Physics and Mathematics
Surface Energy
1. Concept Overview
When a liquid surface is formed, work must be done against molecular forces to bring molecules from the interior to the surface. This work done gets stored as surface energy.
Thus, surface energy is the potential energy stored in the surface of a liquid due to intermolecular forces.
It is directly proportional to the surface area of the liquid.
2. Explanation and Mathematical Derivation
Let:
- Surface tension of the liquid = [T]
- Increase in surface area = [ΔA]
- Work done to increase surface area = [W]
Then,
[
W = T \ ΔA
]
This work done is stored as surface energy (E).
Hence,
[
E = T \ A
]
where
[E] = Surface energy
[T] = Surface tension (N/m)
[A] = Surface area (m²)
👉 Therefore, surface energy per unit area = surface tension.
3. Dimensions and Units
| Quantity | Symbol | SI Unit | Dimensions |
|---|---|---|---|
| Surface Energy | [E] | Joule (J) | [M¹L⁰T⁻²] |
| Surface Tension | [T] | N/m or J/m² | [M¹T⁻²] |
4. Key Features
- Surface energy and surface tension have the same dimensional formula.
- Increasing the surface area requires external work, which raises potential energy.
- Liquids tend to minimize their surface area (hence form spherical drops).
- If a soap film doubles its surface area, work is done against cohesive forces.
5. Important Formulas to Remember
| Concept | Formula | Description |
|---|---|---|
| Surface Energy | [E = T \ A] | Total energy stored in surface |
| Energy per unit area | [E/A = T] | Defines surface tension |
| Work done for ΔA increase | [W = T \ ΔA] | Energy required to stretch surface |
6. Conceptual Questions with Solutions
1. What causes surface energy in a liquid?
Molecules at the surface experience an unbalanced inward force due to fewer neighboring molecules, leading to potential energy called surface energy.
2. Is surface energy a type of potential or kinetic energy?
It is a form of potential energy, stored due to molecular attraction forces.
3. What happens to surface energy when the surface area increases?
It increases, since more molecules are brought to the surface and energy must be supplied.
4. What is the relation between surface energy and surface tension?
They are numerically equal for a given surface: [E/A = T].
5. What is the unit of surface energy?
Joule (J), since it represents work done or energy stored.
6. Why does a drop of liquid assume spherical shape?
To minimize surface area and hence minimize surface energy.
7. If surface area doubles, how does surface energy change?
It also doubles because [E = T × A].
8. Does temperature affect surface energy?
Yes, surface energy decreases with increase in temperature, as surface tension reduces.
9. Is surface energy scalar or vector?
Scalar, since it represents stored potential energy.
10. What happens to surface energy if a soap film is stretched?
Work is done against cohesive forces, increasing surface energy.
11. Can a liquid have zero surface energy?
No, because molecular forces always exist at the surface.
12. What is the physical significance of surface energy per unit area?
It represents the energy required to create unit area of surface.
13. Is surface energy related to adhesive forces?
Yes, surface energy depends on cohesive and adhesive forces between molecules.
14. What happens if we add detergent to water?
Surface tension decreases, thus surface energy also decreases.
15. Why does heating reduce surface energy?
Because molecular cohesion weakens with temperature, reducing surface tension.
7. FAQ / Common Misconceptions
1. Does surface energy depend on the volume of liquid?
No, it depends only on surface area and surface tension.
2. Are surface energy and surface tension different quantities?
Conceptually yes (energy vs. force per length), but numerically they are equivalent.
3. Is surface tension always positive?
Yes, because energy must be supplied to increase surface area.
4. Can surface energy be negative?
No, since it represents energy required to form a surface.
5. Do solids have surface energy?
Yes, though surface tension is mainly discussed for liquids, solids also possess surface energy.
6. Is surface energy a measurable quantity?
Yes, it can be calculated from measurable surface tension and area.
7. Does surface energy affect evaporation?
Yes, lower surface energy means molecules can escape more easily.
8. Is surface energy the same for all liquids?
No, it varies with molecular structure and temperature.
9. Why do oily liquids have low surface energy?
Because cohesive forces among molecules are weaker.
10. Can we have surface energy without surface tension?
No, they are inseparable — surface energy arises because of surface tension.
8. Practice Questions (with Step-by-Step Solutions)
Q1. A liquid has surface tension [T = 0.05 , N/m]. Calculate the surface energy for a surface of area [A = 0.2 , m²].
Solution:
[E = T \times A] [= 0.05 \times 0.2] [= 0.01 \ J]
Q2. What work is required to increase the surface area of a soap film by [100 , cm²] if [T = 0.03 , N/m]?
Solution:
For soap film, there are two surfaces, so effective tension = [2T].
[W = 2T \ ΔA] [= 2(0.03)(100 \times 10^{-4})] [= 6.0 \times 10^{-4} \ J]
Q3. If surface area of a liquid is doubled, how does the surface energy change?
Solution:
Since [E = T \times A], doubling [A] doubles [E].
Q4. The surface energy of a liquid is [0.2 , J] and area is [0.01 , m²]. Find surface tension.
Solution:
[T = \dfrac{E}{A}] [= \dfrac{0.2}{0.01}] [= 20 \ N/m]
Q5. If surface tension of a liquid falls from [0.07 , N/m] to [0.06 , N/m] with temperature, find percentage change in surface energy per unit area.
Solution:
[\% \ \text{decrease}] [= \dfrac{0.07 – 0.06}{0.07} \times 100] [= 14.3%]
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