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CBSE Class 11 Lab Manual for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise PDF Download
CBSE Class 11 Lab Manual Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise Download here in pdf format. These Lab Manual may be freely downloadable and used as a reference book. Learning does not mean only gaining knowledge about facts and principles rather it is a path which is informed by scientific truths, verified experimentally. Keeping these facts in mind, CBSE Class 11 Lab Manual for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise have been planned, evaluated under subject Improvement Activities. Check our CBSE Class 11 Lab Manual for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise. We are grateful to the teachers for their constant support provided in the preparation of this CBSE Class 11 Lab Manual.
CBSE Class 11 Lab Manual for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise
The laboratory is important for making the study complete, especially for a subject like Science and Maths. CBSE has included the practicals in secondary class intending to make students familiarised with the basic tools and techniques used in the labs. With the help of this, they can successfully perform the experiments listed in the CBSE Class 11 Lab Manual.
CBSE Class 11 Lab Manual for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise Features:
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By performing the experiments, students will know the concept in a better way as they can now view the changes happening in front of their eyes. Their basics will become solid as they will learn by doing things. By doing this activity they will also get generated their interest in the subject. Students will develop questioning skills and start studying from a scientific perspective. Here we have given all the necessary details that a Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise student should know about CBSE Class 11 Lab Manual. From CBSE Science practical to Lab manual, project work, important questions and CBSE lab kit manual, all the information is given in the elaborated form further in this page for Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise students.
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To Find the Surface Tension of Water by Capillary Rise Method
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.
(Image will be Uploaded soon)
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:
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.
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
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:
T avg =(T 1 +T 2 + T 3 )/3
So, T avg = _____ 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 M 1 L 0 T -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.
T t = T o (1 − αt),
T t , T 0 is the surface tensions at t 0 C 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.
(i) To demonstrate the shape of capillary rise in a wedge-shaped gap between two glass sheets
materials required .
- Cleaned and dried two slides
- Rubber band
- Matchstick
- Petri dish
- Distilled water
- Potassium permanganate
- Clamps and stand
Procedure
Real lab procedure.
- Take two slides, clean and dry them well.
- Tie two slides together with a rubber band at one end.
- Fix the matchstick at the other ends of the slides.
- Take a dish. Fill half of the dish with water.
- Add potassium permanganate for colouring.
- Clamp this arrangement on a stand.
- Dip this arrangement into water like the bottom of slides are dip in the water.
- Observe what happens.
Simulation Procedure
- Answer the following question.
- Drag and drop the rubber band towards the slides.
- Drag and drop the matchstick towards the slide to put it at the other end.
- Drag and drop the connected slides towards the stand to place them.
- Click the Potassium permanganate bottle to open it.
- Drag and drop the spatula towards the bottle to take the sample.
- Drag and drop the spatula towards the Petri dish with water to put the sample into the water.
- Drag and drop the glass rod towards the Petri dish to stir the solution.
- Click on the clamp to move the slide towards the tip of the water and observe.
- Click on the petri dish to view the zoomed view of water rising inside the two slides.
- Observe the water level rising inside the connected slide.
- Click on the Inference icon to understand the observation.
- Click on the Reset button to redo the experiment or go to the next experiment.
Observation
When we use two slides to see the capillary rise, the separation between the two slides increases from the tied end to the matchstick end. Then, capillary rise decreases from the tied end to the matchstick end.
Conclusion
Capillary rise is inversely proportional to radius of capillary tube.
(ii) To demonstrate capillary rise using capillary tubes of different radius
materials required.
- China dish
- Potassium Permanganate
- Capillary tubes of different radius
- Capillary tube stand
- Travelling microscope
- Take capillary tubes of different radius and the same length.
- Clean and dry it well.
- Find the radius of each capillary tube using a travelling microscope.
- Place the laboratory stand with a capillary tube clamp on the table.
- Fix capillary tubes on the capillary tube clamp.
- Place capillary tubes together in increasing order of radius of capillary tubes.
- Take a dish and fill half of the dish with water.
- Add granules of potassium permanganate for colouring.
- Place the dish below the capillary tubes.
- Adjust the pointer so that it just touches the surface of the water.
- Adjust the vertical stand so that the capillary tube dips in the water.
- Find the capillary rise using a travelling microscope.
- Observe how capillary rise changes with the radius of the capillary tube.
- Select the method.
- Select the temperature.
- Click the Potassium permanganate bottle to open it.
- Drag and drop the spatula towards the bottle to take the sample.
- Drag and drop the spatula towards the China dish with water to put the sample into the water.
- Drag and drop the glass rod towards the China dish to stir the solution.
- Drag and drop one clamp with capillary tubes towards the stand to hold it.
- Drag and drop the other clamp with capillary tubes towards the stand to hold it.
- Click on the clamps to move the capillary tubes toward the water and observe.
- Drag and drop the scale near capillary tubes.
- Click all the capillary tubes one by one to view the zoomed view of the water level and the scale to observe the height of the water.
- Observe the height calculated with surface tension and density of water on the control part.
- Click on the Inference icon to understand the observation.
- Click on the Reset button to redo the experiment or go to the next experiment.
Observation
Water rises more at capillary tubes of a small radius. The water level in the capillary tube decreases as the radius of the capillary tube increases.
Precautions
- Glass sheets and glass tubes should be cleaned and dried well before the experiment.
- Ensure no air bubbles are trapped in the capillary tube.
- Make sure the microscope is thoroughly dried and devoid of any powder.
Developed by Amrita Vishwa Vidyapeetham & CDAC Mumbai. Funded by MeitY (Ministry of Electronics & Information Technology)
English हिंदी മലയാളം मराठी
To Determine the Surface Tension of Water by Capillary Rise Method
Aim To determine the surface tension of water by capillary rise method.
Apparatus Three capillary tubes of different radii and a tipped pointer clamped in a metallic plate with a handle, travelling microscope, clamp and stand, a fine motion adjustable height stand, a flat bottom open dish, clean water in a beaker, thermometer.
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Target Exam ---
Procedure (a) Setting the apparatus 1. Place the adjustable height stand on the table and make its base horizontal by level-ling screws. 2. Take dirt and grease free water in an open dish with flat bottom and put it on the top of the stand. 3. Take three capillary tubes of different radii (ranging from 0.05 mm to 0.15 mm). 4. Clean and dry them, clamp the capillary tubes in a metallic plate in order of increasing radius. Also clamp a pointer after third capillary tube. 5. Clamp the horizontal handle of the metallic plate in a vertical stand, so that the capillary tubes and the pointer become vertical. 6. So adjust the height of metallic plate that the capillary tubes dip in water in open dish. 7. Adjust the position of the pointer, such that its tip just touches the water surface. (b) Measurement of capillary rise 8. Find the least count of the travelling microscope for the horizontal and the vertical scale. Record the same in the note-book. 9. Raise the microscope to a suitable height, keeping its axis horizontal and pointed towards the capillary tubes. 10. Bring the microscope in front of first capillary tube (which has maximum rise). 11. Make the horizontal cross wire just touch the central part of the concave meniscus seen convex through microscope. 12. Note the reading of the position of the microscope on the vertical scale. 13. Now move the microscope horizontally and bring it in front of the second capillary tube. 14. Lower the microscope and repeat steps 11 and 12. 15. Repeat steps 11 and 12 for third capillary tube. 16. Lower the stand so that pointer tip becomes visible. 17. Move the microscope horizontally and bring it in front of the pointer. 18. Lower the microscope and make the horizontal cross wire touch the tip of the pointer. Repeat step 12. (c) Measurement of the internal diameter of the capillary tube 19. Place the first capillary tube horizontally on the adjustable stand. 20. Focus the microscope on the end dipped in water. A white circle (inner bore) surrounded by a green circular strip (glass cross section) will be seen. 21. Make horizontal cross-wire touch the inner circle at A. Note microscope reading on vertical scale. 22. Raise the microscope to make the horizontal cross-wire touch the circle at B. Note the reading (the difference gives the vertical internal diameter AB of the capillary tube). 23. Move the microscope on horizontal scale and make the vertical cross wire touch the inner circle at C. Note microscope reading on horizontal scale. 24. Move the microscope to the right to make the vertical cross-wire touch the circle at D. Note the reading (the difference gives the horizontal internal diameter CD of the capillary tube). 25. Repeat steps 19 to 24 for other two capillary tubes. 26. Note temperature of water in dish. 27. Record your observations as given ahead.
Result The surface tension of water at t°C = …….. dynes cm -1 .
Precautions
- Capillary tube and water should be free from grease.
- Capillary tube should be set vertical.
- Microscope should be moved in lower direction only to avoid back lash error.
- Internal diameter of capillary tube should be measured in two mutually perpendicular directions.
- Temperature of water should be noted.
Sources of error Water and capillary tube may not be free from grease.
Question. 1. Give symbol and unit of surface tension. Answer. The symbol is T and S.I. unit is N m -1 .
Question. 2. Give relation between surface tension and surface energy. Answer. Surface energy = Surface tension x Change in area.
Question. 3. Why liquids surfaces are generally curved ? Answer. It is due to surface tension.
Question. 4. Why is there a pressure difference on the two sides of a curved liquid surface ? Answer. Curved free liquid surface has more area. It tends to become flat to minimise the surface area (property of surface tension). Hence pressure is not the same above and below the surface.
Question. 5. On which side of the liquid surface, pressure is more ? Answer. Pressure is more on the concave side of the free liquid surface.
Question.7. What is a capillary ? Answer. It is an open ended tube with very uniform fine bore.
Question.8.Why the liquid should be free from grease ? Answer. Grease reduces surface tension of liquid.
Question.9.Do all liquids rise in a capillary tube ? Answer. No, liquids which make a convex meniscus in capillary tube, are depressed. Mercury is depressed in glass capillary tube.
Question.11. Why do we prefer fresh tap water rather than pure distilled water for determination of surface tension ? Answer. Distilled water is slightly greasy and its surface tension will be less.
Question.12. What is surface tension of water ? Answer. It is 7.275 x 10 -2 N-m -1 at 20°C.
Question.13. Why do you measure the internal diameter of the capillary tube in two mutually perpendicular directions ? Answer. It is done to take the mean to eliminate the error if the bore is not circular.
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To determine the surface tension of a liquid by capillary rise method.
How do you define surface tension?
Surface tension is the property of a liquid, by virtue of which its free surface at rest behaves like an elastic skin or a stretched rubber membrane, with a tendency to contract so as to occupy minimum surface area. This property is caused by cohesion of molecules and is responsible for much of the behaviors of liquids.
The property of surface tension is revealed, for example, by the ability of some objects to float on the surface of water, even though they are denser than water. Surface tension is also seen in the ability of some insects, such as water striders, and even reptiles like basilisk, to run on the water’s surface.
The Theory Behind Surface Tension
Surface tension has been well- explained by the molecular theory of matter. According to this theory, cohesive forces among liquid molecules are responsible for the phenomenon of surface tension. The molecules well inside the liquid are attracted equally in all directions by the other molecules. The molecules on the surface experience an inward pull.
So, a network is formed against the inward pull, in order to move a molecule to the liquid surface. It results in a greater potential energy on surface molecules. In order to attain minimum potential energy and hence stable equilibrium, the free surface of the liquid tends to have the minimum surface area and thereby it behaves like a stretched membrane.
Surface tension is measured as the force acting normally per unit length on an imaginary line drawn on the free liquid surface at rest. It is represented by the symbol T (or S). It's S.I. The unit is Nm -1 and dimensional formula is M 1 L 0 T -2.
Capillarity in Liquids
When a capillary tube is dipped in a liquid, the liquid level either rises or falls in the capillary tube. The phenomena of rise or fall of a liquid level in a capillary tube is called capillarity or capillary action.
How do we define the surface tension of a liquid through the capillary rise method?
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 around the circumference of the points of contact.
Thus, surface tension;
Where, h - height of the liquid column above the liquid meniscus ρ - Density of the liquid r - Inner radius of the capillary tube θ - Angle of contact
Learning Outcomes
- Students understand the theory of the surface tension of liquids.
- Students correlate the property of surface tension with different natural phenomena.
- Students understand the concept of capillarity in liquids.
- They are able to relate surface tension and capillarity.
IMAGES
VIDEO
COMMENTS
Surface tension is the tendency of a liquid surface to shrink into the minimum surface area possible. The capillary rise method is one of the techniques to determine the surface tension of a liquid such as water. While experimenting with a capillary tube, it is observed that when a liquid rises in the tube, the weight of the liquid column is ...
The difference in the two readings (i.e., height of water meniscus and height of the tip of pointer) will give the capillary rise of the given liquid. We can repeat the experiment by changing the height of the wooden stand. To find the internal diameter of the capillary tube : Place the capillary tube horizontally on the adjustable stand.
We can define capillary action as a phenomenon where the ascension of liquids through a tube or cylinder takes place. This primarily occurs due to adhesive and cohesive forces. The liquid is drawn upward due to this interaction between the phenomena. The narrower the tube, the higher will the liquid rise.
CBSE Class 11 Lab Manual Chapter 4 To Study the Effect of Detergent on Surface Tension of Water by Observing Capillary Rise Download here in pdf format. These Lab M. Download CBSE Sample Paper 2024-25 for class 12th to 8th. ... With the help of this, they can successfully perform the experiments listed in the CBSE Class 11 Lab Manual.
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.
The capillary rise method is a common technique used to measure the surface tension of a liquid, such as water. When a capillary tube is placed in a liquid, the liquid will rise in the tube due to the surface tension acting along the circumference of the tube's contact points. Here, we'll delve deeper into this experiment and its findings.
1. Do the experiment in a well-lit place for example, near a window or use an incandescent bulb. 2. Clean the capillary tube and beaker successively in caustic soda and nitric acid and finally rinse thor oughly with water . 3. Fill the beaker with water and measure its temperature. 4. Clamp the capillary tu be near its upper end, keeping it ...
Viva Questions to determine the surface tension of water by capillary rise method. Physics Practical Class 11 Surface Tension Viva Questions with Answers. Login. Study Materials. ... Classwise Physics Experiments Viva Questions ; Physics MCQs. Class 12 Physics MCQs ; ... To Determine the Surface Tension of Water by Capillary Rise Method ...
end of a capillary tube of radius, r, is immersed in a liquid of density ρ. For sufficiently small capillaries, one observes a substantial rise of liquid to height, h, in the capillary, because of the force exerted on the liquid due to surface tension. Equilibrium occurs when the force of gravity on the volume of liquid balances the force due to
Diagrams. Procedure. (a) Setting the apparatus. 1. Place the adjustable height stand on the table and make its base horizontal by level-ling screws. 2. Take dirt and grease free water in an open dish with flat bottom and put it on the top of the stand. 3. Take three capillary tubes of different radii (ranging from 0.05 mm to 0.15 mm).
Adjust the vertical stand so that the capillary tube dips in the water. Find the capillary rise using a travelling microscope. Observe how capillary rise changes with the radius of the capillary tube. Figure 2: Experimental setup of Capillary rise using capillary tubes . Simulation Procedure. Select the method. Select the temperature.
The difference in the two readings (i.e., height of water meniscus and height of the tip of pointer) will give the capillary rise of the given liquid. We can repeat the experiment by changing the height of the wooden stand. To find the internal diameter of the capillary tube : Place the capillary tube horizontally on the adjustable stand.
The Physics Lab Manual Class 11 contains all the experiments and activities which students have to perform in the laboratory. CBSE Class 11 Physics Practical is provided here to help students prepare for the annual exams. The practical exam carries a total of 30 marks. ... To determine the surface tension of water by capillary rise method. 6 ...
Diagrams. Procedure. (a) Setting the apparatus. 1. Place the adjustable height stand on the table and make its base horizontal by level-ling screws. 2. Take dirt and grease free water in an open dish with flat bottom and put it on the top of the stand. 3. Take three capillary tubes of different radii (ranging from 0.05 mm to 0.15 mm).
Capillary Rise is given by, h= 4σ/ ρgd where, h is the height of rise, σ is the surface tension, ρ is the density of the liquid and d is the diameter of tube. Procedure i. Capillary tubes are well cleaned. ii. Place the panel in the receiver with a certain level of water iii. Place a cardboard between the capillary tubes. iv.
The difference in the two readings (i.e., height of water meniscus and height of the tip of pointer) will give the capillary rise of the given liquid. We can repeat the experiment by changing the height of the wooden stand. To find the internal diameter of the capillary tube : Place the capillary tube horizontally on the adjustable stand.
The phenomena of rise or fall of a liquid level in a capillary tube is called capillarity or capillary action. How do we define the surface tension of a liquid through the capillary rise method? 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 ...
18.357 Interfacial Phenomena, Lecture 8. 8. Capillary Rise. Capillary rise is one of the most well-known and vivid illustrations of capillarity. It is exploited in a number of biological processes, including drinking strategies of insects, birds and bats and plays an important role in a number of geophysical settings, including flow in porous ...
When the adhesive forces are greater than the cohesive forces between water molecules, the water tends to rise. The height to which the water rises is given by the following relation. h = 2σ / ρrg. where, h is the height of rising of liquid due to capillary action. σ is the surface tension of the liquid. ρ is the density of the liquid.