Dimensional Formula of Surface Tension

Dimensional Formula of Surface Tension is M¹T^-2. As we know, surface tension is the property of liquids that influences various phenomena, from the shape of raindrops to the behavior of small insects on water surfaces. Mathematically it is defined as, the force per unit length acting in the plane of the liquid surface and perpendicular to a line drawn on the surface.

In this article, we will provide a brief overview of surface tension and discuss its dimensions, including the derivation of the dimensional formula using the surface tension formula.

What is Surface Tension?

Surface tension is a property of liquids that arises due to the cohesive forces between the molecules at the surface of the liquid. It is defined as the force acting perpendicular to the surface of a liquid, per unit length along the surface. In simpler terms, it is the measure of the tendency of a liquid to minimize its surface area and is often described as the “contractive” nature of the surface of a liquid.

Surface Tension Definition

Surface tension is a property of liquids that arises from the cohesive forces between molecules at the interface of the liquid and a gas, such as air.

In simpler terms, surface tension is the measure of the tendency of a liquid to minimize its surface area and form into the shape that has the least surface area.

Formula for Surface Tension(T)

Formula for surface tension (T) is given by:

T = F/L

In the above formula,

• T is Surface Tension
• F represents the force acting perpendicular to the surface of the liquid
• L represents the length along which the force is acting.

Dimensional Formula of Surface Tension

The dimensional formula of the surface tension is (T) = M¹T^-2

In the above formula,

• M represents mass
• T represents time

Derivation of Dimensional Formula of Surface Tension:

The formula for surface tension (T) is given by,

T = F/L

By the second law of motion, F = ma, where F represents the force applied, m is mass of the object and a is the acceleration generated with the help of force.

Also, acceleration is change in velocity with unit m/s², which can be written as dimension [L/T²]

Substituting this into the Force equation we get,

F = [M] × [L/T²]

Now, substitute this expression for force (F) back into the formula for surface tension (T) we get,

T = {[M] × [L/T²]}/[L] = [MT^-2]

So, the derived dimensional formula of the Surface Tension if M¹T^-2.

Conclusion

As we discussed in the article, that Surface tension is Force per unit Length, i.e., F/l. Thus, Dimensional Formula for Surface Tension is [MT^-2] and unit is Nm^-1 or Jm^-2.

Read More,

• Dimensional Formulas in Units and Measurements
• Surface Tension
• Surface Energy
• Dimensions of Tension

Surface Tension Dimension: FAQs

1. What is Formula for Surface Tension?

Surface tension (γ) is defined as the force per unit length or as the energy per unit area. It’s given by γ = F/L, where F is the force and L is the length along which the force acts.

2. What is the Dimensional Formula for Tension?

The dimensional formula for tension (as a force) is [M¹L⁰T^-2].

3. How do you Calculate Surface Tension?

To calculate surface tension, measure the force exerted per unit length on an imaginary line drawn on the liquid surface. γ = F/L.

4. What is the Dimensional Formula for Surface Energy?

The dimensional formula for surface energy, which has the same units as surface tension, is [M¹L⁰T^-2].

5. What is SI Unit of Surface Tension?

The SI unit of surface tension is Newton per meter (N/m).