How the molecule of the water at surface has higher potential energy than the molecule of water inside bulk? How is the definition of potential energy (work done by me to put the charge where they are) used here?
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Consider a molecule which is not at the surface of the liquid and is far below the surface. It is attracted equally by the molecules surrounding it and thus sort of "balanced".
Now consider the molecule which is at the surface. Since it is attracted unequally from the sides (liquid below pulls more), so the molecule has to have some sort of "potential energy" to resist this force. So this molecule on the surface has higher energy than the molecules inside the surface.
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1$\begingroup$ The same phenomenon occurs on every phase separation surface if phases has different symmetry group of order parameter. $\endgroup$– kakazCommented Dec 23, 2017 at 17:32