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What will be the diameter (in mm) of a water droplet, the pressure inside which is 0.05 N/cm2 greater than the outside pressure? (Take surface tension as 0.075 N/m)
- a)3
- b)0.6
- c)0.3
- d)6
Correct answer is option 'C'. Can you explain this answer?
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What will be the diameter (in mm) of a water droplet, the pressure ins...
Explanation: p = 4σ/d
where p = pressure difference between the liquid droplet and the surrounding medium, σ = surface tension and d = diameter of the droplet. Substituting all the values,
where p = pressure difference between the liquid droplet and the surrounding medium, σ = surface tension and d = diameter of the droplet. Substituting all the values,
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What will be the diameter (in mm) of a water droplet, the pressure ins...
To calculate the diameter of a water droplet, we need to consider the pressure difference and the surface tension of water.
Given:
Pressure difference = 0.05 N/cm²
Surface tension = 0.075 N/m
To find the diameter of the water droplet, we can use the Laplace's law, which relates the pressure difference across a curved interface to the surface tension and the radius of curvature.
Laplace's law can be written as:
ΔP = 2T/r
Where:
ΔP = pressure difference
T = surface tension
r = radius of curvature
Since we want to find the diameter, we need to find twice the radius of curvature.
Let's substitute the given values into the equation:
0.05 N/cm² = 2 * 0.075 N/m / (2r)
Simplifying the equation:
0.05 N/cm² = 0.075 N/m / r
Cross-multiplying:
0.05 N/cm² * r = 0.075 N/m
Converting units:
(0.05 N/cm² * 100 cm) * r = 0.075 N/m
5 N/m² * r = 0.075 N/m
Dividing both sides by 5 N/m²:
r = 0.075 N/m / 5 N/m²
r = 0.015 m
Since the radius we found is in meters, to find the diameter in millimeters, we need to multiply it by 1000.
diameter = 2 * 0.015 m * 1000 mm/m
diameter = 30 mm
Therefore, the diameter of the water droplet is 30 mm, which corresponds to option C.
Given:
Pressure difference = 0.05 N/cm²
Surface tension = 0.075 N/m
To find the diameter of the water droplet, we can use the Laplace's law, which relates the pressure difference across a curved interface to the surface tension and the radius of curvature.
Laplace's law can be written as:
ΔP = 2T/r
Where:
ΔP = pressure difference
T = surface tension
r = radius of curvature
Since we want to find the diameter, we need to find twice the radius of curvature.
Let's substitute the given values into the equation:
0.05 N/cm² = 2 * 0.075 N/m / (2r)
Simplifying the equation:
0.05 N/cm² = 0.075 N/m / r
Cross-multiplying:
0.05 N/cm² * r = 0.075 N/m
Converting units:
(0.05 N/cm² * 100 cm) * r = 0.075 N/m
5 N/m² * r = 0.075 N/m
Dividing both sides by 5 N/m²:
r = 0.075 N/m / 5 N/m²
r = 0.015 m
Since the radius we found is in meters, to find the diameter in millimeters, we need to multiply it by 1000.
diameter = 2 * 0.015 m * 1000 mm/m
diameter = 30 mm
Therefore, the diameter of the water droplet is 30 mm, which corresponds to option C.
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