Class 11 Physics Notes Chapter 7 (Chapter 7) – Lab Manual (English) Book

Detailed Notes with MCQs of Chapter 7 from your Physics Lab Manual, which deals with Surface Tension. This is an important topic, not just for your practical exams but also for various competitive government exams where fundamental physics concepts are tested.

We'll cover the key experiment associated with this chapter: To determine the surface tension of water by capillary rise method.

1. Aim:
To determine the surface tension (T) of water at room temperature using the capillary rise method.

2. Apparatus Required:

• A capillary tube of uniform bore
• A travelling microscope
• Beaker with clean water
• Adjustable height stand
• Clamp and boss head
• Plumb line
• Thermometer
• Reading lens (optional)
• Piece of paper with a fine tip (pointer) attached to the capillary tube

3. Underlying Theory:

• Surface Tension (T): It is the property of a liquid by virtue of which its free surface behaves like a stretched elastic membrane, tending to contract to occupy the minimum possible surface area. It is defined as the tangential force acting per unit length on an imaginary line drawn on the free surface of the liquid.
  • Formula: T = F/L
  • Units: N/m (SI), dyne/cm (CGS)
  • Dimensions: [ML⁰T⁻²]
• Cohesive Force: The force of attraction between molecules of the same substance (e.g., between water molecules).
• Adhesive Force: The force of attraction between molecules of different substances (e.g., between water and glass molecules).
• Angle of Contact (θ): The angle inside the liquid between the tangent to the liquid surface at the point of contact and the solid surface.
  • For pure water and clean glass, θ is acute (≈ 0° to 8°). Adhesive forces > Cohesive forces. Liquid wets the surface.
  • For mercury and glass, θ is obtuse (> 90°). Cohesive forces > Adhesive forces. Liquid does not wet the surface.
• Capillarity: The phenomenon of rise or fall of a liquid in a narrow tube (capillary tube) compared to the surrounding level.
  • Rise: Occurs when adhesive forces are stronger than cohesive forces (e.g., water in glass). The meniscus is concave.
  • Fall: Occurs when cohesive forces are stronger than adhesive forces (e.g., mercury in glass). The meniscus is convex.
• Derivation for Capillary Rise:
  When a liquid rises in a capillary tube of radius 'r' to a height 'h', the upward force due to surface tension acting along the circumference of contact balances the weight of the liquid column raised.
  • Total upward force = Component of surface tension force acting vertically upwards = (T × 2πr) cosθ
  • Weight of the liquid column raised (W) = Volume × Density × g = (πr²h) × ρ × g
  • (Ignoring the small volume of liquid in the meniscus for simplicity, or considering 'h' as the height to the bottom of the meniscus and adding a correction r/3 if needed for high accuracy, but usually πr²hρg is sufficient for this level).
  • At equilibrium: Upward Force = Weight
    (T × 2πr) cosθ = πr²hρg
  • Therefore, Surface Tension, T = (rhρg) / (2cosθ)
  • For water and clean glass, θ ≈ 0°, so cosθ ≈ 1. The formula simplifies to T = rhρg / 2

4. Procedure Highlights & Key Measurements:

• Cleaning: The capillary tube and beaker must be thoroughly cleaned (using acid, then alkali, then distilled water) to ensure the correct angle of contact.
• Setup: The capillary tube is clamped vertically. The beaker with water is placed below it, and the stand is adjusted so the tube dips into the water.
• Measuring Height (h):
  • A pointer is attached to the capillary tube such that its tip just touches the water surface in the beaker.
  • A travelling microscope is focused on the lower meniscus of the water column inside the capillary tube. The reading is noted (R₁).
  • The microscope is lowered and focused on the tip of the pointer. The reading is noted (R₂).
  • The height of the capillary rise, h = |R₁ - R₂|.
• Measuring Radius (r):
  • The capillary tube is placed horizontally on the stand.
  • The travelling microscope is focused on the internal bore of the tube.
  • Measure the horizontal diameter (d₁) and vertical diameter (d₂) of the bore using the microscope's vernier scale.
  • Mean diameter, d = (d₁ + d₂)/2.
  • Mean radius, r = d/2. (Measurements should be taken at the end that was dipped in water).
• Measuring Density (ρ): The density of water at the measured room temperature is noted from standard tables.
• Value of 'g': Acceleration due to gravity at the location is used (usually 9.8 m/s²).

5. Calculations:
Use the formula T = rhρg / 2 (assuming cosθ ≈ 1 for water). Ensure all values are in a consistent system of units (preferably SI).

6. Precautions:

• The capillary tube must be clean and dry internally.
• The capillary tube must be held perfectly vertical.
• The water should be free from grease or impurities.
• Temperature should remain constant during the experiment.
• Parallax error should be avoided while taking readings with the travelling microscope.
• The radius 'r' should be measured accurately at the end dipped in water, viewing the bore perpendicularly.
• The microscope should be focused correctly on the meniscus and the pointer tip.

7. Sources of Error:

• Non-uniform bore of the capillary tube.
• Capillary tube not vertical.
• Impurities in water or contamination of the glass surface affecting surface tension and angle of contact.
• Errors in measuring 'h' and 'r' using the travelling microscope (least count error, parallax error).
• Temperature fluctuations.

8. Factors Affecting Surface Tension:

• Temperature: Surface tension generally decreases with an increase in temperature. At the boiling point, surface tension becomes zero.
• Impurities:
  • Soluble impurities (like salt in water) increase surface tension.
  • Sparingly soluble impurities (like detergent or soap in water) decrease surface tension significantly.

Key Takeaways for Exams:

• Know the definition, units, and dimensions of surface tension.
• Understand cohesive vs. adhesive forces and their role in determining the angle of contact and meniscus shape.
• Understand the principle of capillary rise/fall.
• Memorize the formula T = rhρg / (2cosθ) and its simplified form T = rhρg / 2 for water.
• Be aware of how 'h' and 'r' are measured experimentally.
• Know the crucial precautions and sources of error.
• Remember how temperature and impurities affect surface tension.

Multiple Choice Questions (MCQs):

1. The SI unit of surface tension is:
   a) N/m²
   b) J/m
   c) N/m
   d) J/m²

2. When a capillary tube is dipped in water, the water rises because:
   a) Cohesive forces are greater than adhesive forces.
   b) Adhesive forces are greater than cohesive forces.
   c) Surface tension forces are negligible.
   d) The density of water is low.

3. The angle of contact for pure water and clean glass is approximately:
   a) 90°
   b) 135°
   c) 180°
   d) 0°

4. If the radius of a capillary tube is doubled, the height to which a liquid rises will become (assuming other factors remain constant):
   a) Double
   b) Half
   c) Four times
   d) One-fourth

5. What happens to the surface tension of water when detergent is added to it?
   a) Increases
   b) Decreases
   c) Remains unchanged
   d) Becomes zero instantly

6. The dimensional formula for surface tension is:
   a) [MLT⁻²]
   b) [ML⁰T⁻²]
   c) [ML⁻¹T⁻²]
   d) [M⁰L¹T⁻²]

7. In the capillary rise experiment, the radius 'r' of the capillary tube is measured using:
   a) A screw gauge
   b) A vernier caliper
   c) A travelling microscope
   d) A spherometer

8. Surface tension of a liquid generally ______ with increase in temperature.
   a) Increases
   b) Decreases
   c) Remains constant
   d) First increases then decreases

9. The shape of the meniscus of mercury in a glass capillary tube is:
   a) Concave
   b) Convex
   c) Plane
   d) Cylindrical

10. For the accurate determination of surface tension by capillary rise, which precaution is crucial?
    a) Using a wide bore tube
    b) Ensuring the liquid is coloured
    c) Keeping the capillary tube perfectly vertical
    d) Conducting the experiment at boiling point

Answer Key for MCQs:

1. c) N/m
2. b) Adhesive forces are greater than cohesive forces.
3. d) 0° (or very small acute angle)
4. b) Half (Since h ∝ 1/r from T = rhρg/2)
5. b) Decreases
6. b) [ML⁰T⁻²]
7. c) A travelling microscope
8. b) Decreases
9. b) Convex
10. c) Keeping the capillary tube perfectly vertical

Study these notes thoroughly. Understanding the concepts behind the experiment is key to tackling questions in competitive exams. Let me know if you have any specific doubts!