Surface Energy Formula

Surface energy quantifies the disruption of intermolecular bonds that occurs when a surface is created.  It is also called surface-free energy or interfacial-free energy. In simple language, surface energy can be defined as the work per unit area done by the force that creates the new surface.

Surface energy is the energy that exists between the surface molecules of solid materials or substances when a comparable attractive force exists. The Ratio of Surface Energy to the Surface Area is known as Surface Tension. Low to high energies, or vice versa, are different. It is impossible to measure surface energy. It occurs as a result of a molecule-molecule interaction. A stretched membrane refers to the free surface of a liquid. The surface, which is known as surface-free energy, holds some Potential Energy on the liquid surface. Surface energy will be discussed in detail in this article.

What is Surface Energy?

The work done on the outer portion of a material when the atoms are not bonded to another atom in their immediate vicinity is known as surface energy. Any material’s atoms must be joined to other atoms to function properly. This is due to the fact that connected atoms completely encircle the material’s physical aspect, which remains constant. When the material reaches the surface, however, the atom’s bonds rip open, and there are no bonds on the substance’s outer surface. Surface energy is the technical term for this. Higher surface energy indicates that atoms are more motivated to rejoin links.

Surface energy refers to the extra potential energy per unit area of a liquid’s free surface.

When a spring is stretched, some work is done on it, and the work is stored as Potential energy, also known as Elastic potential energy. There will be no potential energy if the body is in its undamaged state. When we talk about free surfaces of liquids, we know that they are stretched membranes, thus the surface will store some potential energy due to the stretched surface, which is referred to as Surface energy or Surface free energy because it is just at the liquid’s surface. The diagram given below shows the surface energy of the drop of water.

Unit and Dimension of Surface Energy

• Joules/m² or Newton/meter (N/m) is the SI unit for surface energy.
• Dimensional Formula for Surface energy is: [M¹L⁰T^-2]

Surface Energies of a few materials are as follows:

Material	Surface Energy (Joules/m2)
Glass	83.4
Lead	442
Polystyrene	40.6

Surface Energy Formula

Surface Energy is calculated using the following formula:

Surface Energy = Work Done / Area

E = S × ΔA

where,

• E is the Surface Energy
• S is the Surface Tension
• ΔA is the Increase in Surface Area

Relationship Between Surface Tension and Surface Energy

The relation between Surface Energy and Surface Tension is given by the expression

T = ΔU / ΔS

Surface Energy = Energy / Area

Surface Energy = joule / m²

Surface Energy = Newton × m / m²

Surface Energy = Newton / m

Surface Energy = Force / Length

Surface Energy = Surface Tension

Pressure Inside a Liquid Drop and a Bubble

For any small drop of water, it does not collapse because of Surface Tension on the surface of the water which is given by,

σ = F/L

where,

• σ is surface tension of the liquid
• F is force per unit length
• L is line over which the force acts

If the drop doesn’t collapse, it implies that the pressure within the drop is greater than that outside. The extra pressure (p) is given by subtracting the outside pressure (p_o) from the inside pressure (p_i);

p = p_i – p_o

Outside Force = p × Surface Area of Drop

Outside Force = (p_i – p_o) x 4πr²

where,

• r is radius of the drop

Solved Examples on Surface Energy

Example 1: If the Surface Tension of water is 24 × 10^-3 N/m and the Increase in Surface Area is 20 m. Find its Surface energy.

Solution:

Given:

S = 24 × 10^-3 N/m, ΔA = 20 m

Since,

E = S × ΔA

E = 24 × 10^-3 × 20

E = 0.480 Joules/m²

Example 2: Find the Surface Tension if the Surface Energy is 32 × 10^-3 Joules/m² and the Surface Area Increase is 12 m.

Solution:

Given:

E = 32 × 10^-3 Joules/m², ΔA = 12 m

Since,

E = S × ΔA

S = E / ΔA

S = 32 × 10^-3 / 12

S = 2.666 × 10^-3 N/m

Example 3: If the liquid’s surface tension is 40 × 10^-3 N/m and the increase in surface area is 12 mm, Find out what its surface energy is.

Solution:

Given:

S = 40 × 10^-3 N/m, ΔA = 12 mm = 12 × 10^-3 m

Since,

E = S × ΔA

E = 40 × 10^-3 × 12 × 10^-3

E = 0.480 × 10^-3 Joules/m²

Example 4: Assume that the Surface Tension is 9 × 10^-3 N/m and the Increase in the Surface Area is 23 m then Find its Surface energy.

Solution:

Given:

S = 9 × 10^-3 N/m, ΔA = 23 m

Since,

E = S × ΔA

E = 9 × 10^-3 × 23

E = 0.207 Joules/m²

Example 5: Find Surface Energy when surface tension is 12 × 10^-3 N/m and the Increase in Surface Area is 31 m.

Solution:

Given:

S = 12 × 10^-3 N/m, ΔA = 31 m

Since,

E = S × ΔA

E = 12 × 10^-3 × 31

E = 0.372 Joules/m²

Example 6: Surface tension of water is 20 × 10^-3 N/m and surface energy is 0.121 Joules/m² then find the increase in surface area.

Solution:

Given:

S = 20 × 10^-3 N/m, E = 0.121 Joules/m² = 121 × 10^-3 Joules/m²

Since,

E = S × ΔA

ΔA = E / S

ΔA = 121 × 10^-3 / 20 × 10^-3

     = 6.05 m

FAQs on Surface Energy

1. What is meant by Surface Energy?

Surface Energy is the work done per unit area by the force that creates the new surface.

2. What is the Formula of Surface Energy?

The formula of surface energy is Energy/Area. It can be also expressed as

Surface Energy = Energy × [Area]^-1

3. What is the Unit of Surface Energy?

SI unit for measuring Surface Energy is N/m.

4. What are Examples of Surface Energy?

Glasses, Ceramics, Metals, and various other materials are held together by stronger bonds which are examples of surface energy.

5. What is the Dimensions of Surface Energy?

Dimensions of Surface Energy is [MT^{– 2}].

6. What is Relationship Between Surface Tension and Surface Energy?

The relation between Surface Tension and Surface Energy is given by,

Surface Energy = Surface Tension

7. What is Surface Free Energy?

Surface Free Energy is defined as the work done required to increase the surface area of the solid phase. Surface Free Energy affects the wettability of the solid.