  An exact equation for determining the Tolman length (TL) as a function of
radius is obtained and a computational procedure for solving it is proposed. As
a result of implementing this procedure, the dependences of the TL and surface
tension on radius are obtained for the drop and bubble cases and various
equations of state. As one of the results of the thermodynamic study, a new
equation for the dependence of surface tension on radius (curvature effect),
alternative to the corresponding Tolman equation and associated with the
spinodal point, is obtained. The Kelvin type equation for the equimolecular
radius is shown to be exact over the entire metastability region and serves as
the basis for the TL equation. The expansions of surface tension near the
spinodal and binodal points show that the correction to Rusanov s linear
asymptotics in the first case is a series in cubes of the radius, whereas a
series in curvature holds in the second case. As a result of the analysis of
these expansions, the fundamental impossibility to determine the curvature
effect analytically from the binodal point is established; the computational
procedure determines it from the spinodal point. It is shown that just the
characteristics of the system on the spinodal, mainly the TL value at zero
radius, determine the curvature effect. In general, the theory reveals a close
connection between surface and bulk properties.
