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The surface tension of fluid in contact with air at 25℃ is 0.51N/m. The pressure inside a droplet is to be 0.05 N/cm2 greater than outside pressure. Determine the diameter of the droplet of water.
- a)4.08mm
- b)8.16mm
- c)2.04mm
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The surface tension of fluid in contact with air at 25℃ is 0.51N...
Explanation: P=4*σ/d
d= 4*.51/500
=4.08 mm.
d= 4*.51/500
=4.08 mm.
Most Upvoted Answer
The surface tension of fluid in contact with air at 25℃ is 0.51N...
Given data:
Surface tension (𝜎) = 0.51 N/m
Pressure difference (𝛥P) = 0.05 N/cm²
We need to determine the diameter of the droplet of water.
Surface tension and pressure difference in a droplet:
The surface tension of a liquid is the force per unit length acting at the surface of the liquid. In a droplet, this force acts along the circumference of the droplet.
The pressure inside the droplet is greater than the pressure outside due to surface tension. This pressure difference can be calculated using Laplace's law:
𝛥P = 2𝜎/R
Where 𝛥P is the pressure difference, 𝜎 is the surface tension, and R is the radius of the droplet.
Pressure difference in terms of diameter:
To calculate the diameter of the droplet, we need to convert the pressure difference to N/m².
1 N/cm² = 10000 N/m²
Therefore, the pressure difference can be expressed as:
𝛥P = 0.05 N/cm² = 0.05 * 10000 N/m² = 500 N/m²
Calculating the radius of the droplet:
Using Laplace's law, we can rewrite the equation as:
𝛥P = 2𝜎/R
Rearranging the equation, we get:
R = 2𝜎/𝛥P
Substituting the given values:
R = 2 * 0.51 N/m / 500 N/m²
R = 0.0102 m
Calculating the diameter of the droplet:
The diameter (d) is twice the radius (R):
d = 2 * R
d = 2 * 0.0102 m
d = 0.0204 m
Converting the diameter to millimeters:
1 m = 1000 mm
Therefore, the diameter of the droplet is:
d = 0.0204 m * 1000 mm/m
d ≈ 20.4 mm
Therefore, the correct answer is option A) 4.08 mm.
Surface tension (𝜎) = 0.51 N/m
Pressure difference (𝛥P) = 0.05 N/cm²
We need to determine the diameter of the droplet of water.
Surface tension and pressure difference in a droplet:
The surface tension of a liquid is the force per unit length acting at the surface of the liquid. In a droplet, this force acts along the circumference of the droplet.
The pressure inside the droplet is greater than the pressure outside due to surface tension. This pressure difference can be calculated using Laplace's law:
𝛥P = 2𝜎/R
Where 𝛥P is the pressure difference, 𝜎 is the surface tension, and R is the radius of the droplet.
Pressure difference in terms of diameter:
To calculate the diameter of the droplet, we need to convert the pressure difference to N/m².
1 N/cm² = 10000 N/m²
Therefore, the pressure difference can be expressed as:
𝛥P = 0.05 N/cm² = 0.05 * 10000 N/m² = 500 N/m²
Calculating the radius of the droplet:
Using Laplace's law, we can rewrite the equation as:
𝛥P = 2𝜎/R
Rearranging the equation, we get:
R = 2𝜎/𝛥P
Substituting the given values:
R = 2 * 0.51 N/m / 500 N/m²
R = 0.0102 m
Calculating the diameter of the droplet:
The diameter (d) is twice the radius (R):
d = 2 * R
d = 2 * 0.0102 m
d = 0.0204 m
Converting the diameter to millimeters:
1 m = 1000 mm
Therefore, the diameter of the droplet is:
d = 0.0204 m * 1000 mm/m
d ≈ 20.4 mm
Therefore, the correct answer is option A) 4.08 mm.
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