A glass capillary tube has a diameter of 2.00 mm and contains a small amount of liquid that forms a concave spherical meniscus. A particle of the liquid located where the liquid surface meets the tube wall is subject to a cohesive force of 4.00 N at an angle of 18.0 ∘ to the wall and an adhesive force of 6.47 N.
What is the radius of curvature of the meniscus?
To find the radius of curvature of the meniscus, we need to use the Young-Laplace equation, which relates the pressure difference across a curved liquid interface to the radius of curvature.
The Young-Laplace equation is given by:
ΔP = (2σ) / r
Where:
ΔP is the pressure difference across the curved interface.
σ is the surface tension of the liquid.
r is the radius of curvature.
In this case, the cohesive force (Fc) acting on the liquid particle is equal to the pressure difference across the meniscus, and the surface tension (σ) is related to the adhesive force (Fa) as:
Fc = ΔP = 2πrσ + Fa
Now, we can rearrange the equation to solve for the radius of curvature (r):
r = (Fc - Fa) / (2πσ)
Given that the cohesive force (Fc) is 4.00 N, the adhesive force (Fa) is 6.47 N, and the diameter of the tube is 2.00 mm (which gives us a radius of 1.00 mm or 0.001 m), we can substitute these values into the equation to find the radius of curvature (r):
r = (4.00 N - 6.47 N) / (2πσ)
Next, we need to calculate the surface tension (σ). To find this value, we would need additional information or look it up in a reference source or experimentally measured data, as it is specific to the liquid in the capillary tube.
Once we know the value of the surface tension (σ), we can substitute it into the equation to find the radius of curvature (r).