Surface Tension & Capillarity – important Q&A
Q1. Define surface tension on the basis of intermolecular forces.
Definition: Surface tension is the property of a liquid at rest by which its free surface behaves like a stretched elastic membrane.
Molecular Basis: Inside the liquid, a molecule is attracted equally in all directions (net force = 0). A molecule on the surface has no liquid molecules above it. Thus it experiences a net inward force. This inward pull creates tension on the surface.
Molecular Basis: Inside the liquid, a molecule is attracted equally in all directions (net force = 0). A molecule on the surface has no liquid molecules above it. Thus it experiences a net inward force. This inward pull creates tension on the surface.
Q2. What is surface energy? Derive the relation between surface tension and surface energy.
Surface Energy: The potential energy per unit area of the liquid surface.
Derivation: Consider a soap film on a wire frame of length L. Let the film be stretched by a distance dx by a force F.
Derivation: Consider a soap film on a wire frame of length L. Let the film be stretched by a distance dx by a force F.
Total force due to surface tension (2 sides) = \(F\)
\(F = T \times 2L\)
Work done = \(W = F \times dx\)
\(W = (T \times 2L) \times dx\)
Increase in surface area = \(ΔA = 2L \times dx\) (two surfaces)
Surface Energy per unit area = \(E = \frac{W}{ΔA}\)
\(E = \frac{T \times 2L \times dx}{2L \times dx}\)
\(\therefore E = T\)
Conclusion: Surface Energy per unit area = Surface Tension.
\(F = T \times 2L\)
Work done = \(W = F \times dx\)
\(W = (T \times 2L) \times dx\)
Increase in surface area = \(ΔA = 2L \times dx\) (two surfaces)
Surface Energy per unit area = \(E = \frac{W}{ΔA}\)
\(E = \frac{T \times 2L \times dx}{2L \times dx}\)
\(\therefore E = T\)
Q3. Explain why liquid drops are always spherical in shape.
Surface tension acts to minimize the surface area of a liquid. For a fixed volume, a sphere has the smallest surface area. To achieve the lowest potential energy state, a liquid drop naturally takes a spherical shape.
Q4. Define angle of contact. Why is the angle of contact acute for water–glass and obtuse for mercury–glass?
Angle of Contact: The angle between the tangent to the liquid surface and the solid surface inside the liquid.
- Water–Glass: Adhesive force (water–glass) > Cohesive force (water–water). Thus, liquid wets the glass. Angle = acute (< 90°).
- Mercury–Glass: Cohesive force (Hg–Hg) > Adhesive force (Hg–glass). Thus, liquid pulls away. Angle = obtuse (> 90°).
Q5. Derive an expression for the excess pressure inside: (a) a liquid drop (b) a soap bubble.
(a) Liquid Drop: Let excess pressure be P, radius increase from r to r+dr.
Work done = \(P \times 4πr² \times dr\)
Surface area increase = \(4π(r+dr)² − 4πr² = 8πr·dr\)
Surface energy increase = \(T \times 8πr·dr\)
At equilibrium, \(P \times 4πr² \,dr = T \times 8πr \,dr\)
\(P = \frac{2T}{r}\)
(b) Soap Bubble: Two surfaces.
Surface area increase = \(4π(r+dr)² − 4πr² = 8πr·dr\)
Surface energy increase = \(T \times 8πr·dr\)
At equilibrium, \(P \times 4πr² \,dr = T \times 8πr \,dr\)
\(P = \frac{2T}{r}\)
Work done = \(P \times 4πr² \, dr\)
Area increase (two sides) = \(2 \times [4π(r+dr)² − 4πr²] = 16πr·dr\)
Energy increase = \(T \times 16πr \,dr\)
Equate: \(P \times 4πr² \,dr = T \times 16πr \,dr\)
\(P = \frac{4T}{r}\)
Conclusion: Excess pressure inside a soap bubble = \(\frac{4T}{r}\) (twice that of a liquid drop).
Area increase (two sides) = \(2 \times [4π(r+dr)² − 4πr²] = 16πr·dr\)
Energy increase = \(T \times 16πr \,dr\)
Equate: \(P \times 4πr² \,dr = T \times 16πr \,dr\)
\(P = \frac{4T}{r}\)
Q6. What is capillarity? Derive the ascent formula.
Capillarity: The rise or fall of liquid in a narrow tube.
Upward force = \(T cosθ \times 2πr\)
Weight = \((πr² h) ρ g\)
When upward force and equals, \(T cosθ \times 2πr = πr² h ρ g\)
\(h = \frac{2T cosθ}{r ρ g}\)
Weight = \((πr² h) ρ g\)
When upward force and equals, \(T cosθ \times 2πr = πr² h ρ g\)
\(h = \frac{2T cosθ}{r ρ g}\)
Q7. Explain the effect of temperature on the surface tension of a liquid.
Q8. Explain the effect of dissolved impurities (such as salt or detergents) on the surface tension of a liquid.
Q9. Why is it easier to wash clothes in hot water or by using detergents?
Q10. Explain why a small oily needle can float on the surface of water.
Temperature: Temperature increases → kinetic energy increases → cohesive forces decrease → surface tension decreases.
Impurities: - Soluble (Salt) = surface tension increases.
- Detergents = surface tension decreases.
Washing: Hot water and detergents lower surface tension, allowing water to enter small pores of clothes easily.
Needle: An oily needle floats because the surface tension of water acts like a support membrane.
Impurities: - Soluble (Salt) = surface tension increases.
- Detergents = surface tension decreases.
Washing: Hot water and detergents lower surface tension, allowing water to enter small pores of clothes easily.
Needle: An oily needle floats because the surface tension of water acts like a support membrane.
Q11. Pressure vs Radius in Soap Bubble
Formula: \(P = \frac{4T}{r}\)
∴ \(P ∝ \frac{1}{r}\)
If radius (r) increases → pressure (P) decreases.
∴ \(P ∝ \frac{1}{r}\)
If radius (r) increases → pressure (P) decreases.
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