Notes : Define Surface Energy , Relation Surface Tension and Energy

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Surface Tension , Relation With Surface Tension and Surface Energy, Formula, Derivation, MCQs , FAQs class 11 physics chapter 9 Mechanical Properties of fluids 

Surface Energy

Define surface energy. Write its SI unit and dimensional formula.

We know that the molecules on the liquid surface experience a net downward force. So, to bring a molecule from the interior of the liquid to the free surface, some work is required to be done against the intermolecular force of attraction. This work is stored as the potential energy of the molecule on the surface. The potential energy of surface molecules per unit area of the surface is called surface energy.

$$ \text{Surface Energy}=\frac{\text{Potential Energy}}{\text{Area}} $$

Units of Surface Energy

System of Unit Unit of Surface Energy
CGS erg cm-2
SI J m-2

Dimensional Formula of Surface Energy

Surface energy is defined as:

$$ \text{Surface Energy}=\frac{\text{Potential Energy}}{\text{Area}} $$

The dimensional formula of potential energy is:

$$ [M L^2 T^{-2}] $$

The dimensional formula of area is:

$$ [L^2] $$

Therefore,

$$ [\text{Surface Energy}] = \frac{[M L^2 T^{-2}]}{[L^2]} = [M L^0 T^{-2}] $$

Hence, the dimensional formula of surface energy is:

$$ \boxed{[M L^0 T^{-2}]} $$

Relation Between Surface Tension and Surface Energy

Show that surface tension is numerically equal to the surface energy.

Relation Between Surface Tension and Surface Energy

Consider a rectangular frame of wire (PQRS), whose arm RS can slide on the arms PR and QS. If this frame is dipped in a soap solution, then a soap film is produced in the frame PQRS.

Due to surface tension (T), the soap film exerts a force on the frame towards the interior of the film. Let l be the length of the arm RS. Then the force acting on the arm RS towards the film is given by

$$ F=T\times2l=2Tl $$

Since a soap film has two surfaces, the length is taken twice. The area of the film can be increased by pulling the movable arm RS outwards with force

$$ F=2Tl $$

Let the arm RS be displaced to a new position R'S' through a distance $x$ so that the temperature of the film remains the same.

Therefore, the work done is

$$ W=Fx=2Tlx $$

This work done is equal to the potential energy of the liquid film.

Increase in the surface area of the film is

$$ A=2lx $$

Now,

$$ \text{Surface Energy} = \frac{\text{Potential Energy}}{\text{Area}}$$

$$S = \frac{2Tlx}{2lx} = T $$

Thus, surface tension is numerically equal to surface energy.

Frequently Asked Questions (FAQs)

Q1. What is surface energy?

Surface energy is the potential energy of surface molecules per unit area of the liquid surface.

Q2. What is the SI unit of surface energy?

The SI unit of surface energy is J m-2.

Q3. What is the CGS unit of surface energy?

The CGS unit of surface energy is erg cm-2.

Q4. What is the dimensional formula of surface energy?

The dimensional formula of surface energy is [ML0T-2].

Q5. Why does a soap film have two surfaces?

A soap film is exposed to air on both sides; therefore, it has two free surfaces.

Q6. Why is the force on the movable wire equal to 2Tl?

Each surface of the soap film exerts a force of Tl. Since there are two surfaces, the total force becomes 2Tl.

Q7. What is the relation between surface tension and surface energy?

Surface tension is numerically equal to surface energy per unit area.

Multiple Choice Questions (MCQs)

1. Surface energy is

  1. Force per unit length
  2. Potential energy per unit area
  3. Pressure per unit area
  4. Energy per unit volume

Answer: B. Potential energy per unit area

2. The SI unit of surface energy is

  1. N
  2. J
  3. J m-2
  4. N m

Answer: C. J m-2

3. The force acting on the movable wire of a soap film is

  1. Tl
  2. 2Tl
  3. T/2
  4. l/T

Answer: B. 2Tl

4. The work done in stretching the soap film is

  1. Tx
  2. 2Tlx
  3. Tlx
  4. 2Tx

Answer: B. 2Tlx

5. Surface tension is numerically equal to

  1. Pressure
  2. Density
  3. Surface energy
  4. Volume

Answer: C. Surface energy

True or False

1. Surface energy is the potential energy per unit area of the liquid surface. True

2. The SI unit of surface energy is N/m. False

3. A soap film has two free surfaces. True

4. Surface tension is numerically equal to surface energy. True

5. The force acting on the movable wire is Tl. False

Fill in the Blanks

1. Surface energy is the __________ energy per unit area of a liquid surface.

Answer: Potential

2. The SI unit of surface energy is __________.

Answer: J m-2

3. The force acting on the movable wire is __________.

Answer: 2Tl

4. The increase in surface area of the soap film is __________.

Answer: 2lx

5. Surface tension is numerically equal to __________.

Answer: Surface energy

Very Short Answer Questions

Q1. Define surface energy.

Answer: Surface energy is the potential energy of surface molecules per unit area of the liquid surface.

Q2. Write the SI unit of surface energy.

Answer: J m-2.

Q3. Write the dimensional formula of surface energy.

Answer: [ML0T-2].

Q4. Why does a soap film have two surfaces?

Answer: Because it is exposed to air on both sides.

Q5. State the relation between surface tension and surface energy.

Answer: Surface tension is numerically equal to surface energy.

Short Answer Questions

Q1. Explain surface energy.

Answer: Surface molecules have higher potential energy because they experience an unbalanced inward force. The potential energy per unit area of the surface is called surface energy.

Q2. Why is the force on the movable wire equal to 2Tl?

Answer: A soap film has two free surfaces. Each surface exerts a force of Tl, so the total force is 2Tl.

Q3. Derive the expression for work done in stretching a soap film.

Answer:

$$F=2Tl$$

$$W=Fx=2Tlx$$

Long Answer Questions

Q1. Define surface energy. Write its SI unit and dimensional formula. Derive the relation between surface tension and surface energy.

Answer:

Surface energy is the potential energy of surface molecules per unit area of the liquid surface.

SI Unit: J m-2

Dimensional Formula: [ML0T-2]

For a soap film,

$$F=2Tl$$

$$W=Fx=2Tlx$$

$$A=2lx$$

$$ \text{Surface Energy} = \frac{W}{A} = \frac{2Tlx}{2lx} = T $$

Hence, surface tension is numerically equal to surface energy.

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