Final answer:
No, the free expansion of an ideal gas cannot be represented on a pV diagram because it is an irreversible and non-quasi-static process where pressure and volume are not defined through intermediate states. The correct option is B.
Step-by-step explanation:
The question at hand is whether the free expansion of an ideal gas from an initial state (pi, Vi) to a final state (pf, Vf) can be represented on a pV diagram. Free expansion implies that the process is irreversible and non-quasi-static; that is, it does not go through intermediate equilibrium states.
Thus, pressure and volume during the transition cannot be measured or defined, making it impossible to represent this process with a specific curve on a pV diagram. This contrasts with isothermal, isobaric, and adiabatic processes, which can be depicted on a pV diagram because they are quasi-static, involving a series of infinitesimally small steps where the system remains in thermal equilibrium.