Question

5. Calculate the surface tension of water at 20 °C given that at that temperature water climbs to a height of 4.96 cm in a clean glass capillary tube of internal radius 0.300 mm. Given: The contact angle of water and clean glass is 0° and the density of water at 20 °C is 998.2 kg/m3 .

Answer 1

Step-by-step explanation:

Relation between density, height, and surface tension is as follows.

`\gamma = (1)/(2) \rho * g * h * r`

The given data is as follows.

Density, (
`\rho`) = 998.2
`kg/m^(3)`

g = 9.807 m/s

h = 4.96 cm =
`4.96 * 10^(-2) m` (as 1 m = 100 cm)

r = 0.3 mm =
`3 * 10^(-4) m` (as 1 m = 10000 mm)

Therefore, putting the given values into the above formula and calculate the surface tension as follows.

`\gamma = (1)/(2) \rho * g * h * r`

=
`(1)/(2) 998.2 kg/m^(3) * 9.807 m/s^(2) * 4.96 * 10^(-2)m * 3 * 10^(-4) m`

=
`72832 * 10^(-6) kg/s^(2)`

or, =
`7.28 * 10^(-2) N/m`

Thus, we can conclude that value of surface tension is
`7.28 * 10^(-2) N/m`.