Surface tension of two liquids (having same densities), T₁ and T₂ , are measured using capillary rise method utilizing two tubes with inner radii of r₁ and r₂ where r₁>r₂ . The measured liquid heights in these tubes are h₁ and h₂ respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h₁ and h₂ and surfaces tensions T₁ and T₂ satisfy the relation:

Step-by-step solution

For capillary rise, the height of liquid in a tube is given by: h = 2T g r , where T is surface tension and r is the tube radius. For two liquids with equal density and contact angles: h₁ = 2T₁ g r₁ and h₂ = 2T₂ g r₂ Taking the ratio: h₁ h₂ = T₁ T₂ r₂ r₁ Since r₁ > r₂ , we have r₂ r₁ r₂ , and they have the same density, the empirical relation shows that both liquids rise to different heights inversely proportional to their radii. For liquids with the same density measured in different tubes, if the heights and radi