Laplace Pressure in Drops and Bubbles
The Young-Laplace relation connects pressure jump across an interface to surface tension times the sum of its principal curvatures; spherical interfaces give inverse-radius laws.
Why this shows up in the exam
Pressure comparison between drops and bubbles · Common films between touching soap bubbles · Bubble pressure at depth in a liquid
Learn the idea
Curved interfaces sustain an excess pressure proportional to surface tension and curvature. A smaller curved surface must bend more sharply, so it needs a larger pressure difference to balance the same interfacial pull. A soap bubble has two pressure-bearing surfaces.
🧠 Memory hook: One spherical surface gives 2T/r; a soap bubble has two.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta P = T(1/R₁ + 1/R₂) — pressure jump across one interface with signed principal radii and uniform surface tension
- Delta P_drop = 2T/r — excess pressure inside a spherical liquid drop or one gas-liquid interface
- Delta P_soap = 4T/r — excess pressure inside a thin spherical soap bubble with two interfaces
How to approach it
- 1Count pressure-bearing interfaces
- 2Add ambient and hydrostatic pressure separately
- 3Use pressure difference between bubbles to determine common-film curvature
Common slip-ups that cost marks
- •Using the soap-bubble factor for an air bubble in liquid
- •Ignoring ambient hydrostatic pressure at depth
- •Assuming larger bubbles have larger excess pressure
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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