• Tags: surface-tension, capillary, meniscus
• Difficulty: Moderate

Surface tension T causes liquid to rise in a narrow capillary tube. At equilibrium: upward surface tension force = weight of liquid column. T x 2pircos(theta) = rhogpi$r^2$h, giving T = rhogr$\frac{h}{2*cos(theta}$). For water-glass: theta ≈ 0 (complete wetting), so T = rhogr*h/2. Meniscus correction: the liquid above the flat surface forms a hemispherical meniscus of volume ≈ $\frac{2}{3}$pi$r^3$. Corrected height: $h_{eff}$ = h + r/3. Measure the capillary radius using a traveling microscope (view the bore end-on). Measure h as the difference between the meniscus top and the flat surface level. For mercury-glass: theta ≈ 140 degrees (obtuse), so the meniscus is convex and the mercury level depresses below the flat surface. Surface tension decreases with increasing temperature (molecular cohesion weakens).