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 determine the angle of contact, we need to apply the concept of capillary action.
Capillary action is the phenomenon in which a liquid rises or falls in a narrow tube due to the balance between the adhesive forces between the liquid and the tube, and the cohesive forces within the liquid itself.
In this case, the water rises in the capillary tube. We can use the equation for capillary rise in a vertical tube:
h = (2T cosθ) / (ρgr)
where:
h is the height of 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 capillary tube.
Given that h = 7 cm (0.07 m) and the length of the tube above water is 5 cm (0.05 m), we can calculate the height of capillary rise inside the tube:
h' = h - (length above water)
h' = 0.07 m - 0.05 m
h' = 0.02 m
Assuming a clean glass capillary tube, the angle of contact (θ) is very close to zero degrees. This means that the water wets the glass surface completely, resulting in a low contact angle.
Therefore, the angle of contact in this case is approximately 0 degrees.
To find the angle of contact, we first need to understand the concept of capillary action.
Capillary action is the ability of a liquid to flow against gravity in a narrow space, such as a capillary tube. It occurs due to the combined effect of adhesive forces between the liquid and the tube's surface, as well as cohesive forces within the liquid itself.
In this case, we have a clean glass capillary tube being held vertically in water. The water rises inside the tube due to capillary action, creating a concave meniscus.
To find the angle of contact, we can use the formula:
cosθ = (h₁ - h₂) / L
Where:
θ is the angle of contact (between the surface of the liquid and the capillary tube)
h₁ is the initial height of the liquid above the capillary tube
h₂ is the final height of the liquid inside the capillary tube
L is the length of the capillary tube above the liquid level
Given the information in the question, we know that h₁ = 7cm, h₂ = 5cm, and L = 5cm.
Plugging these values into the formula, we have:
cosθ = (7cm - 5cm) / 5cm
cosθ = 2cm / 5cm
cosθ = 0.4
To find the angle of contact, we can take the inverse cosine of 0.4:
θ = cos^(-1)(0.4)
Using a calculator, we find that θ is approximately 66.42 degrees.
Therefore, the angle of contact in this scenario is approximately 66.42 degrees.