It is a well known model of either fully ionized matter or of simple metals, the system which consists of an assembly of point charges (either ions or electrons) immersed in a neutralizing background and which was introduced by E. Wigner in 1938. In the last decades, this model has given rise to extensive numerical, heuristic and rigourous investigations. However, the fact that, until recently, most of the many-body theoretical investigations and of the numerical simulations (particularly in 2 and 3 D.) have been carried out on systems subject to periodic boundary conditions, has not permitted to consider the questions dealt with in this paper. We report new results on the equation of state of the classical version of this model, known as one component plasma, obtained by imposing free boundary conditions on the system, i.e. by confining the particles in a given domain [1,5]. These conditions enable be the investigation of the physically meaningfull kinetic pressure, i.e. the pressure due to the transfer of momentum flow of the particles at the walls of the domain with the background being considered as strictly passive. It is shown i) that the kinetic pressure is equal to the virial pressure ; ii) that it consists always of the thermal pressure (erroneously called virial pressure in the litterature), plus an excess pressure which can be analyzed in therms of a wall part and a bulk part ; iii) that, in the thermodynamic limit, the bulk part of the excess pressure is a linear functional of the long range order parameter (periodic charge density), It is pointed out that since the kinetic pressure is ⩾ 0 while the thermal pressure becomes < 0, in all dimensions for low enough temperatures, then the excess pressure has to make up for the difference. This means in particular that, in the ground state, the excess pressure compensates exactly the Madelung pressure. Theoretical and numerical results obtained from molecular dynamics simulations (1 D. [2, 3]) and preliminary results from Monte-Carlo simulations (2 D. [4], and 3 D. [5]) are presented for high and low temperatures where particle clustering is observed.