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The capillary rise at 20℃ in a clean glass tube of 1 mm diameter containing water is approximately
- a)15 mm
- b)50 mm
- c)20 mm
- d)30 mm
Correct answer is option 'D'. Can you explain this answer?
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The capillary rise at 20℃ in a clean glass tube of 1 mm diameter cont...
The capillary rise refers to the phenomenon where a liquid rises in a narrow tube due to the combination of adhesive and cohesive forces. In this case, we have a clean glass tube with a diameter of 1 mm containing water at 20℃. Let's understand why the correct answer is option 'D' (30 mm) through the following explanations:
Adhesive and Cohesive Forces:
- Adhesive forces: These are the attractive forces between the molecules of different substances. In this case, it refers to the attraction between the water molecules and the glass tube.
- Cohesive forces: These are the attractive forces between the molecules of the same substance. In this case, it refers to the attraction between the water molecules themselves.
Capillary Action:
- Capillary action occurs due to the combination of adhesive and cohesive forces. When a narrow tube is placed in a liquid, the liquid rises in the tube against the force of gravity.
- The height of capillary rise depends on various factors including the diameter of the tube, the surface tension of the liquid, and the angle of contact between the liquid and the tube.
Capillary Rise Formula:
- The capillary rise in a tube can be calculated using the following formula:
h = (2Tcosθ)/(ρgr)
where h is the capillary rise, T is the surface tension of the liquid, θ is the angle of contact, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.
Calculating Capillary Rise:
- In this case, we are given that the diameter of the tube is 1 mm, which means the radius is 0.5 mm or 0.0005 m.
- The surface tension of water at 20℃ is approximately 0.0728 N/m.
- The angle of contact between water and clean glass is close to zero, which means cosθ is approximately equal to 1.
- The density of water is 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².
- Substituting these values into the formula:
h = (2 * 0.0728 * 1)/(1000 * 9.8 * 0.0005)
h ≈ 0.0293 m
- Converting the capillary rise from meters to millimeters:
h ≈ 0.0293 * 1000 mm
h ≈ 29 mm
Therefore, the correct answer is option 'D' (30 mm), which is the closest approximation to the calculated capillary rise of 29 mm.
Adhesive and Cohesive Forces:
- Adhesive forces: These are the attractive forces between the molecules of different substances. In this case, it refers to the attraction between the water molecules and the glass tube.
- Cohesive forces: These are the attractive forces between the molecules of the same substance. In this case, it refers to the attraction between the water molecules themselves.
Capillary Action:
- Capillary action occurs due to the combination of adhesive and cohesive forces. When a narrow tube is placed in a liquid, the liquid rises in the tube against the force of gravity.
- The height of capillary rise depends on various factors including the diameter of the tube, the surface tension of the liquid, and the angle of contact between the liquid and the tube.
Capillary Rise Formula:
- The capillary rise in a tube can be calculated using the following formula:
h = (2Tcosθ)/(ρgr)
where h is the capillary rise, T is the surface tension of the liquid, θ is the angle of contact, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.
Calculating Capillary Rise:
- In this case, we are given that the diameter of the tube is 1 mm, which means the radius is 0.5 mm or 0.0005 m.
- The surface tension of water at 20℃ is approximately 0.0728 N/m.
- The angle of contact between water and clean glass is close to zero, which means cosθ is approximately equal to 1.
- The density of water is 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².
- Substituting these values into the formula:
h = (2 * 0.0728 * 1)/(1000 * 9.8 * 0.0005)
h ≈ 0.0293 m
- Converting the capillary rise from meters to millimeters:
h ≈ 0.0293 * 1000 mm
h ≈ 29 mm
Therefore, the correct answer is option 'D' (30 mm), which is the closest approximation to the calculated capillary rise of 29 mm.
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The capillary rise at 20℃ in a clean glass tube of 1 mm diameter containing water is approximatelya)15 mmb)50 mmc)20 mmd)30 mmCorrect answer is option 'D'. Can you explain this answer?
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