Measuring Water Surface Tension: Capillary Rise Method

Learn to determine the surface tension of water using the capillary tube method with Jurin's Law, force derivations, and laboratory procedures.

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Determination of Surface Tension of Water

Capillary Rise Method | Undergraduate Physics Laboratory

clean scientific close-up photography of water in a glass capillary tube forming a meniscus, laboratory lighting, high definition, blue and white tones

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Theory: What is Surface Tension?

Surface tension (T) is a property of liquid surfaces that allows them to resist an external force. It arises due to the cohesive nature of liquid molecules.

Key Concepts:
• Cohesion: Attraction between like molecules (water-water).
• Adhesion: Attraction between unlike molecules (water-glass).
• In a capillary tube, adhesion > cohesion, causing the water to rise and form a concave meniscus.

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Apparatus Required

Capillary Tubes: Fine uniform bore glass tubes.
Traveling Microscope: For precise height measurement (0.001 cm precision).
Adjustable Stand: To hold the capillary tube vertical.
Beaker & Pointer: Clean glass beaker and an index pin.
Thermometer: To record experimental temperature.
Cleaning Agents: Chromic acid or Nitric acid, distilled water.

physics laboratory travel microscope setup with capillary tube and beaker

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Theory: Jurin's Law

T = (r h ρ g) / (2 cosθ)

Where:
T = Surface Tension (N/m)
h = Height of liquid rise (m)
r = Radius of capillary bore (m)
ρ = Density of liquid (kg/m³)
g = Acceleration due to gravity (9.8 m/s²)
θ = Angle of contact

Assumption: For a clean glass-water interface, the angle of contact θ is extremely small (≈ 0). Thus, cosθ ≈ 1.

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Force Balance Derivation

1. Upward Force due to Surface Tension:
Surface tension T acts tangentially to the meniscus along the circumference (2πr). The vertical component upward is:

F_up = (T cosθ) × (Circumference)
F_up = 2πr T cosθ

2. Downward Force (Weight of Column):
The weight of the liquid column of height h is mass × gravity. Mass = Volume × Density.

Volume = πr²h
W = πr²h ρ g

At Equilibrium: F_up = W
2πr T cosθ = πr²h ρ g

Solving for T:
T = (r h ρ g) / 2 cosθ

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Diagram: Forces & Geometry

diagram of capillary rise, showing forces, angle of contact theta, meniscus curvature, height h, and radius r, scientific textbook style, white background

• θ: Contact angle
• h: Height of rise
• T: Surface Tension vector
• mg: Weight vector

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Procedure: Setup & Cleaning

1. Clean the Capillary: Wash the capillary tube with chromic acid or nitric acid to remove grease, then rinse thoroughly with distilled water. Caution: Grease alters the contact angle.

2. Clamp Vertically: Clamp the capillary tube on the adjustable stand. Ensure it is perfectly vertical using a plumb line if available.

3. Liquid Setup: Fill a beaker with distilled water. Place it on the stand such that the capillary tube dips into the water. Adjust a pointed index pin (pointer) so its tip just touches the water surface outside the tube.

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Procedure: Measurement

Focus Telescope: Focus the traveling microscope on the meniscus of the water in the capillary tube. Align the horizontal cross-wire ensuring it is tangent to the meniscus curve. Record Reading (A).
Focus on Pointer: Lower the microscope to focus on the tip of the pointer touching the water surface. Record Reading (B).
Calculate h: Rise in capillary, h = Reading A - Reading B.
Find Radius (r): Cut the tube at the meniscus level (or use method to focus on edges). Measure internal diameter in two perpendicular directions using the microscope cross-wires. Calculate mean radius.

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Precautions & Sources of Error

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Cleanliness is Crucial: Presence of oil or grease drastically changes the surface tension.
Vertical Alignment: The capillary tube must be perfectly vertical to ensure a uniform meniscus.
No Air Bubbles: Ensure the liquid column contains no air bubbles.
Parallax Error: Avoid parallax when reading the microscope scale.
Temperature Stability: Surface tension decreases with temperature; minimize fluctuations during the experiment.

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Observations & Calculation

S.No	Microscope Reading Meniscus (cm)	Microscope Reading Pointer (cm)	Height h = Difference (cm)	Radius r (cm)	Surface Tension T (dynes/cm or N/m)
1	...	...	...	...	...
2	...	...	...	...	...
3	...	...	...	...	...

Calculate Mean T:
1. Compute T for each trial using T = (rhρg)/2.
2. Take the average of calculated T values.
3. Ensure units are consistent (CGS: dynes/cm, SI: N/m).

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Conclusion

The surface tension of water at room temperature was determined to be approximately 72.8 mN/m (at 20°C).

The experiment validates that measurement precision (especially of the hair-thin capillary bore radius) is critical for accurate results.

Height (h) is inversely proportional to radius (r).

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Measuring Water Surface Tension: Capillary Rise Method

Learn to determine the surface tension of water using the capillary tube method with Jurin's Law, force derivations, and laboratory procedures.

Determination of Surface Tension of Water

Capillary Rise Method | Undergraduate Physics Laboratory

Theory: What is Surface Tension?

Surface tension (T) is a property of liquid surfaces that allows them to resist an external force. It arises due to the cohesive nature of liquid molecules. Key Concepts: • Cohesion: Attraction between like molecules (water-water). • Adhesion: Attraction between unlike molecules (water-glass). • In a capillary tube, adhesion > cohesion, causing the water to rise and form a concave meniscus.

Apparatus Required

<ul><li>Capillary Tubes: Fine uniform bore glass tubes.</li><li>Traveling Microscope: For precise height measurement (0.001 cm precision).</li><li>Adjustable Stand: To hold the capillary tube vertical.</li><li>Beaker & Pointer: Clean glass beaker and an index pin.</li><li>Thermometer: To record experimental temperature.</li><li>Cleaning Agents: Chromic acid or Nitric acid, distilled water.</li></ul>

Theory: Jurin's Law

T = (r h ρ g) / (2 cosθ)

<div>Where: T = Surface Tension (N/m) h = Height of liquid rise (m) r = Radius of capillary bore (m) ρ = Density of liquid (kg/m3) g = Acceleration due to gravity (9.8 m/s2) θ = Angle of contact</div> <div style='background:#e1f5fe; padding:15px; border-radius:5px;'>Assumption: For a clean glass-water interface, the angle of contact θ is extremely small (≈ 0). Thus, cosθ ≈ 1.</div>

Force Balance Derivation

1. Upward Force due to Surface Tension: Surface tension T acts tangentially to the meniscus along the circumference (2πr). The vertical component upward is: Fup = (T cosθ) × (Circumference) Fup = 2πr T cosθ

2. Downward Force (Weight of Column): The weight of the liquid column of height h is mass × gravity. Mass = Volume × Density. Volume = πr2h W = πr2h ρ g

At Equilibrium: Fup = W 2πr T cosθ = πr2h ρ g Solving for T: T = (r h ρ g) / 2 cosθ

Diagram: Forces & Geometry

• θ: Contact angle • h: Height of rise • T: Surface Tension vector • mg: Weight vector

Procedure: Setup & Cleaning

1. Clean the Capillary: Wash the capillary tube with chromic acid or nitric acid to remove grease, then rinse thoroughly with distilled water. Caution: Grease alters the contact angle.

2. Clamp Vertically: Clamp the capillary tube on the adjustable stand. Ensure it is perfectly vertical using a plumb line if available.

3. Liquid Setup: Fill a beaker with distilled water. Place it on the stand such that the capillary tube dips into the water. Adjust a pointed index pin (pointer) so its tip just touches the water surface outside the tube.

Procedure: Measurement

<ol><li>Focus Telescope: Focus the traveling microscope on the meniscus of the water in the capillary tube. Align the horizontal cross-wire ensuring it is tangent to the meniscus curve. Record Reading (A).</li><li>Focus on Pointer: Lower the microscope to focus on the tip of the pointer touching the water surface. Record Reading (B).</li><li>Calculate h: Rise in capillary, h = Reading A - Reading B.</li><li>Find Radius (r): Cut the tube at the meniscus level (or use method to focus on edges). Measure internal diameter in two perpendicular directions using the microscope cross-wires. Calculate mean radius.</li></ol>

Precautions & Sources of Error

<ul><li>Cleanliness is Crucial: Presence of oil or grease drastically changes the surface tension.</li><li>Vertical Alignment: The capillary tube must be perfectly vertical to ensure a uniform meniscus.</li><li>No Air Bubbles: Ensure the liquid column contains no air bubbles.</li><li>Parallax Error: Avoid parallax when reading the microscope scale.</li><li>Temperature Stability: Surface tension decreases with temperature; minimize fluctuations during the experiment.</li></ul>

Observations & Calculation

<table style='width:100%; border-collapse:collapse; font-size:22px; text-align:center;'><thead><tr style='background:#0277bd; color:white;'><th style='padding:15px; border:1px solid #ccc;'>S.No</th><th style='padding:15px; border:1px solid #ccc;'>Microscope Reading Meniscus (cm)</th><th style='padding:15px; border:1px solid #ccc;'>Microscope Reading Pointer (cm)</th><th style='padding:15px; border:1px solid #ccc;'>Height h = Difference (cm)</th><th style='padding:15px; border:1px solid #ccc;'>Radius r (cm)</th><th style='padding:15px; border:1px solid #ccc;'>Surface Tension T (dynes/cm or N/m)</th></tr></thead><tbody><tr><td style='padding:15px; border:1px solid #ccc;'>1</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td></tr><tr><td style='padding:15px; border:1px solid #ccc;'>2</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td></tr><tr><td style='padding:15px; border:1px solid #ccc;'>3</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td><td style='padding:15px; border:1px solid #ccc;'>...</td></tr></tbody></table>

Calculate Mean T: 1. Compute T for each trial using T = (rhρg)/2. 2. Take the average of calculated T values. 3. Ensure units are consistent (CGS: dynes/cm, SI: N/m).

Conclusion

The surface tension of water at room temperature was determined to be approximately 72.8 mN/m (at 20°C). The experiment validates that measurement precision (especially of the hair-thin capillary bore radius) is critical for accurate results.

Height (h) is inversely proportional to radius (r).

physics-experiment
surface-tension
capillary-rise
fluid-mechanics
undergraduate-physics
jurin-law
laboratory-guide

Determination of Surface Tension of Water

Capillary Rise Method | Undergraduate Physics Laboratory

Theory: What is Surface Tension?

Apparatus Required

Theory: Jurin's Law

Force Balance Derivation

Diagram: Forces & Geometry

Procedure: Setup & Cleaning

Procedure: Measurement

Precautions & Sources of Error

Observations & Calculation

Conclusion

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Measuring Water Surface Tension: Capillary Rise Method

DESIGNER-MADE
PRESENTATION,
GENERATED FROM
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