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Answer :
The height of the liquid column in the second capillary should be 6 cm.
The capillary depression for mercury in a glass capillary tube 2 mm in diameter should be -0.75 cm.
The radius of the capillary where water rises 7 cm is estimated at 0.02 cm.
The height of a liquid column in a capillary is inversely proportional to the radius of the capillary, according to the capillary action equation:
h = 2σ cos θ / ρgr.
1. We can use the ratio of the radii of the two capillaries to calculate the height of the liquid column in the second capillary. The new height, h2, is given by:
h1*r1 = h2*r2
where h1, r1 are the initial height and radius, and h2, r2 are the final height and radius.
Thus, h2 = (h1*r1)/r2
= (9 cm * 0.02 cm) / 0.03 cm
= 6 cm.
2. To estimate the capillary depression, we utilize the capillary action equation:
h = 2σ cos θ / ρgr.
We know that for mercury,
cos θ = cos 140
= -0.766
ρ ~ 13.6 g/cm³, g ~ 980 cm/sec².
The radius of the capillary r = D/2 = 0.1 cm.
Thus, h = [2*0.514 N*m / (13600 kg*m³ * 9.8 m*s² * 0.001 m)]*100 cm/m
h = -0.75 cm. The minus sign indicates a depression.
3. To find the radius of the capillary, we rearrange the capillary action equation to solve for r:
r = 2σ cos θ / ρgh.
Using a surface tension,
σ = 70 dynes/cm
We get r = 2*70 dynes/cm * cos 0 / (1 g/cm³ * 980 cm/sec <>em²<>/em * 7 cm)
r = 0.02 cm.
Therefore,
The height of the liquid column in the second capillary should be 6 cm.
The capillary depression for mercury in a glass capillary tube 2 mm in diameter should be -0.75 cm.
The radius of the capillary where water rises 7 cm is estimated at 0.02 cm.
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