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Surface tension, surface Helmholtz and Gibbs energies, and entropies

The surface tension is related to the derivative of the Helmholtz energy by the equations

where in the last equality is the Helmholtz energy of the whole system, and
and refer to the volumes of the bulk phases relative to the Gibbs surface; and to the derivative of the Gibbs energy by the equations

Expressed in terms of integral quantities
or
Under equilibrium conditions the superscripts and attached to the terms may be omitted.
*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

** Next:** Solid adsorbent/gas interface: characteristic
** Up:** MECHANICAL AND THERMODYNAMIC PROPERTIES
** Previous:** Surface chemical potentials
** Contents**
2002-09-05