Surface Tension 💧
Have you noticed how water beads up on a waxy leaf 🌿 while oil spreads across a pan? This magic comes from surface tension, the tendency of a liquid’s surface to behave like a stretched elastic skin.:contentReference[oaicite:0]{index=0}
1. Why does a liquid have surface tension?
Inside the liquid, every molecule feels friendly pulls from all directions. A molecule at the surface gets fewer “hugs,” giving it extra energy. The liquid shrinks its surface to save that energy, creating surface tension.:contentReference[oaicite:1]{index=1}
2. Surface energy and the definition of S
Slide a light bar of length l and stretch a soap film by a tiny distance d. You add area 2 l d (two sides!). The work done \(F\,d\) becomes surface energy, letting us define:
\( S = \dfrac{F}{2l} \) (N m–1)
So S is both energy per unit area and force per unit length acting along the interface.:contentReference[oaicite:2]{index=2}
3. Measuring S (simple balance experiment) ⚖️
Hang a glass plate from a balance so its lower edge just touches the liquid. Add extra mass m until the plate lifts free. Then
\( S_{la} = \dfrac{m g}{2 l} \).:contentReference[oaicite:3]{index=3}
4. Angle of contact θ and wetting
- Young’s equation: \( S_{la}\cos\theta + S_{sl} = S_{sa} \).:contentReference[oaicite:4]{index=4}
- Acute θ (e.g., water on clean glass) → liquid spreads.
- Obtuse θ (e.g., mercury on glass) → liquid forms rounded drops and doesn’t wet.
- Detergents lower θ so water sneaks into fabrics 🧼.
5. Drops & bubbles: pressure inside
- Spherical drop (one surface): \( P_i – P_o = \dfrac{2S}{r} \).:contentReference[oaicite:5]{index=5}
- Soap bubble (two surfaces): \( P_i – P_o = \dfrac{4S}{r} \).:contentReference[oaicite:6]{index=6}
That’s why you blow a bit harder to start a bubble but keep it gentle afterward 🎈.
6. Capillary rise 🌱
In a thin tube of radius a, water climbs to height h because the surface-tension pull balances the weight of the column:
\( h = \dfrac{2 S \cos\theta}{\rho g a} \).:contentReference[oaicite:7]{index=7}
Smaller tube → greater rise. For \(a = 0.05\;{\rm cm}\), water rises about 3 cm.:contentReference[oaicite:8]{index=8}
7. Temperature effect 🔥
Surface tension drops as the liquid warms. Typical 20 °C values:
- Water: 0.0727 N m–1
- Ethanol: 0.0227 N m–1
- Mercury: 0.4355 N m–1 (huge!)
Heating makes molecules jiggle more, weakening the “surface skin.”:contentReference[oaicite:9]{index=9}
8. Quick look at viscosity & Stokes’ law (bonus!) 🏊♂️
Viscosity \(\eta\) measures a fluid’s “thickness.” For a slow-moving sphere of radius a in a fluid, the viscous drag is
\( F = 6 \pi \eta a v \). (Stokes’ law):contentReference[oaicite:10]{index=10}
Terminal speed becomes \( v_t = \dfrac{2 a^{2} (\rho – \sigma) g}{9 \eta} \). Honey (high η) slows spheres down, while air (tiny η) lets hailstones drop fast.
High-Yield Ideas for NEET 🏆
- Definition of surface tension as force per unit length and energy per unit area.
- Pressure difference inside drops \(\left( \dfrac{2S}{r} \right)\) and bubbles \(\left( \dfrac{4S}{r} \right)\).
- Capillary rise formula \( h = \dfrac{2 S \cos\theta}{\rho g a} \) and its dependence on tube radius.
- Angle of contact, wetting vs non-wetting, and the role of detergents.
- Temperature dependence of surface tension and typical values (water, ethanol, mercury).
Keep exploring—you’ll see surface tension everywhere, from dew drops on spider webs to the way insects walk on water 🌊🐜!
