Question

The surface tension of water was determined in a laboratory by using the drop weight method. 100 drops were released from a burette the inner diameter of whose opening is 1.8 mm

Answer 1

0.06563 N/m

The percentage difference between the calculated and tabulated value of water surface tension is 9.78%

Step-by-step explanation:

Solution:-

- Surface tension is the ability of any fluid to resist any external force due to cohesive nature of the fluid molecules.

- Surface tension ( γ ) is defined as the force imparted per unit length on the fluid.

γ = F / L

Where,

F: Force

L: The length over which force is felt

- The mass ( M = 3.78g ) of ( n = 100 ) water droplets are carefully burette. We need to determine the mass of a single droplet as follows:

m = M / n

m = 3.78 / 100

m = 0.0378 g

- Assuming the distance over which the drop falls is negligible and resistive forces are negligible. Then the only force acting on the droplet is due to gravity ( Weight of the droplet ):

F = m*g

F = 0.0378*9.81*10^-3

F = 0.000370818 N

- The length over which the force is felt can be modeled into a circular patch with diameter ( d ) = equal to the diameter ( d ) of the single water drop. The length ( L ) is defined as the circumference of the patch:

L = π*d

L = π*( 0.0018 )

L = 0.00565 m

- The surface tension would be:

γ = F / L

γ = 0.000370818 / 0.00565

γ = 0.06563 N / m

- The given value of water's surface tension is given as follows:

γa = 0.07275 N/m

- To compare the two values we will determine the percentage difference between the value evaluated and tabulated value as follows:

%
`diff = (0.07275- 0.06563)/(0.07275) * 100 \\\\diff = 9.78 \\\\`

- The percentage difference ( 9.78% ) between the two values is within practical limits of 10%. Hence, the calculated can be accepted.