# What is Surface Tension? – Calculating Surface Tension

## Origin of Surface Tension – Basic Understanding

Surface tension is a fascinating concept that plays a crucial role in our daily lives. It stems from the cohesive forces between molecules at the surface of a liquid. These attractive forces create a sort of “skin” on the liquid surface, allowing insects to float and certain objects to “float” on water. The origin of surface tension can be traced back to the molecular-level interactions that occur between liquid molecules.

### Cohesion and Surface Tension Relation

To truly understand surface tension, we must delve into the concept of cohesion. Cohesion refers to the attraction between molecules of the same substance. In the case of liquids, this cohesive force leads to molecules at the surface being drawn inward, creating a tension that resists external forces. This cohesive force is what gives rise to surface tension.

## What is Surface Tension?

Surface tension can be defined as the property of a liquid that allows it to resist an external force due to the cohesive nature of its molecules. It is essentially the measure of the strength of the liquid’s surface layer. This phenomenon is what causes liquid droplets to form spherical shapes and enables some insects to walk on water.

### Examples of Surface Tension

Surface tension manifests in various everyday phenomena, such as:

• Water droplets form on a leaf.
• Insects walking on the surface of the water.
• Formation of soap bubbles.

### The Formula for Surface Tension

The formula to calculate surface tension is given by:

$$\gamma = \frac{F}{l}$$

Where:

$$\gamma$$ = Surface tension

( F ) = Force acting perpendicular to the line of length

( l ) = Length of the line over which the force acts

#### Units of Surface Tension to Measure

Surface tension is typically measured in units of force per unit length, such as Newtons per meter (N/m) in the International System of Units (SI). This unit reflects the amount of force required to increase the surface area of the liquid by a certain amount.

#### Dimension of Surface Tension

The dimension of surface tension is,

$$M^{1} L^{0} T^{-2}$$

where M represents mass and T represents time. This reflects the force per unit length nature of surface tension.

## Calculating Surface Tension with Mathematical Derivation

To derive the formula for surface tension, consider a liquid film with width ( l ) and surface tension ( \gamma ). The force acting to stretch this film is ( F ). By applying the principles of equilibrium, we can obtain the formula:

$$\gamma = \frac{F}{l}$$

We know the pressure balancing equation,

$$P_{0} -P= \frac{2 \gamma }{r}$$ (Assume it as Equation 1)

But the Hydrostatic Pressure Difference is

$$P_{0} -P= \rho gh$$ (Assume it as Equation 2)

By equating the above two equations,

$$\rho gh=\frac{2 \gamma }{r}$$

Finally,

$$\gamma = \frac{2 \rho gh}{d}$$

This derivation highlights the relationship between force, length, and surface tension.

## Causes of Surface Tension

Various factors contribute to a liquid’s surface tension, including the cohesive forces between molecules, temperature, and the liquid’s nature. These forces work together to create the unique properties of surface tension.

## Surface Tension of Various Liquids

Different liquids exhibit varying degrees of surface tension based on their molecular composition and interactions. For example, water has a higher surface tension compared to alcohol due to the stronger hydrogen bonding between water molecules.

Here we have tabulated the surface tension of various liquids,

 Liquid Surface Tension (N/m) Water 0.072 Mercury 0.465 Ethanol 0.022 Olive Oil 0.033

## Concept of Surface Tension at the Molecular Level

At the molecular level, surface tension arises from an imbalance of forces at a liquid’s surface. Molecules at the surface experience a net inward force, leading to the formation of the liquid’s “skin.” This molecular-level understanding sheds light on the macroscopic properties of surface tension.

## Final Notes

Surface tension is a complex yet intriguing phenomenon that impacts various aspects of our daily lives. By understanding the cohesive forces at play and the mathematical principles governing surface tension, we can appreciate the beauty of this property in liquids. Remember to explore the world around you with a curious mind to uncover the wonders of surface tension.

This discussion revolves around the concept of surface tension along with the surface tension derivation and calculation. For more insightful explanations on various topics, explore our blog section. If you seek comprehensive understanding through personalized guidance, Tutoroot offers one-on-one online tuition for physics with doubt-clearing sessions and study materials. Book a FREE DEMO now to experience it firsthand.

## FAQs

What is the meaning of surface tension?

Surface tension is the measure of the strength of cohesive forces between molecules at the surface of a liquid.

Explain the stalagmometer method.

The stalagmometer method is a technique used to measure surface tension by observing the height of a liquid column in a capillary tube.

Write the surface energy formula.

The formula for surface energy,

$$M^{1} L^{0} T^{-2}$$

Surface tension definition.

Surface tension is the measure of the strength of cohesive forces between molecules at the surface of a liquid.

What is the surface tension of water?

The surface tension of water at 20°C is approximately 0.072 N/m.