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pressure.
-- A lot of wet area created at boundary at outer radius: R dTheta
-- A little wet area destroyed at boundary at inner radius: r dTheta
-- Balance of wet area destroyed by shrinkage underwater: (R-r) dTheta
Area corresponds to energy. The area balances. The energy balances. No
perpetual motion machine.
4) The work done by the meniscus is real. It is just the boundary term
necessary to balance the area shrinkage.
Surface tension (force per unit length) is related to interfacial energy
(energy per unit area) in the same way that gas pressure (force per unit
area) is related to energy density (energy per unit volume). It's a
boundary term.
To say it another way: surface tension is the Flatland equivalent of
Being able to see the connection between a boundary term and the
corresponding integral quantity comes in handy in lots of situations. For
instance, Bernoulli's principle is easier to understand in terms of energy
than pressure.