What is Surface Tension – Dimensions, Derivations, Causes and Examples

# What is Surface Tension – Dimensions, Derivations, Causes and Examples

Surface tension is a characteristic exhibited by all fluids, where they endeavor to reduce their exposed surface area. To quantify the surface tension of a liquid, it is measured as the force acting per unit length along an imaginary line drawn tangentially on the liquid’s free surface. This can be expressed as Surface tension (S) = Force/Length, which is equivalent to F/l, or work done per change in area.

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The standard unit for surface tension is either Newtons per meter (Nm⁻¹) or Joules per square meter (Jm⁻²), and its dimensional formula is [MT⁻²]. Surface tension is a scalar quantity. It arises from molecular interactions, specifically electrical cohesive forces, which are the fundamental source of this phenomenon.

The surface tension of a liquid is solely dependent on the intrinsic properties of the liquid and is unaffected by the size of the surface or the length of the line in question. Consequently, small drops of the liquid tend to assume a spherical shape due to the inherent surface tension.

1. Adhesive Force: Adhesive force refers to the attractive interaction between molecules of different substances. For example, it is the force of attraction between paper and ink molecules or between water and glass molecules.
2. Cohesive Force: Conversely, cohesive force pertains to the attractive forces between molecules of the same substance. For instance, it describes the force of attraction between water molecules or between glass molecules. Both cohesive and adhesive forces are manifestations of Van Der Waals’ Forces.

## Dimensional Formula of Surface Tension

The dimensional formula of surface tension is given by,

M1 L0 T-2

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Surface Tension (T) = Force × Length-1 . . . . . (1)

Since, Force = Mass × Acceleration

And, acceleration = velocity × time-1 = [L T-2]

∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)

On substituting equation (2) in equation (1) we get,

Surface Tension (T) = Force × Length-1

Or, T = [M1 L1 T-2] × [L-1] = M1 T-2.

Therefore, surface tension is dimensionally represented as M1 T-2.

## Causes of the Surface Tension

Surface tension arises due to the cohesive forces between molecules in a liquid. These forces are the result of intermolecular interactions, such as van der Waals forces, hydrogen bonding, and other attractive forces that hold the liquid molecules together.

The molecules at the surface experience an unbalanced force, causing them to be more attracted to their neighbors below and at the sides, creating a ‘skin’ or ‘film’ at the surface.

Intermolecular forces, such as the Van der Waals force, create an attractive interaction among the particles within a liquid, drawing them closer together. On the liquid’s surface, these particles experience an inward pull, directed toward the bulk of the liquid. This phenomenon is quantified as surface tension, which is defined as:

The ratio of the surface force (F) to the length (L) along which this force is applied.

Expressed mathematically, surface tension (T) can be represented as:

T = F / L

Where:

F represents the force per unit length.

L signifies the length over which the force acts.

T denotes the surface tension of the liquid.

### Unit of Surface Tension

The unit of surface tension in the International System of Units (SI) is the Newton per meter (Nm⁻¹). This unit represents the force (in Newtons) per unit length (in meters) along the liquid’s surface. Refer to the table below for the units of surface tension –

 SI Unit N/m CGS Unit dyn/cm

## Dimension of Surface Tension

The dimensional formula for surface tension is [MT⁻²], where M represents mass and T represents time. This signifies that surface tension has dimensions of force per unit length.

As we know, surface tension is given by the formula,

Surface tension = F/L

We know that F = ma, substituting the value in the equation, we get

=ma/L

Equating the fundamental quantities into the equation, we get

=MLT-2L-1

Solving further, we get

=MT-2

Hence, the dimensional formula of surface tension is MT-2.

### Examples of Surface Tension

There are numerous everyday examples of surface tension:

1. Water droplets forming on a car windshield.
2. A needle or paperclip floating on the surface of water.
3. Surface tension disinfectants (disinfectants are solutions of low surface tension).
4. The rise of water in a narrow glass capillary tube.
5. Clinical test for jaundice
6. The spherical shape of raindrops or small liquid droplets.
7. Surface Tension is also responsible for the shape of liquid droplets.
8. Insects like water striders walking on the surface of water due to surface tension.
9. Rainproof tent materials where the surface tension of water will bridge the pores in the tent material
10. Cleaning of clothes with soaps and detergents, which lowers the surface tension of the water
11. Washing with cold water
12. Round bubbles where the surface tension of water provides the wall tension for the formation of water bubbles.

## How to Calculate Surface Tension?

Surface tension (S) can be calculated using the formula: S = F/l, where S is the surface tension, F is the force acting tangentially on the liquid’s surface, and l is the length of the line along which the force is acting. Surface tension can also be calculated using the energy method, where it is the change in energy per unit change in surface area.

Methods of Measurement

There are several methods to measure surface tension, including:

1. Capillary Rise Method: Measuring the height to which a liquid rises in a narrow capillary tube due to surface tension.
2. Maximum Bubble Pressure Method: Determining surface tension by measuring the pressure inside a bubble formed in a liquid.
3. Wilhelmy Plate Method: Measuring the force required to detach a thin plate (usually made of glass or filter paper) from the surface of a liquid.
4. Drop Weight Method: Measuring the weight of a liquid drop as it detaches from a thin tube or nozzle.
5. Pendant Drop Method: Analyzing the shape of a hanging liquid drop to calculate surface tension.

These methods provide accurate measurements of surface tension, and the choice of method depends on the specific characteristics of the liquid and the equipment available for measurement.

## FAQ’s on Surface Tension

### What is the dimensional formula of surface tension, and explain?

The dimensional formula of surface tension is MT⁻², where: M represents mass, which is the dimension of force. T represents time, which is the dimension associated with the rate of change. The exponent -2 indicates that surface tension is the force per unit length (length being the denominator) or energy per unit area.

### What is the formula for dimensional tension?

The formula for the dimensional tension is T = ML⁻¹T⁻², where: M represents the dimension of mass. L represents the dimension of length. T represents the dimension of time.

### What is surface tension, and what is its formula?

Surface tension is a property of liquids that describes their ability to resist external forces that tend to increase their surface area. It arises due to cohesive forces between liquid molecules at the surface. The formula for surface tension is: T = F / L Where: T is surface tension (N/m or J/m²). F is the force acting tangentially on the liquid's surface (N). L is the length along which the force acts (m).

### What is surface tension Class 11 notes?

In Class 11 physics or chemistry, surface tension is typically introduced as a fundamental property of liquids. Class 11 notes on surface tension would cover its definition, causes, measurement, examples, and related concepts such as cohesive and adhesive forces. These notes help students understand the basic principles and applications of surface tension in the context of their studies.

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