Chapter -6(Section-1) Surface Tension Free surface of the liquid tends to minimize the surface area. e.g.(1)if the small quantity of mercury is allowed to fall on the floor, it converted in to small spherical shaped droplets, which has least surface area. (2) If the ring of thin wire tie a thread loosely between any two points A&B.Dip the ring in the soap solution Free surface of the liquid behaves like stretched elastic membrane under surface a soap film is produced within the ring as shown in fig.a If the film to the right is broken, the thread is pulled in the opposite direction, forming the circular arc as shown in fig.b If the film to the left of AB is broken the thread is pulled to the right & forming the circular arc as shown in fig.c. The circular shape of the thread is due to contraction of the surface area of the film above experiment shows that that the free surface of liquid tends to minimize surface area as it is under tension called as surface tension. Que.1:Explain the term Intermolecular force of attraction. Ans : Intermolecular force of attraction:-the force of attraction between two molecules of liquid is called intermolecular force of attraction. It is a short range force I.e. It is effective over short distance (about 10-9 m). Beyond this distance, this force is negligible. Intermolecular forces of two types (a) Cohesive force (b) Adhesive force Que.2: Define 1. Cohesive force 2. Adhesive force 3. Range of molecular attraction 4. Sphere of influence Ans: 1. Cohesive force The force of attraction between two molecules of same substance is called as cohesive force.
2. Adhesive force The force of attraction between two molecules of different substances is called as adhesive force. These intermolecular forces, cohesive & adhesive both are short rang forces i.e. effective over very short distance, beyond which they are negligible 3. Range of molecular attraction: - The maximum distance between two molecules unto which the intermolecular forces are effective is called as range of molecular attraction. it is denoted by R. 4. Sphere of influence:- An imaginary sphere drawn round a molecule as the centre, with a radius equal to the range of molecular attraction is called as sphere of influence. Que.3 Explain the phenomenon of surface tension on the basis of molecular theory i. The molecules are attracted if other molecules are inside the sphere. Three molecules A, B,& C of liquid with their spheres of influence are shown in fig. ii. The sphere of influence of molecule A is well inside the liquid. Other molecules of the liquid are symmetrically distributed around the molecules A. the molecule A is equally attracted in all direction by the cohesive forces so that resultant cohesive force acting on it is zero. iii. The molecule B is just inside the liquid surface, the part of sphere of influence lies outside the liquid containing air molecules, but there is very small so that adhesive force exerted by the air molecules is neglected as compared to the cohesive force exerted by the molecules of the water inside the sphere of influence. The resultant down ward force acts on the molecule B & try to pull it inside the liquid. iv. The molecule C is on the surface of the water, half sphere of influence is in water & half is in air. Molecules of liquidate extremely large than molecules air in the upper part of the sphere of influence therefore molecule C experiences maximum downward force, try to full it into the liquid. v. Thus all the molecules in the layer of thickness R, below the free surface of the liquid, experiences the maximum inward pull. The pull is greater, if the molecules on the surface of the liquid. vi. In order to increased surface area of the liquid surface, molecules from inside the liquid is brought to the surface. The work must be down against the inward pull exerted by the liquid. This work done is stored in the form of potential energy. vii. But the nature tendency of a body is to attain the minimum potential energy. Thus the free surface of the liquid has a tendency to minimize the surface area which has the tendency to minimize the potential energy, which give raise the phenomenon of surface tension. In order to minimize the surface area the force due to surface tension must be acts tangentially to the liquid surface.
Que.4: Define, Surface energy and Give its S.I. unit and dimension Ans:- In order to increased the surface area of the liquid, the number of molecules must be increased. The motion of the molecules towards the surfaces opposed by the inward pull exerted the molecules of the liquid. The work is down against the inward pull, which is stored in the form of potential energy. The potential energy per unit surface area of the liquid is called as surface energy. S.I. unit is J/m 2 & C.G.S. unit is erg/cm 2 the dimensions of the surface energy is [surface energy] = [work] [area] = [M1 l 2 T 2 ] [M 0 L 2 T 0 ] = [M 1 L 0 T 2 ] Que.5: Define surface Tension and give its S.I. unit and dimension. Also five application of surface tension. Surface tensions: - surface tension of the liquid is defined as the force per unit length, acting at right angles to an imaginary line drawn in the free surface of the liquid. If l = length of the line & F = force acting on it. Then surface tension acting on the liquid (T) is T = F l S.I. unit is N m & C.G.S. unit is dyne /cm [Surface tension]= [force] [length] = [M1 L 1 T 2 ] [L 1 ] = [M 1 L 0 T 2 ].
As shown in the fig. the force due to surface tension is acting on the both side of the line drown on the surface of the liquid Application of surface tension: i) Tooth paste spreads more freely in the mouth while clearing the mouth because it contains soap which reduces surface tension ii) If detergent is added in water, the surface tension of resulting detergent solution becomes less than water. This increases area of contact and cleaning iii) Mosquito eggs float on the surface of water due to surface tension of water. when Kerosene is sprayed on the surface of water, the surface tension is lowered and eggs go down inside the water and breeding of mosquitoes stops. Que.6: Obtain the relation between surface tension & surface energy. Ans:- i. ABCD is the open rectangular frame of the wire on which a wire PQ can side with friction. The frame is held in the horizontal position as shown in the fig. ii. The frame is dipped into soap solution & taken out so that soap film APQB is form. Due to surface tension of soap, a force F will act on the wire PQ tends to pull towards AB. iii. If T is S.T. Of soap solution & PQ= I then total force acting on PQ is F = 2Tl the factor 2 is appears because the soap film has two surfaces, both are contact with wire. iv. If the wire PQ is pulled outwards through a small distance x to the position P Q by the application of external force F, the work done against the inward pull of surface tension is given by work = applied force displacement W = Fx = 2Tlx
The increased in surface area is da = 2lx hence the mechanical work done per unit surface area W da = surface energy = 2Tlx 2lx = T This shows that surface tension is equal to work done per unit surface area of the liquid ie. Surface tension is equal to surface energy per unit area of the liquid since surface tension S. I. of surface tension is J/m 2 work done (w) = T increase in area (T) = work area = W A W = T da Que.7: What is angle of contact? State its Characteristics. Ans: Angle of contact:- when liquid is contact with solid, the angle between the surface of solid & tangent drawn to the surface of the liquid, at a point of contact, measured on the side of the liquid is called as angle of contact. Characteristics of angle of contact: - (1) The angle of contact is constant for the given solid liquid pair. (2) For the liquid which partially wets the solid, the angle of contact is acute. e.g. kerosene in contact with glass. (3)For the liquid which does not wets the solid, the angle of contact is obtuse. e.g. mercury in contact with glass. (4) For the liquid which completely wets the solid, the angle of contact is zero e.g. water in the contact with glass. (5) For the given solid liquid pair, even a small contamination of the surface causes a large change in the angle of contact. (6) The angle of contact changes due to temperature. Que.8: Explain the phenomenon of angle of contact on the basis of intermolecular forces.
Ans: Explanation of angle of contact:-the phenomenon of angle of contact can be explained by considering the intermolecular forces of attraction, acting on the molecules A in contact solid. As shown in fig its sphere of influence is partly in solid, party in liquid & party in air. The molecule A is acted upon by following forces (1) Adhesive force exerted by the molecules of the solid, such that resultant adhesive force is perpendicular to the surface of the solid, APrepresented by P. (2) Cohesive force exerted by the molecules of the liquid, by the symmetry, the resultant cohesive force is inclined at 45 0 with the surface of the solid, represented by AQ. (3) Adhesive forces exerted by the molecules of air. Since the number of molecules of air in the sphere of influence A is very small, the resultant adhesive force due to the air molecules can be neglected. (4) The molecule A i.e. also exerted by the gravitation force, equal to its weight acting vertically downward which very small as compared to strong adhesive & cohesive force s hence can be neglected. it. In the state of the equilibrium, the free surface of a liquid is always perpendicular to the resultant force on (1) For the liquid partially wets solid: - For the liquid which partially wets the solid, the resultant adhesive force AP is quit large than the resultant cohesive force AQ. Therefore their resultant AR lies outside the liquid. As shown in fig. In order to be perpendicular to this resultant AR, the molecule A moves upwards & surface of the liquid becomes concave. If tangent AT is drawn to the surface of the liquid, forming a acute angle of contact
(2) Liquid does not wets the solid:- For the liquid which does not wets the solid, the resultant cohesive force AQ is quite large than resultant adhesive force AP.Therefore their resultant force AR lies inside the liquid as shown in fig. In order to be perpendicular to AR, a liquid molecule moves downwards & liquid surface becomes convex, forming an obtuse angle of contact, by drawing a tangent to the surface of liquid. (3) For liquid completely wets the solid:- In case of the liquid which completely wets the solid, the resultant adhesive force AP is so large that the resultant cohesive force AQ can be neglected. In such a case the resultant force AR is almost coinciding with AP. Therefore the liquid surface in contact is almost tangent to the surface of solid & the angle of contact is zero. Que.9 : Explain why angle of contact is acute for water glass pair and is obtuse for mercury glass pair. of the liquid drop: - Consider the equilibrium of a liquid drop on a flat solid surface. Shape Let T 1 be the surface tension for solid-liquid interface T 2 be the surface tension for air-solid interface T 3 be the surface tension for air-liquid interface, as shown in fig. For the equilibrium position of the drop. T 2 = T 1 + T 3 cos θ cosθ = T 2 T 1 T 3 This expression leads the following conclusion (1 ) If T 2 > T 1, cosθ is +ve & θ is acute
(2) If T 2 < T 1. cosθ is ve, & θ is obtuse (3) T 2 T 1 = T 3 cosθ, cosθ = 1 & θ is nearly equal to one (4) If T 2 T 1 > T 3 cosθ, cosθ > 1 which is impossible, equilibrium is not possible, liquid is spread on the ground & drop shall not be formed on the solid. Que.10: Derive Laplace s law for spherical membrane. OR Derive an expression for excess pressure inside a liquid drop. Ans:- i. Free surface of drop or bubbles are spherical in shape. Let, P i = inside pressure of drop or air bubble P o = Outside pressure of bubble
r = radius of drop or bubble. PHYSICS-MANIA P i - P o = excess pressure ii. iii. Let the radius of drop increases from r to r+δr so that inside pressure remains constant. Initial area of drop A 1 = 4πr 2, Final surface area of drop A 2 = 4π(r + r) 2 Increase in surface area A = A 2 A 1 = 4π[(r + r) 2 r 2 ] = 4π[r 2 + 2r r + ( r) 2 r 2 ] = 4π[2r r + ( r) 2 ] A = 8πr r + 4π( r) 2 iv. As r is very small, ( r) 2 is neglected A = 8πr r v. work done by force of surface tension dw = T A = (8πr r)t..(i) But dw == F r = (P i P o )A r from equation (i) (8πr r)t = (P i P o )A r But surface area of sphere is 4πr 2 (P i P o ) = (8πr r)t 4πr 2 r (P i P o ) = 2T r This is called Laplace s law of spherical membrane. in case of soap bubble there are two free surface in contact with air. hence the total increase in surface area is 2(8πr r)t and dw=(16πr r)t
hence PHYSICS-MANIA (P i P o ) = 4T r Que10: Explain the nature of pressure on two side of liquid surface. Also, state their causes. Ans: Pressure on two sides of a liquid surface:-the surface of the liquid is sometimes concave or convex due to angle of contact phenomenon (1) If the surface of the liquid is plane, the force due to surface tension acting on two sides of the element AB are equal but opposite, so that the resultant force is zero. Therefore no pressure difference on two side of the plane surface. as shown in fig. a (2) If the surface is concave, the forces of surface tension on the element AB produces the resultant force vertically upwards To counter balance the effect of this resultant force, the pressure on concave side is greater than that of convex side. As in fig.b. (3) If the surface is convex the resultant force due to surface tension acting vertically downwards To counter balance the effect of this resultant force, the pressure on convex side is less than that of concave side. As shown in fig. c Que. 11: What is capillarity? give its examples. Ans:- A tube having a very small bore is called as capillary tube or capillary. If the capillary tube is dipped in a liquid which partially wets or wholly wets the solid, there is rise of liquid in the capillary tube, If the capillary tube is dipped in the liquid which does not wets the solid, the liquid level lowered inside the capillary. The phenomenon of rise or fall of a liquid inside a capillary tube is called as capillarity. Examples of capillarity:- (1) Blotting paper absorbs ink or water. (2) Ink rises in a pen or oil rises up the wick of a lamp, due to capillary action. (3) Water & minerals rise up through the root of the tree, due to capillary action. (4) Oil rises up the wick of lamp on account of capillarity.
Que.12: Explain the cause of capillary action. Ans:-Explanation of the capillary action:- PHYSICS-MANIA Suppose that capillary tube is dipped into a liquid, which wets the capillary tube. The shape of the water inside the capillary tube is concave. Let us consider four points A,B,C,&D such that (1) A is just above the curve surface, inside the capillary (2) B is just below the curve surface inside the capillary (3) C is just above the plane surface of the water & (4) D is just inside the plane surface of water, outside the capillary. Let P A, P B, P C & P D be the pressures at the points A, B, C, &D respectively. Since pressure on the concave since is greater than that of convex P A > P B as the pressure on the both of plane surface is same we have P C = P D AS P A = P C = atmospheric pressure i.e. P A = P D P D > P B Therefore pressure at D is greater than that of the point B hence there is flow of liquid from the point D to the point B, inside the capillary so that liquid rises in the capillary tube, still the pressure at B is same that the point D. I.e. for the liquid which is partially wets or completely wets the capillary,there is rise of the liquid. for the liquid which does not wets the solid i.e. mercury in the capillary, surface is convex. Hence there is fall of liquid inside the capillary for it we have P A < P B P D < P B fall of liquid in the capillary tube Que. 13 : Derive T = hrρg 2 cos θ Ans: Rise of a liquid in the a capillary tube:-
If a glass capillary tube is inserted into a liquid which wets the glass, the liquid rises in the capillary to a height h. If T is the surface tension of the liquid, a force of magnitude T acts on each it length of the liquid surface, which is contact with the wall of the capillary. This force acts along a tangent to the liquid meniscus, making an angle θ with the wall of the capillary. The force of reaction on each unit length can be resolved in two components, i. vertical component T cos θ & ii. Horizontal component T sin θ. All horizontal cancel each other, while vertical com. Add to each other. The liquid surface inside the capillary is in contact with capillary along a length 2πr, which is circumference of it.the total vertical force acting on the liquid column inside the capillary is 2πrTcosθ, The weight of liquid column V = volume of liquid column M = mass of it & ρ = density of liquid V = area height = πr 2 h M = volume density = πr 2 h ρ (W) = Mg = πr 2 h ρ g= total downward force(gravitational force) for the equilibrium of the liquid column
We have, PHYSICS-MANIA upword force = downward force 2πrTcosθ = πr 2 h ρ g T = hrρg 2cosθ h = 2Tcosθ rρg This formula is used to determine the surface tension of the liquid in the capillary. Que. 14 : Explain the effect of impurity and temperature on surface tension. Ans: Effect of impurity on surface tension: if the surface of a liquid contains impurities of any kind, there is a marked change in the surface tension of the liquid. (1) when the highly soluble inorganic substance like sodium chloride is dissolved in water, the surface tension of water increases (2) When a sparingly soluble substance like phenol, is dissolved in water, decreases the surface tension. (3) When soap is dissolved in water, the surface tension of the solution decreases to a great extent. This is the reason why a soap bubble in air remains stable for a reasonable time or why soap is used for washing clothes. Effect of temperature on surface tension:- Surface tension of a liquid depends on the temperature. Surface tension of the liquid decreases as the temperature increases. Only in case of molten copper & cadmium, the surface tension increases with the rise in the temperature. The temperature at which surface tension of liquid is zero such temperature called as the critical temperature of the liquid. Effect of contamination on surface tension : The presence of dust particles or lubricating materials on the liquid surface decreases its surface tension. i. Surface tension Important formulae
T = F l, T = hrρg 2cosθ PHYSICS-MANIA ii. Work done = surface area x surface tension. W = T da iii. Laplace s law of spherical membrane (P i P o ) = 2T r iv. Laplace s law of spherical membrane (hollow sphere) (P i P o ) = 4T r