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

Explanation:

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

              $\gamma = \frac{1}{2} \rho \times g \times h \times r$

The given data is as follows.

        Density, ($\rho$) = 998.2 $kg/m^{3}$

         g = 9.807 m/s

         h = 4.96 cm = $4.96 \times 10^{-2} m$    (as 1 m = 100 cm)

         r = 0.3 mm = $3 \times 10^{-4} m$    (as 1 m = 10000 mm)

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

          $\gamma = \frac{1}{2} \rho \times g \times h \times r$

              = $\frac{1}{2} 998.2 kg/m^{3} \times 9.807 m/s^{2} \times 4.96 \times 10^{-2}m \times 3 \times 10^{-4} m$

              = $72832 \times 10^{-6} kg/s^{2}$

or,          = $7.28 \times 10^{-2} N/m$

Thus, we can conclude that value of surface tension is $7.28 \times 10^{-2} N/m$.