A tapering glass capillary tube A of length `0.1 m` has diameters `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 contact with liquid surface, the liquid rises `8 × 10^(-2)` m in the tube. In another experiment, in a 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//14) × 10^(4) kg//m^(3)` and the angle of contact is zero. Effect of temperature on the density of liquid and glass is negligible.

Answer

`-1.4xx10^(-4) N/(m^(@)C`