Notes : Define Surface Tension and Molecular Theory - Definition Formula Units Dimensions

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Surface Tension and Molecular Theory class 11 physics chapter 9 Mechanical Properties of fluids Notes with definition, formula, units, dimensional formula, sphere of influence, FAQs, MCQs, true/false, fill in the blanks, very short, short & long question answers based on NCERT - Physicskund 

Surface Tension

Surface Tension

Definition:
Surface tension is the property of a liquid at rest by virtue of which its free surface tends to occupy the minimum possible surface area and behaves like a stretched elastic membrane.

Mathematical Definition

Surface tension is defined as the force acting per unit length on either side of an imaginary line drawn tangentially on the free surface of a liquid. The force acts normal (perpendicular) to the imaginary line.

$$ T=\frac{F}{l} $$

Where,

  • T = Surface tension
  • F = Force acting on either side of the imaginary line
  • l = Length of the imaginary line

Units of Surface Tension

System Unit
SI N m-1
CGS dyne cm-1

Dimensional Formula

$$ T=\frac{F}{l} $$  

$$ [F]=[MLT^{-2}] $$ 

$$ [T]=\frac{[MLT^{-2}]}{[L]}$$

$$[T]=[ML^{0}T^{-2}] $$

Nature

Surface tension is a Scalar Quantity.

Molecular Theory of Surface Tension

Molecular Theory of Surface Tension

The molecular theory explains surface tension on the basis of cohesive forces acting between liquid molecules.

The liquid enclosed between the free surface (AB) and an imaginary plane (CD), at a distance equal to the molecular range, forms a liquid film.

Sphere of Influence

The sphere of influence of a molecule is an imaginary sphere around it whose radius is equal to the molecular range.

Behaviour of Molecules

Molecule P (Inside the Liquid)

  • Located well inside the liquid.
  • Attracted equally in all directions.
  • Resultant force is zero.
  • Moves freely inside the liquid.

Molecule Q (Just Below the Surface)

  • Located just below the free surface.
  • Sphere of influence remains completely inside the liquid.
  • Attracted equally in all directions.
  • Resultant force is zero.

Molecule R (Inside the Liquid Film)

  • Part of its sphere of influence lies outside the liquid.
  • Number of molecules above is less than below.
  • Downward attraction is greater than upward attraction.
  • Experiences a net downward force.

Molecule S (On the Free Surface)

  • Located exactly on the free surface.
  • Upper half of its sphere of influence contains no liquid molecules.
  • Experiences the maximum downward force.

Conclusion

  • Interior molecules experience zero resultant force.
  • Surface molecules experience a net downward cohesive force.
  • The liquid surface behaves like a stretched elastic membrane.
  • Surface molecules possess higher potential energy.
  • The liquid always tends to occupy the minimum possible surface area.

Why Does a Liquid Occupy Minimum Surface Area?

When the surface area increases, molecules from the interior move towards the free surface. Work has to be done against the cohesive force, which is stored as potential energy. Therefore, surface molecules possess greater potential energy than interior molecules. Since every system tends to attain minimum potential energy, the liquid contracts its surface and occupies the minimum possible surface area.

Important Points

  • Surface tension is due to cohesive force.
  • Interior molecules experience zero resultant force.
  • Surface molecules experience an unbalanced downward force.
  • Surface molecules have higher potential energy.
  • Liquid surface behaves like a stretched elastic membrane.
  • Surface tension is a scalar quantity.
  • SI Unit = N m-1.
  • Dimensional Formula = $$[ML^{0}T^{-2}]$$

Frequently Asked Questions (FAQs)

Q1. What is surface tension?
Surface tension is the property of a liquid by virtue of which its free surface tends to occupy the minimum possible surface area and behaves like a stretched elastic membrane.

Q2. What causes surface tension?
Surface tension is caused by cohesive intermolecular forces.

Q3. What is the SI unit of surface tension?
N m-1.

Q4. What is the dimensional formula of surface tension?
$$[ML^{0}T^{-2}]$$

Q5. Why do liquids occupy minimum surface area?
To attain minimum potential energy.

Multiple Choice Questions (MCQs)

  1. Surface tension is measured in
    • A. Pascal
    • B. Joule
    • C. Newton per metre ✓
    • D. Watt
  2. Surface tension is due to
    • A. Adhesive force
    • B. Cohesive force ✓
    • C. Magnetic force
    • D. Gravitational force
  3. Surface tension is a
    • A. Vector
    • B. Scalar ✓
    • C. Tensor
    • D. None of these
  4. Surface molecules possess
    • A. Lower potential energy
    • B. Higher potential energy ✓
    • C. Zero potential energy
    • D. Equal potential energy
  5. Interior molecules experience
    • A. Zero resultant force ✓
    • B. Maximum upward force
    • C. Maximum downward force
    • D. Magnetic force

True / False

  1. Surface tension is a vector quantity. False
  2. Surface molecules have higher potential energy than interior molecules. True
  3. Interior molecules experience zero resultant force. True
  4. Surface tension is caused by cohesive force. True
  5. Liquids always tend to occupy minimum surface area. True

Fill in the Blanks

  1. Surface tension is caused by __________ force.
    Answer: Cohesive
  2. The SI unit of surface tension is __________.
    Answer: N m-1
  3. Surface molecules possess __________ potential energy than interior molecules.
    Answer: Higher
  4. Surface tension is a __________ quantity.
    Answer: Scalar
  5. Liquids always try to occupy __________ surface area.
    Answer: Minimum

Very Short Answer Questions (1 Mark)

Q1. Define surface tension.
Surface tension is the force acting per unit length along the free surface of a liquid.

Q2. Write the SI unit of surface tension.
N m-1.

Q3. Write the dimensional formula of surface tension.
$$[ML^{0}T^{-2}]$$

Q4. Is surface tension a scalar or vector quantity?
Surface tension is a scalar quantity.

Q5. What is the sphere of influence?
The imaginary sphere around a molecule whose radius is equal to the molecular range.

Short Answer Questions (2–3 Marks)

Q1. Why do interior molecules experience zero resultant force?
Interior molecules are surrounded by neighbouring molecules in all directions. Therefore, the cohesive forces balance each other and the resultant force becomes zero.

Q2. Why do surface molecules have higher potential energy?
Work is required to bring molecules from the interior to the free surface against cohesive forces. Hence, surface molecules possess higher potential energy.

Q3. Why does the liquid surface behave like a stretched elastic membrane?
Surface molecules experience an unbalanced inward cohesive force, causing the surface to contract and behave like a stretched elastic membrane.

Long Answer Questions (5 Marks)

Q1. Explain the molecular theory of surface tension.

  • Surface tension arises due to cohesive intermolecular forces.
  • Interior molecules are attracted equally in all directions.
  • Surface molecules experience an unbalanced inward force.
  • Surface molecules possess higher potential energy.
  • The liquid tends to reduce its surface area to attain minimum potential energy.
  • Hence, the free surface behaves like a stretched elastic membrane.

Q2. Define surface tension and derive its dimensional formula.

Surface tension is defined as force acting per unit length on the free surface of a liquid.

$$ T=\frac{F}{l} $$ $$ [F]=[MLT^{-2}] $$ $$ [T]=\frac{[MLT^{-2}]}{[L]} =[ML^{0}T^{-2}] $$

Therefore, the dimensional formula of surface tension is

$$ [ML^{0}T^{-2}] $$

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