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A conical glass capillary tube A of length 0.1 m has diameters 10 –3 m and 5 × 10–4 mat the ends.

When it is just immersed in a liquid at 0ºC with larger diameter in contact with it, the liquid rises by 8 × 10 –2 min the tube. In another cylindrical glass capillary tube B, when immersed in the same liquid at 0ºC, the liquid rises by 6 × 10 –2 m. The rise of liquid in tube B is only 5.5 × 10 –2 m when the liquid is at  50ºC. Find the rate at which the surface tension charges with temperature considering the change to be linear.The density of the liquid is(1/14) × 104 kg/m3 and the angle of contact is zero.Effect of temperature on the density of liquid and glass is negligible.

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

Surface tension of the liquid at 0ºC

If r´ is the radius of the cylindrical tube B, then at 0º C

and at 50ºC

Rate of change of surface tension with temperature, assumed constant for S (θ) as a linear function, will be

Thus, the surface tension decreases at the rate of 1.4 × 10–4 N/m per degree celsiusrise in temperature.

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