  We show that to investigate the thermodynamic properties of charged phantom
spherically symmetric anti-de-Sitter black holes, it is necessary to consider
the cosmological constant as a thermodynamic variable so that the corresponding
fundamental equation is a homogeneous function defined on an extended
equilibrium space. We explore all the thermodynamic properties of this class of
black holes by using the classical physical approach, based upon the analysis
of the fundamental equation, and the alternative mathematical approach as
proposed in geometrothermodynamics. We show that both approaches are compatible
and lead to equivalent results.
