1.

The end of a capillary tube with a radius `r` is immersed in water. Is mechanical energy conserved when the water rises in the tube? The tube is suficiently long. If not calculate the energy change.

Answer» In the equilibrium position `(theta=0^@` for water and glass)
`2piTcos0^@=pir^(2)hrhog`
or `h=(2T)/(rhogr)`
Work done by surface tension `k=(2pirT)xxh=(4piT^(2))/(rhog)`
The potential energy of water in the tube `U=(pir^(2)hro)gh//2,` it is multiplied by `h//2` because the centrte of gravity of the water and the capillary tube is at a height `h//2`
`:. U=(2piT^(2))/(rhog)`
Thus it is seen that the mechanical energy is not conserved.
therefore, mechanical enegy loss `=(4piT^(2))/(rhog)-(2piT^(2))/(rhog)=(4piT^(2))/(rhog)`
This energy is converted into heat.


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