Home › Blog › Physics › Surface Tension Guide
Surface Tension & Capillarity in Physics: Formula, Excess Pressure & Drops Guide
Surface Tension is the elastic membrane-like property of a liquid surface that causes it to contract and assume the minimum possible surface area. From rain drops taking perfect spherical shapes to water strider insects walking on water and sap rising up tall forest trees via capillary action, surface tension is a vital topic in fluid mechanics.
This 4,000+ word comprehensive exam guide covers **Molecular Origin of Surface Tension**, **Formula ($T = F/L$)**, **Surface Energy ($W = T \cdot \Delta A$)**, **Cohesive vs Adhesive Forces**, **Angle of Contact ($\theta$)**, **Capillarity & Jurin's Law ($h = \frac{2 T \cos\theta}{\rho g r}$)**, **Excess Pressure in Liquid Drops ($\frac{2T}{r}$) & Soap Bubbles ($\frac{4T}{r}$)**, **Factors Affecting Surface Tension (Temperature, Detergents, Impurities)**, and solved numerical problems for SSC CGL, RRB NTPC, and UPSC Prelims.
Table of Contents
- 1. Molecular Origin & Definition of Surface Tension ($T = F/L$)
- 2. Surface Energy & Work Done in Blowing Bubbles ($W = T \cdot \Delta A$)
- 3. Cohesive vs Adhesive Forces & Meniscus Shape
- 4. Angle of Contact ($\theta$) & Wetting Properties
- 5. Capillarity & Jurin's Law of Capillary Rise ($h = \frac{2T\cos\theta}{\rho g r}$)
- 6. Excess Pressure inside Liquid Drops ($\frac{2T}{r}$) & Soap Bubbles ($\frac{4T}{r}$)
- 7. Factors Affecting Surface Tension (Temperature, Detergents)
- 8. Real-World Phenomena & Everyday Applications
- 9. Solved Numerical Examples for Competitive Exams
- 10. Must Remember Points for Quick Revision
- 11. Frequently Asked Questions (FAQ)
Key Takeaways & Core Highlights
- Surface Tension ($T$): Force per unit length acting along an imaginary line drawn on liquid surface ($T = F/L$). SI Unit: $\text{N/m}$ or $\text{J/m}^2$. Scalar quantity.
- Spherical Drop Rule: Liquids contract to minimize surface area. For a fixed volume, a **sphere** has the minimum surface area, making drops spherical.
- Cohesion vs Adhesion: Cohesion is attraction between like liquid molecules. Adhesion is attraction between liquid and solid container molecules.
- Water in glass: Adhesion $>$ Cohesion $\rightarrow$ **Concave Meniscus** ($\theta < 90^\circ$). Wets glass.
- Mercury in glass: Cohesion $>$ Adhesion $\rightarrow$ **Convex Meniscus** ($\theta > 90^\circ$). Does NOT wet glass.
- Capillary Rise (Jurin's Law): $h = \frac{2 T \cos\theta}{\rho g r}$. Height is inversely proportional to tube radius ($h \propto 1/r$).
- Excess Pressure ($\Delta P$):
- Liquid Drop (1 free surface): $\Delta P = \frac{2 T}{r}$.
- Soap Bubble (2 free surfaces): $\Delta P = \frac{4 T}{r}$.
- Temperature Effect: Surface tension **decreases with temperature rise**, becoming zero at Critical Temperature. Hot soup tastes better because lower surface tension lets it spread wider across tongue taste buds!
1. Molecular Origin & Definition of Surface Tension ($T = F/L$)
Molecules inside a liquid bulk experience equal cohesive forces in all directions. Molecules on the surface layer experience a net downward inward pull toward the bulk, pulling the surface taut like an elastic skin.
$$T = \frac{\text{Force (}F\text{)}}{\text{Length (}L\text{)}} \quad (\text{Unit: N/m})$$2. Surface Energy & Work Done in Blowing Bubbles ($W = T \cdot \Delta A$)
Work done ($W$) in increasing the surface area of a liquid film by $\Delta A$ against surface tension is stored as **Surface Energy**:
$$W = T \cdot \Delta A$$Work Done to Blow a Soap Bubble of Radius $R$:
Because a soap bubble has **2 free surfaces** (inner and outer air-liquid interfaces), total surface area $\Delta A = 2 \times (4\pi R^2) = 8\pi R^2$:
$$W_{\text{soap bubble}} = 8 \pi R^2 \cdot T$$3. Cohesive vs Adhesive Forces & Meniscus Shape
- Water in Glass: Adhesive force between water and glass is stronger than cohesive force between water molecules. Water rises up container walls forming a **Concave Meniscus**.
- Mercury in Glass: Cohesive force between mercury atoms is far stronger than adhesive force with glass. Mercury depresses forming a **Convex Meniscus**.
5. Capillarity & Jurin's Law of Capillary Rise ($h = \frac{2T\cos\theta}{\rho g r}$)
The rise or fall of liquid in a narrow glass tube (capillary) is governed by **Jurin's Law**:
$$h = \frac{2 T \cos\theta}{\rho \cdot g \cdot r}$$Everyday Examples of Capillarity:
- Water and nutrients rising from roots to leaves in tall trees through xylem vessels.
- Kerosene oil rising up the cotton wick of a lantern lamp.
- Blotting paper absorbing ink.
- Ploughing fields breaks soil capillary pores, preserving underground moisture!
6. Excess Pressure inside Liquid Drops ($\frac{2T}{r}$) & Soap Bubbles ($\frac{4T}{r}$)
| Spherical Geometry | Number of Free Surfaces | Excess Pressure Formula ($\Delta P$) |
|---|---|---|
| Liquid Drop (or Air Bubble in Water) | 1 Free Surface | $\Delta P = \frac{2 T}{r}$ |
| Soap Bubble in Air | 2 Free Surfaces (Inside & Outside) | $\Delta P = \frac{4 T}{r}$ |
9. Solved Numerical Examples for Competitive Exams
Numerical Problem 1 (Capillary Rise Calculation):
Question: Water ($T = 0.07\text{ N/m}$, $\theta = 0^\circ$, $\rho = 1000\text{ kg/m}^3$) rises in a capillary tube of radius $r = 0.5\text{ mm}$ ($5 \times 10^{-4}\text{ m}$). Calculate the height of capillary rise ($g = 9.8\text{ m/s}^2$).
Solution:
$$h = \frac{2 T \cos\theta}{\rho g r} = \frac{2 \times 0.07 \times 1}{1000 \times 9.8 \times (5 \times 10^{-4})} = \frac{0.14}{4.9} = 0.02857 \text{ m} \approx 2.86 \text{ cm}$$Answer: Capillary rise height is $2.86\text{ cm}$.
Numerical Problem 2 (Excess Pressure in Soap Bubble):
Question: Calculate the excess pressure inside a soap bubble of radius $2.0\text{ mm}$ ($2 \times 10^{-3}\text{ m}$) if surface tension of soap solution is $T = 0.03\text{ N/m}$.
Solution:
$$\Delta P = \frac{4 T}{r} = \frac{4 \times 0.03}{2 \times 10^{-3}} = \frac{0.12}{0.002} = 60 \text{ Pascals (Pa)}$$Answer: Excess pressure inside the soap bubble is $60\text{ Pa}$.
10. Must Remember Points for Quick Revision
Exam Revision Cheat Sheet:
- Formula: $T = F/L$. SI Unit: $\text{N/m}$ or $\text{J/m}^2$.
- Raindrops: Spherical shape due to minimum surface area condition.
- Water in Glass: Adhesion $>$ Cohesion $\rightarrow$ Concave meniscus.
- Mercury in Glass: Cohesion $>$ Adhesion $\rightarrow$ Convex meniscus.
- Jurin's Law: $h = \frac{2 T \cos\theta}{\rho g r}$. Height $h \propto 1/r$.
- Excess Pressure: Liquid drop $= 2T/r$; Soap bubble $= 4T/r$.
- Hot Soup: Lower surface tension allows wider spreading on tongue!
11. Frequently Asked Questions (FAQ)
Why are liquid droplets and rain drops spherical in shape?
Surface tension causes the surface of a liquid to contract and minimize its surface area. For a given volume, a sphere has the minimum surface area of any 3D geometric shape. Thus, surface tension forces liquid drops to assume spherical shapes.
What is Capillarity and Jurin's Law formula for capillary rise?
Capillarity is the phenomenon of rise or fall of a liquid inside a narrow tube (capillary). Height of capillary rise is given by Jurin's Law: h = (2 T cos θ) / (ρ g r), where T is surface tension, θ is angle of contact, ρ is liquid density, g is gravity, and r is capillary radius.
Why does adding detergent or soap lower the surface tension of water?
Detergents act as surfactants (surface-active agents). Their amphiphilic molecules disrupt the cohesive hydrogen bonds between surface water molecules, reducing surface tension from ~0.073 N/m to ~0.025 N/m, allowing water to penetrate fabric fibers and wash away dirt.
Related Physics & Science Guides
Continue your exam preparation with our comprehensive, deep-dive physics modules:
Master General Science & Physics on RRBCONTENTS
Practice PYQs, read formulas cheat sheets, and explore complete exam study modules.
Solve Physics PYQs → Explore Science Notes →Join our official Telegram channel: @rrbcontents