Surface Tension & Capillary Action
Master intermolecular cohesion, surface energy, surface tension γ = F/L, excess pressure inside drops ΔP = 2γ/R and soap bubbles ΔP = 4γ/R, contact angle θ, and Jurin’s capillary rise law h = (2γ cosθ)/(ρ g r).
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Explain surface tension in terms of unbalanced cohesive intermolecular forces and surface free energy.
- Derive excess pressure inside spherical liquid drops (2γ/R) and thin hollow soap bubbles (4γ/R).
- Apply Jurin’s Law h = (2γ cosθ)/(ρ g r) to determine capillary rise or depression and calculate surface tension.
Core Theory & Concepts
Molecules inside the bulk of a liquid experience cohesive attractions symmetrically in all directions. At the surface boundary, missing upward neighbors leave an unbalanced inward attraction, creating a microscopic surface tension that behaves like a stretched elastic membrane.
Excess Pressure Formulas
Inside a spherical liquid drop (1 surface) ΔP = 2γ/R. Inside a hollow soap bubble (2 surfaces) ΔP = 4γ/R.
Jurin’s Capillary Law
Capillary height h attained in a tube of radius r is directly proportional to surface tension and inversely proportional to radius and liquid density.
Common Misconceptions
A soap bubble and a water droplet of the same radius have the same excess internal pressure.
Syllabus Topic Outline
- 1Molecular origin of surface tension: cohesion vs adhesion
- 2Surface tension force (γ = F/L) and surface energy (γ = W/ΔA)
- 3Excess pressure in drops (ΔP = 2γ/R) and bubbles (ΔP = 4γ/R)
- 4Angle of contact θ, meniscus shapes, and wetting phenomena
- 5Capillary rise (Jurin’s Law): h = (2γ cosθ) / (ρ g r)
- 6Experimental determination: capillary rise and microscope glass slide methods