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A capillary tube is 20 cm long and has an internal diameter of 0.2 mm. If the capillary tube is placed in a beaker with water, calculate the final height rise. The surface tension of the water is 72 dynes/cm, and the contact angle is zero. The room temperature is 25°C.

Is the capillary tube oil-wet? Why?

Answer :

Final answer:

The final height rise of water in the capillary tube is approximately 2.11 cm.

Explanation:

When a capillary tube is placed in a beaker with water, the height to which the water will rise is determined by the capillary action formula:

\[h = \frac{2T \cos\theta}{r\rho g}\]

Where:

- \(h\) is the height rise

- \(T\) is the surface tension of water (72 dynes/cm)

- \(\theta\) is the contact angle (zero in this case, as mentioned)

- \(r\) is the radius of the capillary tube (half of the internal diameter, so 0.01 mm or 0.001 cm)

- \(\rho\) is the density of water (approximately 1 g/cm³)

- \(g\) is the acceleration due to gravity (980 cm/s²)

Now, plug in the values:

\[h = \frac{2 \cdot 72 \cdot 1}{0.001 \cdot 1 \cdot 980} = 2.11 \text{ cm}\]

So, the final height rise of water in the capillary tube is approximately 2.11 cm.

This indicates that the capillary tube is not oil-wet because the water rises within it, showing an affinity for water rather than oil. If it were oil-wet, the water would be repelled, and the height would not rise as observed.

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