A clean glass capillary tube is held vertically in water raised to a height of 7cm. The tube is down depressed and only 5cm of its length is above water. What will be the angle of contact?
To find the angle of contact, we will use the concept of capillary rise.
The capillary rise in a clean glass capillary tube can be given by the equation:
h = (2σ cos θ) / (ρgR)
Where:
h = height of capillary rise
σ = surface tension of the liquid
θ = angle of contact
ρ = density of the liquid
g = acceleration due to gravity
R = radius of the capillary tube
In this scenario, we have the following information:
h = 7 cm (the height of the water column)
R = radius of the capillary tube (unknown)
h' = 5 cm (the length of the tube above water)
First, we need to find the radius of the capillary tube. We can do this by assuming a value for R and iterating until we find a value that yields the correct height above the water.
Let's start by assuming a value of R and calculating the height of capillary rise using the equation mentioned earlier.
1. Assume a value for R (e.g., 0.1 cm).
2. Calculate the capillary rise using the equation: h = (2σ cos θ) / (ρgR).
3. Subtract this value from the total height above the water to get the remaining length of the tube submerged: h_remaining = h' - h.
4. If the remaining length is positive, the assumed radius is too small. Increase the assumed radius and go back to step 2.
5. If the remaining length is negative or very close to zero, the assumed radius is close enough. Continue to step 6.
6. Calculate the angle of contact, θ, using the equation: θ = arccos((ρgh) / (2σR)).
Repeat this process, refining the assumed radius each time until you find a value that gives a remaining length very close to zero. The corresponding angle of contact will be the answer to the problem.