Capillary Rise in Glass Tube

Capillary rise is the phenomenon of a liquid rising up in a narrow tube due to the cohesive forces between the liquid molecules and the adhesive forces between the liquid and the tube. The height of the liquid rise depends on various factors such as the diameter of the tube, the surface tension of the liquid, the contact angle between the liquid and the tube, and the temperature of the system.

Given Data

Diameter of the tube = 1 mm
Temperature of the system = 20°C
Liquid = Water

Calculation

The capillary rise in a clean glass tube of 1 mm diameter containing water at 20°C can be calculated using the following formula:

h = (2T cosθ)/ρgr

where,
h = height of the rise
T = surface tension of the liquid
θ = contact angle between the liquid and the tube
ρ = density of the liquid
g = acceleration due to gravity
r = radius of the tube

At 20°C, the surface tension of water is 72.8 mN/m and the density of water is 1000 kg/m^3. The contact angle between water and clean glass is approximately 0°. Therefore, the capillary rise can be calculated as:

h = (2 × 72.8 × cos0°)/(1000 × 9.81 × 0.5)
h = 29.5 mm

Therefore, the capillary rise at 20°C in a clean glass tube of 1 mm diameter containing water is approximately 30 mm (option D).

Conclusion

The capillary rise in a clean glass tube of 1 mm diameter containing water at 20°C can be calculated using the formula h = (2T cosθ)/ρgr. The capillary rise is approximately 30 mm.

For water and glass combination theta= 0 degree and surface tension= 0.0725 so H= (4 x surface tension x cos theta)/ (density x g x D) H = (4x.0725xcos0)÷(1000x9.81x0.001) H= 0.029m H= 30 mm option D is correct.