This paper is yet another study dealing with subtle variations that may be necessary in both methods of simulation and analytical computation of statistical thermodynamic phenomena in nanosystems, especially fluid nanosystems. In the present paper, we deal with the use of the virial in the simulation of the pressure of a nanosystem. Not surprisingly, we find that the use of the virial in this endeavor requires a careful definition of the boundary of the system that includes the potential specifying the interaction of the molecules with that boundary. Without these precautions, when the system is small enough (nanovolumes and less than 100 molecules), the conventional means of using the virial in a Monte Carlo simulation does not yield the experimental thermodynamic pressure, i.e., the pressure measured on the outside of the boundary. The institution of these precautions is generally a nontrivial task. However, there is one case in which the difficulty is minimal. This is the theoretically important case in which the molecules interact with the boundary or "wall" of a container enclosing the system as hard molecules interacting with a hard wall. In the present paper, this problem is studied in depth. However, here it can be mentioned that in this case the problem arises because the virial refers to the volume available to the center of masses of the molecules which differs from the "thermodynamic" volume that encloses the molecules. The error generated by this difference is entirely negligible for a macroscopic system but can be extremely large for a nanosystem. On the basis of this understanding we are able to resolve a puzzle associated with an earlier study of a model (not relying on an intermolecular potential) devised for the calculation of the thermodynamic behavior of a small number of molecules enclosed in a small container.