A tapering glass capillary tube A of length 0.1 m has diameters ${10}^{-3}$ m and  $5\times {10}^{-4}m$  at the ends. When it is just immersed in a liquid at $0{}^{\circ }C$ with larger radius in contact with liquid surface, the liquid rises $8\times {10}^{-2}$ m in the tube. In another experiment, in the cylindrical glass capillary tube B, when immersed in the same liquid at $0{}^{\circ }C$ , the liquid rises to $6\times {10}^{-2}m$  height. The rise of liquid in tube B is only $5.5\times {10}^{-2}m$  when the liquid is at ${50}^{\circ }C$ . Find the rate at which the surface tension changes with temperature considering the changes to be linear. The density of liquid is  $\frac{1}{14}\times {10}^{4}kg/m^3$and the angle of contact is zero. Effect of temperature on the density of liquid and glass is negligible.