# Surface Tension Maharashtra State Board Textual Questions

#### 1.1 Range of molecular attraction :

• The maximum distance between two molecules up to which the intermolecular forces are effective is called the range of molecular attraction.

#### 1.2 Sphere of Molecular Influence:

• An imaginary sphere drawn, with given molecule as a centre and radius equal to the molecular range is called sphere of influence.

#### 1.3 Adhesive Force:

• The attractive force between the two molecules of the different substance is called an adhesive force.
• e.g. Force due to the attraction between water and glass molecules.

#### 1.4 Cohesive Force:

• The attractive force between the two molecules of the same substance is called as a cohesive force.
• e.g. Force due to the attraction between water and water molecules.

#### 1.5 Surface Tension:

• The force per unit length acting at right angles to the imaginary line drawn on the free surface of the liquid is called surface tension.

#### 1.6 Angle of Contact:

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid and the surface of solid at the point of contact, measured from inside the liquid is called the angle of contact.

#### 2.1 c.g.s. and S.I. unit of Surface Tension:

• S.I. unit of surface tension is N/m and c.g.s. unit is dyne/cm.

#### 3.1 Dimensions of Surface Tension:

Surface Tension (T)  = Force (F) / Effective Length (L)

∴   [T] = [F] / [L]

∴   [T] = [L1M1T-2] / [L1]

∴   [T] = [L0M1T-2]

Thus the dimensions of surface tension are [L0M1T-2]

#### 4.1 Surface Energy:

• A molecule on the surface of a liquid experiences a downward pull due to surface tension.  If a molecule deep inside the liquid is to be lifted up towards the fine surface, as soon as it enters the surface film, work will have to be done to lift it further against the unbalanced downward forces of molecular attraction.
• This work will be stored in the molecule as potential energy. This is true of every molecule on the surface film and surface film possesses a certain amount of potential energy. Thus the molecules in surface film possess extra energy. This energy is called as surface energy.

#### 4.2: Relation Between Surface Tension and Surface Energy: • Consider a rectangular frame ABCD in which side CD is made of loose write and other three sides are fixed. The frame is immersed in a soap solution and taken out and held horizontally. A film of soap solution will be formed on the frame and it will at once try to shrink and pull the loose wire CD towards AB. If the length of loose wire CD is  ‘l’ and the film is of finite thickness, therefore the film will be in contact with the wire both on the upper surface as well as along its lower surface.  Hence the length of the wire in contact with the film is ‘ 2l ‘.  The force acting on the wire is directed towards AB, per unit length of the contact line is surface tension (T). By definition of surface tension, we have

T = F / 2l

∴    F  =  T . 2 l     …  (1)

• Imagine an external force is applied on CD which is equal and opposite to force F Let the wire at CD moves to C’D’ through small distance dx.  Then the work done against the force of surface tension is given by

dW  =  F.dx         …  (2)

From equations (1) and (2),

dW = T.2l. dx

But,  2l . dx = dA = increase in Area of both the surface of the film.

∴  dW   =  T.dA

This work done is stored inside the films as potential energy dU.

∴   dU  =  T.dA

• If, initially CD is very close to AB, initial energy and initial area of the film can be taken as zero and dU and dA can be treated as total energy and the total area of the film respectively.

∴  T  =  dU / dA

• This expression indicates that surface tension is equal to surface energy per unit area of the surface film.

#### 6.1 Capillarity:

• The phenomenon of a rise and fall of a liquid inside a capillary tube when it is dipped in the liquid is called capillary action or capillarity.

#### 6.2 Applications of Capillary Action:

• Due to capillary action oil rises through the wicks of lamps.
• Due to capillary action water rises through sap of trees.
• Due to capillary action ink is absorbed by blotting paper.
• Due to capillary action liquids are absorbed by sponges.
• Bricks and mortar, which are porous, permit the rise of soil water through them by capillary action. To avoid it base is made using damp-proof cement.

#### 7.1 Expression for the rise of a liquid in a capillary tube:

• If a glass tube of a smaller bore (capillary tube) is immersed in a liquid which wets the glass (water), then the liquid level inside the tube rises. If the tube is immersed in a liquid which does not wet the glass (mercury), then the liquid level inside the tube decreases. This phenomenon of the rise or fall of liquid in a capillary tube is called capillary action or capillarity.
• Consider a capillary tube immersed in a liquid that wets it. The liquid will rise in the capillary tube. The surface of the liquid will be concave. • The surface tension ‘T’ acts along the tangent to the liquid surface at the point of contact as shown. Let θ be the angle of contact. The force of surface tension is resolved into two components vertical T cos θ and horizontal T sin θ. The components T sinθ cancel each other as they are equal in magnitude and radially outward (opposite to each other). The unbalanced component T cos θ will push the liquid up into the capillary tube. This explains the rise in the liquid layer in the capillary tube.
1. If ‘r’ is the radius of the bore of the capillary tube, the length along which the force of surface tension acts is 2πr. Hence total upward force is  2πr T cos θ.
2. Due to this force the liquid rise up in the tube. The weight of liquid acts vertically downward. The liquid goes on rising till the force of surface tension is balanced by the weight of the liquid column.

Total upward force  =  Weight of liquid in the capillary tube.

2πr T cos θ  =    mg

Where ‘m’ is the mass of liquid in the capillary tube.

2πr T cos θ   =    V ρ g

Where ‘V’ is the volume of liquid in capillary and ρ is the density of the liquid in the capillary tube.

2πr T cos θ   =    π r²h ρ g

Where ‘h’ is the height of the liquid column in the capillary tube. then This is an expression for the rise in the liquid in the capillary tube.

#### 8.1 Explanation of surface tension on the basis of molecular theory: • Consider three molecules A, B and C in a liquid, such that molecule A is well inside the liquid, molecule B is close to the free surface and the molecule C is on the free surface.
• The sphere of influence of the molecule A is completely inside the liquid, and hence it will be acted upon by equal forces in all directions and these forces will balance one another and the net force acting on it is zero.
• For the molecule B, a part of the upper half of the sphere of influence is in the air, which contains air molecules.  Air molecules exert very negligible adhesive forces on molecule B.  Therefore, the cohesive forces due to molecules in the liquid remains unbalanced and thus a net force in downward direction acts on the molecule.
• For the molecule C, the upper half of the sphere of influence is completely in the air. Due to this, the force of attraction due to the molecules inside the lower half of the sphere will remain unbalanced.  This molecule experiences the maximum possible unbalanced force in the downward direction.
• Thus the molecules on the surface and in a surface film of thickness equal to the range of molecular attraction of the liquid molecule experience a net force in the downward direction.  The magnitude of force depends upon the distance of the molecule from the free surface.  The behaviour of this film is different from that of the rest of the liquid.  It is called the surface film.  This film behaves like a film which is under tension.  This phenomenon is known as surface tension.
• If any molecule is brought to the surface from the liquid, the work is to be done against this net downward force. This work increases the potential energy of the surface. But the liquid surface will have the tendency to have minimum potential energy. So a minimum number of molecules remains on the surface of the liquid.
• Thus the free surface of a liquid behaves like a stretched elastic membrane and has a tendency to contract so as to minimize its surface area.

#### 9.1 Floating of Steel Razor Blade on Water:

• A safety razor blade, when placed gently with its flat surface on water floats on it even though the density of steel, is nearly eight times greater than that of water. The surface film forms due to surface tension support the needle/blade and their thickness is not sufficient to break the film.
• But when the detergent is added to the water the surface tension of water decreases and the thickness of the surface film decreases. Now the thickness of the blade is sufficient to break the surface film and it sinks.

#### 11.1 When a chalk piece is immersed in water, bubbles are emitted.

• Chalk is porous in nature. In these pores, air is trapped.
• When chalk piece is dropped in water, due to capillary action water enters the pores of the chalk. Due to which the trapped air comes out of the pores in form of bubbles.

#### 12.1 Water on clean glass surface tends to spread out while mercury forms a drop.

• When a small quantity of liquid is poured on a plane solid surface, a force of surface tension acts along a surface separating the two media. There is a formation of the liquid drop.
• When the drop is in equilibrium, Its shape depends on the forces of interface media. Thus there is surface tension along a surface between a) liquid and air b) solid and air and c) liquid and solid. Let, θ  = the angle of contact of given solid-liquid pair.

T1 = Surface tension at the liquid-solid interface

T2 = Surface tension at the air-solid interface

T3 = Surface tension at the air-liquid interface

For equilibrium of the drop

T2 = T1 + T3 cos θ • In case of pure water on clean glass T2 -T1 = T3, then cos θ is 1 and the angle of contact is zero. Hence water wets the glass and thus water spreads on the glass.
• In the case or mercury on clean glass  T2 < T1, and T1 -T2 < T3, then cos θ is negative and the angle of contact is obtuse. Hence mercury does not wet the glass and thus it forms a drop on the glass.

• #### 13.1 Shape of impure water meniscus is concave

• When impure water or kerosene is taken in a glass vessel, it is found that the surface near the walls is curved concave upwards. • Consider a molecule of water M on the free surface very close to the wall of the glass vessel. The force of cohesion C due to other water molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between water molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of A is greater than the magnitude of C and resultant of the two molecular forces of attraction R is directed towards the glass or outside the liquid. Hence the molecule A is attracted to the walls of the glass vessel.
• The free surface of water adjusts itself at right angles to the resultant R. Therefore molecules like M creep upward on the solid surface. Thus the water surface is curved concave upwards and the angle of contact is acute.

#### 13.2 The shape of mercury meniscus is concave:

• When mercury is taken in a glass vessel, it is found that the surface near the walls is curved convex upwards. • Consider a molecule of mercury M on the free surface very close to the wall of the glass vessel. The force of cohesion C  due to other mercury molecules is as shown in the figure. In addition to this, a force of adhesion A acts due to the glass molecule as shown in the figure. The net adhesive force between mercury molecules and air molecules is negligible. The gravitational force on the molecule is also negligible.
• The magnitude of  A is very less than the magnitude of C and resultant of the two molecular forces of attraction R is directed inside the liquid. Hence the molecule A is attracted to other molecules of mercury.
• The free surface adjusts itself at right angles to the resultant R. The molecule A creeps downwards on the glass surface. Thus the surface of the mercury in the glass is curved convex upwards and the angle of contact is obtuse.

#### 15.1 Angle of Contact:

• When the liquid is in contact with solid, the angle between the solid surface and the tangent to the free surface of the liquid and the surface of solid at the point of contact, measured from inside the liquid is called the angle of contact.
• When the liquid surface is curved concave upwards, the angle of contact is acute and when the liquid surface is curved convex upwards, the angle of contact is obtuse.

#### 15.2 Angle of contact is acute for water glass pair and it is obtuse for mercury glass pair

• When a small quantity of liquid is poured on a plane solid surface, a force of surface tension acts along a surface separating the two media. There is a formation of the liquid drop.
• When the drop is in equilibrium, Its shape depends on the forces of interface media. Thus there is surface tension along a surface between a) liquid and air b) solid and air and c) liquid and solid. Let, θ  = the angle of contact of given solid-liquid pair.

T1 = Surface tension at the liquid-solid interface

T2 = Surface tension at the air-solid interface

T3 = Surface tension at the air-liquid interface

For equilibrium of the drop

T2 = T1 + T3 cos θ • In case of pure water on clean glass T2 -T1 = T3, then cos θ is 1 and the angle of contact is zero. Hence water wets the glass and thus water spreads on the glass.
• In the case or mercury on clean glass  T2 < T1, and T1 -T2 < T3, then cos θ is negative and the angle of contact is obtuse. Hence mercury does not wet the glass and thus it forms a drop on the glass.
• #### 16.1 Tents are coated with thin layers of aluminium hydroxide

• Tent cloths are woven in such a way that the water particles do not penetrate it. But the clothes are able to stop the water drops coming down with high speed (like rain).
• Aluminium hydroxide is insoluble in water and acts as a very good water repellant. So it drains off the water from the tent material preventing it from wetting the cloth.

#### 17.1 Effect of temperature on the surface tension of a liquid.

• The surface tension at t °C is given by T = T0(1 – α t), Where    T0 = Surface tension at 0° C and α = Temperature coefficient of surface tension. Its value depends on the nature of the liquid.
• Generally, the surface tension of liquid decreases with increase in temperature. it is due to the increase in kinetic energy of liquid molecules.
• The temperature at which surface tension of a liquid becomes zero is called a critical temperature of the liquid.
• The surface tension of a liquid at boiling point and at critical temperature is zero.
• The surface tension of molten cadmium and copper increases with increase in temperature.

#### 18.1 Effect of impurities on the surface tension of a liquid.

• If the impurity added in a liquid is highly soluble, then the surface tension of liquid increases.
• If the impurity added in a liquid is partly soluble, then the surface tension of liquid decreases.

#### 19.1 Reason of extra energy of molecules lying on the surface

• A molecule on the surface of a liquid experiences a downward pull due to surface tension.  If a molecule deep inside the liquid is to be lifted up towards the fine surface, as soon as it enters the surface film, work will have to be done to lift it further against the unbalanced downward forces of molecular attraction.
• This work will be stored in the molecule as potential energy. This is true of every molecule on the surface film and surface film possesses a certain amount of potential energy. Thus the molecules in surface film possess extra energy. This energy is called as surface energy.

#### 20.1 Derivation of Laplace’s law of spherical membrane:

• Due to the spherical shape, the inside pressure Pis always greater than the outside pressure Po. The excess of pressure is Pi– Po. • Let the radius of the drop increases from r to r + Δr, where Δr is very very small, hence the inside pressure is assumed to be constant.

Initial surface area = A = 4 π r²

Final surface area = A = 4 π (r + Δr)² = 4 π (r² + 2r.Δr + Δr²) =  4 πr² + 8 πr.Δr + 4 πΔr²

Δr is very very small, hence Δr² still smsll hence the term 4 πΔr² can be neglected.

Final surface area = A =  4 πr² + 8 πr.Δr

Hence Change in area = A – A =  4 πr² + 8 πr.Δr  –  4 πr²

Change in area = dA =  8 πr.Δr

Now, work done in increasing the surface area is given by

dW = T. dA = T.  8 πr.Δr    …………… (1)

By definition of work in mechanics we have

dW = Force ∴ displacement = F .Δr  …………… (2)

But P = F /A, Hence F = Excess pressure × Area

F = (Pi– Po) × 4 πr²

Substituting in equation (2) we have

dW = (Pi– Po) × 4 πr².Δr  …………… (3)

From equations (3) and (4) we have

(Pi– Po) × 4 πr².Δr  = T.  8 πr.Δr

(P– Po) = 2T / r

This relation is known as Laplace’s law for the spherical membrane for a liquid drop.

For a bubble there are two free surfaces hence the same expression for a bubble is

(P– Po) = 4T / r

#### 21.1 Excess of the pressure of liquid drop and a soap bubble

• Due to surface tension, free liquid drops and bubbles are spherical, if the effect of gravity and air resistance are negligible.
• Due to the spherical shape, the inside pressure Pi is always greater than the outside pressure Po. The excess of pressure is Pi– Po.
• By the Laplace’s law for the spherical membrane for a liquid drop the excess of pressure is given by (Pi– Po) = 2T / r.
• By the Laplace’s law for the spherical membrane for a soap bubble the excess of pressure is given by (Pi– Po) = 4T / r.