Question

A capillary tube 2mm in diameter is immersed in a beaker of mercury.The mercury level inside the tube is found to be 0.5cm below the levelof the reservoir. Determine the contact angle between the mercuryand the glass. (T m=0.4N/m, Pm = 13.6 x 103kg/m3).iffin nil if a glass capillary of diameter​

Answer 1

Answer:

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Answer 2

The contact angle between the mercury and the glass is 33.6°

Given:

Diameter of capillary tube = 2 mm.

Mercury level inside the tube = 0.5cm

To Find:

The contact angle between the mercury and the glass.

Solution:

The radius of the capillary tube, r = 1 mm = 1 x $10^{-3}$ m

Height h = 0.5cm = 0.5 x $10^{-2}$ m

Surface tension of mercury, T = 0.4 N/m

Density of mercury, ρ = 13.6 x $10^{3}$ kg/$m^{3}$

We know that

T = hρrg/ (2cosθ)

⇒ cosθ = hρrg/ (2T)

⇒ cosθ = ( 0.5 x $10^{-2}$ x  13.6 x $10^{3}$ x  1 x $10^{-3}$ x 9.8) / (2 x 0.4)= 0.833

⇒ θ = $cos^{-1}$ (0.833) = 33.6°

∴ The contact angle between the mercury and the glass is 33.6°.

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