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# Capillary rise of mercury in a small diameter tube is proportional to (where, d = diameter of the tube, σ = surface tension of mercury)

A. d

B. $$\frac{1}{{\text{d}}}$$

C. $$\sigma$$

D. $$\frac{l}{\sigma }$$

### Solution(By Examveda Team)

The capillary rise of mercury in a small diameter tube is proportional to 1/d, where d is the diameter of the tube, and σ is the surface tension of mercury. Capillary rise occurs due to the balance between cohesive forces within the liquid and adhesive forces between the liquid and the tube wall. In a small diameter tube, the capillary rise is inversely proportional to the diameter of the tube.

Mathematically, the capillary rise h is given by the capillary rise equation:

h = (2σ cosθ) / (ρgr)

Where:

σ is the surface tension of the liquid (mercury).
θ is the contact angle between the liquid and the tube wall (usually close to 0° for mercury in glass).
ρ is the density of the liquid (mercury).
g is the acceleration due to gravity.
r is the radius of the tube (half of the diameter).

Since the radius r is directly proportional to 1/d, and the capillary rise is proportional to the radius r, the capillary rise is inversely proportional to the diameter d, which is represented by option B.

This Question Belongs to Chemical Engineering >> Fluid Mechanics

1. Capillary rise occurs due to the balance between the adhesive forces (attraction between the liquid and the solid surface) and the cohesive forces (attraction between the liquid molecules themselves). In the case of a small diameter tube, the curvature of the liquid meniscus is significant, and this curvature is governed by the balance between these forces.

The capillary rise height (h) is given by the formula:

h = (2 * σ * cosθ) / (ρ * g * d)

Where:

σ is the surface tension of the liquid (mercury in this case).
θ is the contact angle between the liquid and the solid surface.
ρ is the density of the liquid.
g is the acceleration due to gravity.
d is the diameter of the capillary tube.
The proportionality of capillary rise to surfacetension arises from the surface tension's role in determining the strength of the adhesive forces between the liquid and the solid. As surface tension increases, the liquid is more attracted to the solid surface, leading to a greater capillary rise.

2. it's wrong...correct answer is 1/d.

3. h1 r1 = h2 r2
Where h = capalary raise aur dipress in tube
R = radius of of capalary tube
So right answer is (b) 1/d

4. how

5. Plz explain

6. Explain it plz

7. How

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