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 Incoming links: Jurin's law

Past exam of the quantum condensed matter course of the University of Cambridge / 2007 / Section A / A4 / d / Solution Created 2026-10-18 Updated 2026-10-20

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The liquid does not wet the glass because

cos 14 0^{\circ} < 0

. The liquid meniscus is convex, with the capillary mercury level depressed below the reservoir. Balancing vertical surface-tension force against the hydrostatic column gives Jurin's law, using the inner radius

r = 0.5 mm

h = \frac{2 γ cos θ}{ρ g r} = \frac{2 ( 0.436 ) cos 14 0 ^{\circ}}{( 1.35 \times 1 0 ^{4} ) ( 9.81 ) ( 5 \times 1 0 ^{- 4} )} = - 1.01 \times 1 0^{- 2} m .

(1)

Thus the depression is approximately $10.1 mm$ . The simple height law neglects small meniscus-volume corrections. Mercury's high surface tension reflects strong metallic bonding, not merely dispersion between weakly interacting molecular units.

Figure 1.
Nonwetting mercury is depressed in a glass capillary and has a convex meniscus
. Original schematic with the tube width enlarged relative to the vertical scale. The arrow marks the approximate hydrostatic depression; the drawn meniscus shape is schematic. **Details**.

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