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Two capillary tubes with radii of 0.1 mm and 0.04 mm are immersed in a liquid with a density of 791.4 kg/m³. After the liquid rises in the capillary tubes, the height difference between the liquid columns is measured to be 8.9 cm. Assume a contact angle of 0°.

a) Calculate the surface tension of the liquid.
b) In which capillary tube does the liquid rise higher?

Answer :

a) Step 1: Calculate Surface Tension [tex](\(\gamma\))[/tex]:

Using the capillary rise equation:

[tex]\[ \gamma = \frac{hr\rho g}{2} \][/tex]

For the first capillary tube:

[tex]\[ \gamma_1 = \frac{0.089 \times 0.1 \times 10^{-3} \times 791.4 \times 9.81}{2} \][/tex]

For the second capillary tube:

[tex]\[ \gamma_2 = \frac{0.089 \times 0.04 \times 10^{-3} \times 791.4 \times 9.81}{2} \][/tex]

Step 2: Compare Liquid Rise:

The liquid will rise higher in the capillary tube with the smaller radius [tex](\(r_2 = 0.04 \times 10^{-3}\) m).[/tex]

Step 3: Calculate Surface Tension:

Substitute the calculated values into the surface tension equations to find the values of [tex]\(\gamma_1\) and \(\gamma_2\).[/tex]

b) The height of liquid rise in a capillary tube is inversely proportional to the radius of the tube. This means that the smaller the radius, the higher the liquid will rise. Therefore, in this case, the liquid will rise higher in the capillary tube with the smaller radius of 0.04 mm.

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