A glass capillary tube is dipped vertically in a liquid and the entire system is slowly heated. It is observed that the height of the liquid column in the capillary remains exactly constant despite the increase in temperature. If the coefficient of linear expansion of the glass is _g , the coefficient of volume expansion of the liquid is , and the surface tension of the liquid varies with temperature rise T as S = S₀

Step-by-step solution

The height h of the liquid in the capillary tube is given by: h = 2S g r Taking the natural logarithm and differentiating to find the fractional change for a small temperature rise T : h h = S S - - r r From the given relation for surface tension S = S₀(1 - k T) , the fractional change is: S S = -k T The density of the liquid changes with temperature due to volume expansion. Since = ₀ 1 + T ₀(1 - T) , we have: = - T The radius of the glass capillary expands linearly with temperature: r r = _g T Substitute these int