  Due to the non-independence of entropy and thermodynamic volume for
spherically symmetric black holes in the AdS spacetime, when applying the
Ruppeiner thermodynamic geometry theory to these black holes, we often
encounter an unavoidable problem of the singularity about the line element of
thermodynamic geometry. In this paper, we propose a basic and natural scheme
for dealing with the thermodynamic geometry of spherically symmetric AdS black
holes. We point out that enthalpy, not internal energy, is the fundamental
thermodynamic characteristic function for the Ruppeiner thermodynamic geometry.
Based on this fact, we give the specific forms of the line element of
thermodynamic geometry for Schwarzschild AdS (SAdS) black hole in different
phase spaces and the results show that the thermodynamic curvatures obtained in
different phase spaces are equivalent. It is shown that the thermodynamic
curvature is negative which implies that the attractive interaction dominates
between black hole molecules for the SAdS black hole. Meanwhile we also give an
approximate expression of the thermodynamic curvature of the Schwarzschild
black hole which indicates that the black hole is dominated by repulsion on low
temperature region and by attraction on high temperature region.
