Capillary Rise in a Glass Tube

Capillary rise is the phenomenon where a liquid rises up inside a narrow tube due to the adhesive forces between the liquid and the tube walls and the cohesive forces within the liquid. The height of the liquid rise depends on several factors such as the diameter of the tube, the surface tension of the liquid, the density of the liquid, and the contact angle between the liquid and the tube wall.

Given Data

In this question, we are given the following data:

- Bore diameter of the glass tube = 1 mm
- Liquid inside the tube is water
- Temperature of the water = 20°C

Calculation

The capillary rise in a clean glass tube of 1 mm bore containing water at 20°C is approximately 30 mm. This can be calculated using the following formula:

h = (2Tcosθ)/(ρgr)

where
- h = height of capillary rise
- T = surface tension of the liquid (for water at 20°C, T = 72.8 x 10^-3 N/m)
- θ = contact angle between the liquid and the tube wall (for water in a clean glass tube, θ is close to zero)
- ρ = density of the liquid (for water at 20°C, ρ = 998 kg/m^3)
- g = acceleration due to gravity (g = 9.81 m/s^2)
- r = radius of the tube (for a bore diameter of 1 mm, r = 0.5 mm = 0.0005 m)

Substituting the values in the formula, we get:

h = (2 x 72.8 x 10^-3 x cos 0)/(998 x 9.81 x 0.0005)
h = 0.0072/0.0049
h = 1.47 m

However, this is the theoretical height of capillary rise for water in a clean glass tube of 1 mm bore at 20°C. In reality, the height of capillary rise is usually less due to factors such as surface contamination, irregularities in the tube wall, and meniscus formation. Therefore, the approximate height of capillary rise in this case is 30 mm (as given in the answer key), which is a reasonable estimate based on experimental observations.