Dimension of Surface Tension & its Derivation

Dimension of Surface Tension: Surface tension is the propensity of liquid surfaces that are at rest to condense into the smallest surface area. It is due to Surface Tension that objects ranging from small needles to large ships can float over water while being partially submerged. Due to cohesion, liquid molecules are more drawn to one another, increasing surface tension. The Dimension of Surface Tension is

M1L0T -2 

In this article, we obtain the Dimension of Surface Tension along with its derivations.

Dimension of Surface Tension

Dimension of Surface Tension and Its Derivation

The Dimensional Formula of Surface Tension is 

~=~{M^1L^0T^{~-2}}

Derivation of Dimensional Formula of Surface Tension

The Dimensional Formula is written as follows.

~=~{M^{a}L^{b}T^{~c}}

Where L is Length, M is Mass, T is Time and a, b and c are the powers of M, L and T respectively

To Derive the Dimensional Formula of Surface Tension, we need to know the following

Dimension of Mass = M1L0T0

Dimension of Distance = M0L1T0

Dimension of Time = M0L0T1

Dimension of Velocity = M0L1T-1

We know that

Surface~Tension~=~{Force}/Length

Dimension~of~Surface~Tension~=~{Dimension~of~Force}/{Dimension~of~Length}

The Dimensional Formula of Force is M1L1T-2. Click here to view the derivation

~=~{M^1L^1T^{~-2}}/{M^0L^1T^{~0}}

~=~{M^1L^0T^{-2}}

Hence proved that the Dimension of Surface Tension M1L0T-2 

Surface Tension Explained

Surface Tension is a force that compels liquids to contract their surface area. It is a result of the cohesive force experienced between two molecules of the liquid. Due to this, a tangential force and an inward force develop. The tangential force is Surface Tension.

Causes of Surface Tension

The reason behind Surface Tension is the Cohesive Force between the molecules. To properly understand this, you first need to understand what cohesive and adhesive forces are.

Cohesive Force: Cohesive Force is an intrinsic force that exists between the various molecules of a substance. It is an attractive force and results in the substance remaining close to each other. When many molecules of a compound come in contact with each other, their shapes distort the distribution of electrons in the atoms. This results in a force of attraction between the electrons of a certain atom in one molecule and the nucleus of another atom in another molecule, resulting in a cohesive force.

The force of cohesion is a property of a substance. It depends upon the nature of the molecules and their state. Solid substances have more cohesion than liquid substances, and liquid substances have more cohesion than gaseous substances.

Adhesive Force: Adhesive force, on the other hand, is the force experienced between dissimilar molecules, i.e. molecules of different substances. Intermolecular forces are responsible for this force. Although there are a lot of adhesive forces, such as chemical adhesion, the adhesive force of use here is dispersive adhesion. In layman’s terms, it is the force experienced between slightly positive and slightly negative parts of two molecules. This attraction is strong enough to stick two molecules but weak enough to form chemical bonds.

In a liquid, the cohesive force is applied to all molecules equally from all sides except at the interface. At the interface, the molecules experience cohesive force only from one side. At the surface, it is from the bottom. Thus, the excessive inward force prevents the surface from rupturing when an object comes in contact. This is how surface tension is created. However, the force cannot withstand heavier weights.

Phenomena due to surface tension are ubiquitous. Some of them are listed below.

  1. A water droplet is always spherical when at rest. This is due to the surface tension in water.
  2. Tiny insects can stand or walk on water due to surface tension.
  3. Bubbles formed inside water are spherical due to surface tension.
  4. Detergent powder used to wash clothes reduces the surface tension of water helping clothes to soak more water.
  5. While writing with an ink or ball pen, surface tension causes the ink to smoothly flow on the paper.
  6. Oil and water mix well during cooking due to reduced surface tension due to heat.

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