  The necessary conditions to derive the quantum VdW EoS with hard-core
repulsion from the quantum partition are discussed. On a plausible example it
is shown that an alternative way to account correctly for the 3-rd virial
coefficient of classical hard spheres leads to inconsistencies. The
multicomponent formulation of the quantum VdW EoS with hard-core repulsion is
derived within a self-consisting approximation. For practical applications it
is simplified, extended to higher densities and generalized to the case of hard
convex bodies of any dimension $D\ge 2$.
