Question

A conical glass capillary tube A of length 0.1 m has diamters 10^–3 m and 5 × 10^–4 m at the ends. When it is just immersed in a liquid at 0°C with larger radius in constant with it, the liquid rises to 8 × 10^–2 m in the tube. In another cylindrical glass capillary tube B, when immersed in the same liquid at 0°C, the liquid rises to 6 × 10^–2 m height. The rise of liquid in tube B is only 5.5 × 10^–2 m when the liquid is at 50°C. Find the rate at which the surface tension changes with temperature considering the change to be linear. The density of liquid is (1/4) × 10⁴ kg/m³ and the angle of contact is zero. Effect of temp on the density of liquid and glass is negligible.

Answer 1

Let r₁ and r₂ be radii of upper and lower ends of the conical capillary tube. The radius r at the meniscus is given by

The surface tension at 0°C is given by

Considering the change in surface tension as linear, the change in surface tension with temp is given by

Negative sign shows that with rise in temp surface tension decreases.