A glass capillary tube with a radius of 0.2 mm is inserted into an open container filled with an unknown liquid, and the meniscus has an appearance as shown in the figure. It is found that the surface tension causes the liquid in the tube to rise a distance of 4 cm relative to the surface of the liquid outside the tube. If the density of the liquid is 1200 kg/m3, find the surface tension.
To find the surface tension, we can use the concept of capillary rise. The capillary rise is determined by the balance between the surface tension and the weight of the liquid column in the capillary tube.
First, let's calculate the height of the liquid column in the capillary tube. The height can be determined using the formula for capillary rise:
h = (2 * T) / (ρ * g * r)
where:
h = height of the liquid column in the capillary tube
T = surface tension
ρ = density of the liquid
g = acceleration due to gravity
r = radius of the capillary tube
In this case, we are given:
h = 4 cm = 0.04 m (height of the liquid column)
ρ = 1200 kg/m3 (density of the liquid)
r = 0.2 mm = 0.0002 m (radius of the capillary tube)
g = 9.8 m/s2 (acceleration due to gravity)
Now, we can rearrange the formula to solve for surface tension (T):
T = (h * ρ * g * r) / 2
Plugging in the given values:
T = (0.04 * 1200 * 9.8 * 0.0002) / 2
Calculating the value:
T = 0.09408 N/m (surface tension)
Therefore, the surface tension of the unknown liquid is approximately 0.09408 N/m.