A dynamical definition of pressure for grand-canonical Gibbs measures in bounded regions Λ is rigorously discussed: It measures the momentum transferred to the walls of the container by the elastically colliding particles. The local pressureP(r, δΛ) so obtained is proportional to the temperature and the local density at the boundaries of Λ. This allows us to obtain a rigorous proof of the virial theorem of Clausius. In this picture the thermodynamic pressureP d (Λ) is obtained as the average ofP(r, δΛ) onδΛ. Its relationship with the usual equilibrium pressureP eq(Λ) = (βsΛ¦)−1lnZ Λ (Z Λ is the grand-canonical partition function) is then discussed. In the particular case in which the regions A are spheres, it is shown that Pd(Λ) converges in average so that, if the limit of Pd(Λ) exists, it equals Peq, the thermodynamic limit of the equilibrium pressure Peq(Λ). Finally, convergence ofP d(Λ) is proven to hold in the particular case of one-dimensional hard cores in the absence of phase transitions.