)T.