The surface tension is related to the derivative of the Helmholtz energy by the equations
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Note: Only when
is
equal to the
surface (excess) Helmholtz energy per unit area. In general, for a multicomponent system it is not possible to define either an interfacial layer, or a Gibbs surface, for which this condition is satisfied. However, it is satisfied automatically when the system exhibits an adsorption azeotrope at which all the
are zero.
For a one-component system, treated in terms of a Gibbs surface it is always possible to choose this surface so that
, so that the surface tension is equal to the value of
relative to this surface; on the other hand
must always be positive for an interfacial layer so that
and
can never be equated.
The surface excess entropy is given by