The Young-Dupre equation for the work of adhesion of a liquid drop to a solid surface, where the solid surface is in equilibrium with the vapor of the liquid, is given as W = (gamma L)(1 + cos theta), where (gamma L) is the surface tension of the liquid and theta the contact angle. This work (W) has generally been identified with the free energy of adhesion. It is shown here that it constitutes the total work of adhesion only under the artificial condition that the sessile drop retains its shape after detaching from the solid surface. Under "real conditions, W represents only one component of the total free-energy change taking place when a drop is separated from, or attached to, a vapor-equilibrated smooth solid surface. In the present work, a Net Free Energy of Adhesion, Delta F-N, is derived which gives the total free energy necessary to separate a sessile drop from a smooth solid surface to form a free sphere (its negative, of course, is the free energy of attachment of the sphere). It is given by Delta F-N = pi r(2) (gamma L)[(2a/sin theta)(2/3) - alpha], where r is the radius of the solid-liquid interface and a, called the "effective area", is [2/(1 + cos theta)] - cos theta. The Net Free Energy of Adhesion and Young-Dupre work of adhesion are compared as functions of the contact angle. This is done for systems of constant solid-liquid interfacial area and for systems of constant drop volume.