To Find the Surface Tension of Water by Capillary Rise Method

Dhristi JEE 2022-24

Surface Tension By Capillary Rise Method

The surface tension is the ability of a liquid to stay in its fixed shape. For example, when a drop of oil falls, it tries to remain in a spherical shape; this is the case in surface tension. When we experiment with a capillary tube, we observe that when a liquid rises in a capillary tube, the weight of the column of the liquid of density ρ inside the tube is supported by the upward force of surface tension acting along the circumference of the points of contact. Here, we will learn to find the surface tension of water by the capillary rise method and derive the rise in capillary tube formula.


Capillary Rise Method

A liquid of density ρ and surface tension σ rises in a capillary of inner radius ‘r’ to a height ‘h’ is given by:

h = 2σ cosθ/ρgr

where 

Θ = The contact-angle made by the liquid meniscus with the surface of the capillary.


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Point to Note:

The liquid rises because of the three types of forces, viz: adhesion, cohesion, and surface tension. 

If adhesive force/the liquid capillary is greater than the cohesive force between two liquids, then liquid rises as we see in the case of water rise in a glass capillary. 

If in this case, the contact angle is less than 90 degrees, then the meniscus is concave. However, when the adhesive force is less than the cohesive force, then liquid depresses or reduces in height, as in the case of mercury in a glass capillary. 

Now, let’s suppose that the contact angle is greater than 90 deg, the meniscus is convex.

We can derive the capillary rise formula by balancing forces on the liquid column. The weight of the liquid is given by:

πr² hρg

This weight is balanced by the upward force due to surface tension, whose formula is 2πrσcosθ

Please note that this formula can also be derived by using a pressure balance.


To Find the Surface Tension of Water by Capillary Rise Method

Our Objective:

The surface tension of water by capillary rise method using capillary tube method.

Materials Required

  • Two-three capillary tubes of different radii

  • A pointed clamp in a metallic plate with a handle

  • Travelling microscope

  • Movable and adjustable height stand

  • A flat bottom open dish

  • Clinical thermometer

  • Fresh water in a beaker

  • A clamp and a stand


Theory

The  rise in capillary tube formula is given by the following surface tension of water formula:

T= r(r+h/3)ρg2cosθ


Steps to Follow for Arranging the Apparatus:

  1. Place the movable height stand on the table and adjust its base horizontally by leveling the screws.

  2. Take a speck of dirt and grease-free water in an open dish with a flat bottom and put it on the top of the height stand.

  3. Now, take three capillary tubes of different radii.

  4. Clean the capillary tubes with a clean cloth and dry them. 

  5. Clamp these tubes to a metallic plate to increase their radius. Next, clamp a pointer after the third capillary tube.

  6. Clamp/affix the horizontal handle of the metallic plate in a vertical stand in such a way that the capillary tube and the pointer become vertical.

  7. Now, adjust the height of the metallic plate in a way that the capillary tubes dip in the water in an open dish.

  8. Adjust the position of the pointer in such a manner that the tip touches the surface of the water.


Steps to Follow to measure the Capillary Rise:

  1. Find the LC of the traveling microscope for the horizontal and the vertical scale. Record the same in the tabular form.

  2. Increase the height of the microscope by keeping its axis horizontal and pointing towards the capillary tubes.

  3. Now, bring the microscope in front of the first capillary tube that has a maximum rise.

  4. Adjust the horizontal crosswire touching the central part of the concave meniscus observed convex through a microscope.

  5. Note all the readings of the position of the microscope on the vertical scale.

  6. Now bring the microscope in front of the second capillary tube.

  7. Lower the height of the microscope and repeat steps 12 and 13.

  8. Repeat steps 12 and 13 for the third capillary tube.

  9. Lower the height stand to make the pointer tip visible.

  10. Place the movable microscope horizontally in front of the pointer and lower it to make the horizontal crosswire touch the tip of the pointer. Then repeat step 13.


Observation: Height of Liquid Rise


S.No

Reading of Meniscus

Reading of Pointer Tip

Height

h1 – h2

= h cm

M.S.R

N (cm)

V.S.R

n × LC (cm)

Total Reading

N + n (LC)

h1 (cm)

M.S.R

N (cm)

V.S.R

n × LC (cm)

Total Reading

N + n (LC)

h2 (cm)

1.








2.








3.








4.








5.









Calculation Part:

Take the value h and r for all three capillary tubes separately and find the values of T using the following formula:

T= r(h+r/3)ρg2cosθ

Find the mean value of the obtained T values as follows:

Tavg=(T1 +T2 + T3)/3

So, Tavg = _____ dynes/cm.

FAQs on To Find the Surface Tension of Water by Capillary Rise Method

1. Define surface tension?

Surface tension is a liquid property, due to this the free surface at equilibrium behaves as an elastic property or a rubber membrane, with a tendency to compress and occupy a small surface area. This property is due to the cohesion of molecules and is responsible for almost all the behaviors of liquids. The property of surface tension can be seen in an object which floats on the surface of the water, even when they are denser than water.  It can also be seen in the ability of some insects, such as water striders, and reptiles which run on the water surface.  

2. What is the theory behind surface tension?

Surface tension can be learned by the molecular theory of matter. According to this theory, surface tension is caused by the cohesive forces among liquid molecules. The molecules of the liquid are equally attracted to other molecules in all directions. An inward pull is experienced on the surface of the molecules. 


Therefore, a network is created opposite to the inward pull to move a molecule to the liquid surface. It results in higher potential energy on the molecules at the surfaces. To reach the lower potential energy and stable equilibrium, the free surface of the liquid favors the minimum surface area and behaves like a stretched membrane. The surface tension is measured as the force acting normal (per unit length) to an imaginary line on the free liquid surface at rest. It is denoted by the symbol T (or S). The SI unit is Nm-1 and the dimensional formula is M1L0T-2.

3. What is cohesion and adhesion force?

Cohesion is the intermolecular attraction acting between two similar kinds of molecules. Cohesion within fluids is the fundamental basis of viscosity. Adhesion is the intermolecular attraction acting between two different kinds of molecules. An example of adhesion is the glass surface gets wet due to water. This is because of the intermolecular forces between the water and the glass. In such cases, the adhesion force between the glass and the water will be greater than the cohesion forces within the water. When the liquid is repelled from the surface, the cohesion in the liquid will be greater than the adhesion between the liquid and the solid. For example, raindrops on the freshly waxed car tend to bead on the surface and then easily flow off.

4. How does temperature affect the surface tension?

When temperature increases the surface tension of the liquid decreases. At the boiling point, the surface tension of the liquid is zero and at the critical temperature, it vanishes. At the critical temperature, the intermolecular forces of liquid will be equal to the gases, and liquid is said to expand without restriction. 

When there is a small difference in the temperature, the variation in surface tension becomes linear.

Tt = To(1 − αt),

Where,

Tt, T0 is the surface tensions at t0C and 00C respectively

α is the temperature coefficient.

For example, 

(i) Soup tastes better when it is hot than cold.

(ii) Machinery parts have a high possibility of getting jammed in the winter.

5. Define capillary action?

Tubes that have very small diameters are called capillaries. If these tubes get dipped in liquid it either rises or falls relative to the surrounding liquid level. This process is called capillary action and these tubes are called capillary tubes.


A wet fluid displays a capillary action that is caused due to the combination of cohesion forces and surface tension. It is due to the intermolecular attraction of molecules of water and the adhesive force between the walls of the capillary and the liquid. 

6. Define Capillary Rise.

Capillarity is the rise or depression of a liquid in a small passage such as a tube having a small cross-sectional area, it is similar to the spaces between the fibres of a towel or the openings in a porous material like cotton.


Capillarity not only talks about the vertical direction, but it also considers the horizontal orientation. For example, when water is drawn into the fibres of a towel, no matter how the towel is oriented, the liquid still has capillarity.

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