Question

A conical glass capillary tube of length 0.1 m has diameters 10 ^–3 and 5 × 10 ^–4 m at the ends. When it is just immersed in a liquid at 0 º C with larger diameter in contact with it, the liquid rises to 8 × 10 ^{– 2} min the tube. If another cylindrical glass capillary tube B is immersed in the same liquid at 0 º C, the liquid rises to 6 × 10 ^–2 m height. The rise of liquid in the tube B is only 5.5 × 10 ^–2 m when the liquid is at 50 º C. Find the rate at which the surface tension changes with temperature considering the change to be linear.The density of the liquid is(1/14) × 10⁴ kg/m³ and angle of contact is zero. Effect of temperature on density of liquid and glass is negligible.

Answer 1

If r is the radius of the meniscus in the conical tube, then as shown in Fig.

i.e., r × 10⁴ – 2.5 = 0.2 × 2.5

i.e., r = 3 × 10–4 m

Now as capillarity is independent of the shape of tube so at same temp. θ = 0º C.

Now as from h= (2T/rρg) for cylindrical tube,

T₀ = 8.4 × 10^–2 N/m

Now as for a given tube and liquid T ∝ h (as T = hρgr/2)

So rate of change of surface tension with temperature assuming linearity,

= –1.4 × 10^–2 N/mºC

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