Surface Tension and Surface Energy

Q7. Define surface tension and surface energy. Show that they have the same dimensions.

Q8. Calculate the work done in blowing a soap bubble of radius 5 cm. (Surface tension of soap solution = 3 × 10⁻² N/m)

Q9. Explain why small liquid drops are spherical while larger drops may be flattened.

Q10. In your school, a student observes that a needle carefully placed on water floats, but sinks if detergent is added. Explain using surface tension.

Q11. Derive the expression for excess pressure inside a liquid drop.

Q12. Why does hot soup taste different from cold soup? Explain in terms of surface tension.

Q13. Explain the molecular origin of surface tension. Define surface energy and show that surface energy per unit area equals surface tension. Derive expressions for excess pressure inside:

(i) A liquid drop

(ii) A soap bubble

(iii) An air bubble in water

Discuss why a soap bubble has twice the excess pressure of a liquid drop of the same radius.

Q14. Two soap bubbles of radii 3 cm and 4 cm coalesce to form a single bubble under isothermal conditions.

(a) Calculate the surface energy of each bubble before coalescence. (S = 3 × 10⁻² N/m)

(b) Calculate the radius of the resulting bubble.

(c) Calculate the surface energy of the resulting bubble.

(d) Calculate the energy released during coalescence.

(e) What happens to this released energy?

Q15. Analyse the following phenomena using surface tension concepts:

(i) Water rising in a thin glass tube

(ii) Insects walking on water

(iii) Formation of spherical dewdrops

(iv) Detergents helping in cleaning

For each case, explain:

(a) The role of surface tension

(b) The molecular explanation

(c) Practical significance

Q16. A capillary tube of radius 0.5 mm is dipped vertically in water (surface tension = 7 × 10⁻² N/m, angle of contact = 0°, density = 1000 kg/m³).

(a) Calculate the height to which water rises in the tube.

(b) Calculate the excess pressure inside a meniscus of radius 0.5 mm.

(c) If the tube is dipped to a depth of 2 cm in water and held vertically, what is the length of the water column in the tube?

(d) Calculate the work done by surface tension in raising the water.

(e) What would happen if the tube radius were 0.1 mm?

Q17. A soap bubble of radius 5 cm is blown using a soap solution of surface tension 2.5 × 10⁻² N/m.

(a) Calculate the excess pressure inside the bubble.

(b) Calculate the total surface energy of the bubble.

(c) If the bubble is attached to another bubble of radius 3 cm, calculate the radius of curvature of the common interface.

(d) Calculate the pressure inside each bubble and the common interface.

(e) Discuss why the common interface bulges toward the smaller bubble.

Q18. In a school experiment, students measure surface tension using the capillary rise method.

(a) Describe the experimental procedure.

(b) Water rises to 3 cm in a capillary tube of radius 0.4 mm. Calculate the surface tension of water. (θ = 0°, ρ = 1000 kg/m³)

(c) The same tube is dipped in a soap solution and the rise is 2.5 cm. Calculate the surface tension of the soap solution.

(d) Why must the tube be clean and vertical for accurate results?

(e) Suggest two other methods to measure surface tension in a school laboratory.