  In this work the curvature of Weinhold (thermodynamical) metric is studied in
the case of systems with two thermodynamical degrees of freedom. Conditions for
the Gauss curvature $R$ to be zero, positive or negative are worked out.
Signature change of the Weinhold metric and the corresponding singular behavior
of the curvature at the phase boundaries are studied. Cases of systems with the
constant $C_{v}$, including Ideal and Van der Waals gases, and that of
Berthelot gas are discussed in detail.
