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capillary effect



I have seen capillary tubes narrow enough to draw water
to a hight above 1 cm. Suppose that such tube is inserted
into water vertically and that only 0.5 cm is sticking out.
One might imagine that water flows continuously upward
in such tube. One can also imagine a tiny water wheel
working continuously, next to the tube.

Would this be a perpetual motion machine of the first kind
or of the second kind? I know that this will not happen. But
why not? Suppose that the easy answer "this would conflict
with laws of thermodynamics" is not acceptable.
Ludwik Kowalski