Surface Tension Formula: Explanation, Examples, and Solved Examples

Surface tension is the tendency of liquid surfaces at rest to contract to the smallest surface area possible. Surface tension allows objects with a higher density than water, such as razor blades and insects, to float on the surface of the water without being immersed.

• Surface tension is determined not only by the forces of attraction between particles in a specific liquid.
• But it can also be determined by the forces of attraction of solids, liquids, and gases in contact with it.
• The energy causing surface tension may be thought of as roughly similar to the work or energy necessary to remove the surface layer of molecules in a unit area. 

• Surface tension is commonly measured in dynes/cm, which is the amount of force necessary to break a 1 cm long film. 

Key Terms: Surface Tension, Surface Energy, Energy, Molecules, Adhesive force, Cohesive force, Liquid, Surface area, Surface tension formula

---

What is Surface Tension?

[Click Here for Sample Questions]

Surface tension is the property of a liquid due to which the free surface of the liquid always tries to attain a minimum surface area.

• The surface tension of a liquid is mainly a force that acts to reduce the surface area of the liquid.
• Surface tension is a directed contracting force that draws molecules on a liquid's surface to its interior.
• Liquid surface tension is determined by the composition of the vapor phase.
• The surface tension of liquids plays an essential role in both everyday life and many industrial processes.
• It is measured in dyne/cm in the C.G.S system and N/m in the S.I unit.

Also Read:

---

Surface Tension Formula

[Click Here for Sample Questions]

Surface tension can be expressed mathematically as the force (F) acting on the surface and the length (l) of the surface, as follows:

\(T = \frac{F}{l}\)

Where

• T= surface tension (N/m)
• F = force per unit length (N)
• l = length in which force acts (m)

Surface tension is sometimes defined as the ratio of the amount of work done (W) to the change in surface area (A).

\(T = \frac{W}{A}\)

The surface tension is a result of the Van der Waals force which attracts the debris of liquid together.

Unit of Surface Tension

Surface tension commonly represented by the symbol γ (also σ or T), is measured in force per unit length. Its SI unit is newton per meter but the cgs unit of dyne per centimeter is also used.

Dimensions of Surface Tension

Surface tension is given by the formula,

Surface tension = F/L

We have

• The dimensions of force F is [M L T^-2].
• The dimensions of length L is [L]

Therefore, the dimensional formula of surface tension is given by

[Surface Tension] = [M L T^-2] / [L]

⇒ [Surface Tension] = [M L⁰ T^-2]

---

Factors Affecting Surface Tension

[Click Here for Sample Questions]

The various factors affecting surface tension are

• Impurities: The surface tension decreases with the addition of impurities.
• Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
• Temperature: The surface tension of a liquid reduces as the temperature rises. 

---

Examples of Surface Tension

[Click Here for Sample Questions]

The following are the examples of surface tension

• A needle floats on the water's surface.
• Insects walking on water
• Rainproof tent materials in which water's surface tension bridges the pores in the tent material.
• Surface tension disinfectants (solutions with low surface tension).
• Clinical tests for jaundice.
• Cleaning clothes with soaps and detergents reduces the surface tension of water.
• Wash with cold water.
• Round bubbles in which the surface tension of water serves as the wall tension for the formation of water bubbles.
• This process also determines the shape of liquid droplets.

---

Adhesive and Cohesive Forces

[Click Here for Sample Questions]

Adhesive and cohesive forces are both intermolecular forces, but they differ in the types of molecules they act between.

Adhesive Force

The force of attraction between molecules of different substances is called the force of adhesion or adhesive force.

Examples of Adhesive force are

• It enables us to write on the blackboard with chalk.
• Water wets glass because of adhesive force.

Cohesive Force

The force of attraction between molecules of the same substances is called the force of cohesion or cohesive force.

Examples of Cohesive forces are

• Two drops of liquid collapse into one drop because of cohesive force.
• Mercury did not wet glass because of cohesive force.

---

Solved Examples

[Click Here for Sample Questions]

Ques. Find the surface tension of the liquid with a dragging force of 30 N when the length at which the force acts is 6 m.

Ans. Given

• Force, F = 30 N
• Length, L = 6 m

The formula of surface tension is given by

T = F/L

On substituting the values, we get

Surface tension, T = 30/6 = 5 N/m

Ques. Find the dragging force on the 3 m surface of the liquid if the surface tension is 7 N/m.

Ans. Given

• Surface tension, T = 7 N/m
• Length, L = 3 m

The formula of surface tension is given by

T = F/L

⇒ Force, F = T x L

On substituting the values, we get

F = 7 x 3 = 21 N

---

Things to Remember

• Surface tension is the tendency of liquid surfaces at rest to contract to the smallest surface area possible.
• The SI unit of surface tension is N/m.
• The formula of surface tension is T = F/L.
• The dimensional formula of surface tension is [M L⁰ T^-2].
• The force of attraction between molecules of different substances is called the force of adhesion.
• The force of attraction between molecules of the same substances is called the force of cohesion.

Read More: