Thermodynamic integration, free energy perturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has under- gone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon - systems under- going a change in volume/density - and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach. These results apply to systems with arbitrary particle interactions and densities. The application of this approach to the expansion/compression of particles confined within a vessel with a piston and within a periodic system is considered.