Work is energy related to a force acting over a distance. There are many different forms of work, but in chemistry we are interested in only two of them. Pressure volume work (or PV work), which is related to compression or expansion of materials. And electrical work, which is related to current flow and electrical potential. For now, we will focus all of our attention on PV work and we will address electrical work later on in the context of electrochemistry.
Pressure volume work is important when a system is changing volume. This is because in order to change its volume it will have to push against the force of the pressure that is exerted on the system. Since the atmosphere is always exerting pressure down upon us, any expansion is always acting against this force.
PV work is best visualized as a volume change of a gas in a cylinder with a movable piston. The pressure pushing down on the piston has some force per area. As the gas expands the piston is pushed upward and this requires some energy (a force acting across a distance). The work is equal to the force x distance. For a gas in a cylinder this works out to be the pressure x the change in volume.
Specifically, we will address the case of expansion or compression against a constant external pressure since this is a case that is typically important in chemistry. For this case
\[w = -P_{ex} \Delta V\]
where w is the work, \(P_{ex}\) is the external pressure and \(\Delta V = V_f - V_i\) is the change in the volume of the gas. The negative sign is to keep our sign convention for energy going into or out of the system. Expansion will lower the energy of the system (energy out). Since this process increases the volume, \(\Delta V\) will be positive. To make the work negative we add a negative sign. With a constant external pressure, if there is no change in volume then there is no work.
It should be noted that the work for expansion can depend on how the expansion is done (constant pressure, changing the pressure, one step, 20 steps...). We will be dealing almost exclusively with the case of the constant external pressure. However, you should realize that while the magnitude will change depending on the process, the sign will not. Expansion is always work out, so w<0. Finally, if there is not change in volume, then w = 0
It is important to be careful with your units when combining energies calculated for work and heat. Work almost always ends up with units for pressure times volume (an energy). For example, L-atm. You need to covert this to Joules in most cases. 101.325 J = 1 L-atm (also 100 J = 1 L-bar).