How Does Capillary Rise Reveal the Surface Tension of Water?
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:
Place the movable height stand on the table and adjust its base horizontally by leveling the screws.
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.
Now, take three capillary tubes of different radii.
Clean the capillary tubes with a clean cloth and dry them.
Clamp these tubes to a metallic plate to increase their radius. Next, clamp a pointer after the third capillary tube.
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.
Now, adjust the height of the metallic plate in a way that the capillary tubes dip in the water in an open dish.
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:
Find the LC of the traveling microscope for the horizontal and the vertical scale. Record the same in the tabular form.
Increase the height of the microscope by keeping its axis horizontal and pointing towards the capillary tubes.
Now, bring the microscope in front of the first capillary tube that has a maximum rise.
Adjust the horizontal crosswire touching the central part of the concave meniscus observed convex through a microscope.
Note all the readings of the position of the microscope on the vertical scale.
Now bring the microscope in front of the second capillary tube.
Lower the height of the microscope and repeat steps 12 and 13.
Repeat steps 12 and 13 for the third capillary tube.
Lower the height stand to make the pointer tip visible.
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
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 Surface Tension of Water by Capillary Rise Method: Step-by-Step Guide
1. What is the fundamental principle of the capillary rise method for determining the surface tension of water?
The principle is based on the balance of forces. When a narrow capillary tube is dipped in water, the adhesive forces between the water molecules and the glass walls are stronger than the cohesive forces among the water molecules. This causes the water to wet the glass and form a concave meniscus. The upward pull of surface tension along the line of contact lifts the liquid column until its weight is exactly balanced by this upward force. By measuring the height of this rise, we can calculate the surface tension.
2. What is the formula to calculate surface tension by the capillary rise method as per the CBSE 2025-26 syllabus?
The formula to calculate surface tension (T) by the capillary rise method is: T = (r * h * ρ * g) / 2. In this formula:
- 'r' is the radius of the capillary tube.
- 'h' is the height of the liquid rise.
- 'ρ' (rho) is the density of the liquid.
- 'g' is the acceleration due to gravity.
3. How do cohesive and adhesive forces contribute to capillary action in a narrow tube?
Cohesive and adhesive forces work together to produce capillary action.
- Cohesive forces are the intermolecular attractions between similar molecules (e.g., between water molecules).
- Adhesive forces are the attractions between different molecules (e.g., between water molecules and the glass tube).
4. Why is the meniscus for water in a glass capillary concave, while for mercury it is convex?
The shape of the meniscus depends on the relative strength of cohesive and adhesive forces.
- Water in Glass (Concave Meniscus): The adhesive force between water molecules and glass is stronger than the cohesive force between water molecules. This causes the water to "climb" the walls of the glass tube, resulting in an upward curve or concave meniscus.
- Mercury in Glass (Convex Meniscus): The cohesive force between mercury atoms is much stronger than the adhesive force between mercury and glass. The mercury atoms are pulled more strongly towards each other than to the glass, causing the liquid to pull away from the walls and form a downward curve or convex meniscus.
5. How does an increase in temperature impact the surface tension of water, and what are its practical implications?
An increase in temperature causes the surface tension of a liquid to decrease. This is because higher temperatures increase the kinetic energy of the molecules, which weakens the intermolecular cohesive forces responsible for surface tension. At the boiling point, surface tension becomes zero. A practical implication is seen with hot soup; its lower surface tension allows it to spread more easily over the tongue, enhancing its flavour profile compared to cold soup, which has a higher surface tension.
6. What are some common real-world examples that demonstrate capillary action?
Capillary action is demonstrated in many common phenomena:
- The absorption of water by a paper towel or sponge.
- The wicking of melted wax up the wick of a candle to the flame.
- The movement of water from the soil up into the roots and stems of plants (part of the transpiration process).
- The way a cotton cloth soaks up a spill.
- The functioning of the nib in a fountain pen, which draws ink from the cartridge to the paper.
7. What are the key assumptions made when using the simplified formula for surface tension in the capillary rise experiment?
Several key assumptions are made to simplify the calculation of surface tension using the formula T = (rhρg)/2:
- Zero Angle of Contact: It is assumed that the angle of contact (θ) between the water and the clean glass tube is zero degrees, making cos(θ) equal to 1.
- Uniform Capillary Bore: The formula assumes the capillary tube has a perfectly uniform and circular cross-section along its entire length. Any irregularities can affect the accuracy.
- Negligible Meniscus Weight: The simplified formula often neglects the small amount of liquid present in the meniscus itself, above the measured height 'h'.
- Vertical Tube: The experiment assumes the capillary tube is held perfectly vertical in the liquid.
8. Why must the capillary tube be very narrow for a significant capillary rise to be observed?
The height (h) to which a liquid rises in a capillary tube is inversely proportional to the radius (r) of the tube. This relationship is described by Jurin's Law. The formula for height, h = 2T/(rρg), clearly shows that as the radius 'r' decreases, the height 'h' increases. Therefore, a very narrow tube is required to produce a capillary rise that is large enough to be easily and accurately measured. In a wide tube, the upward force of surface tension would be insufficient to lift the large weight of the liquid column to a noticeable height.
