What is the work done in an expansion against constant external pressure according to the work equation?

The work done during an expansion against constant external pressure can be articulated through the relationship defined in thermodynamics. In this case, the formula W = -P_ext (V_f - V_i) is used, where:

• W represents the work done,

• P_ext is the external pressure,

• V_f is the final volume, and

• V_i is the initial volume.

When a system expands, the final volume (V_f) is greater than the initial volume (V_i), leading to a positive change in volume (V_f - V_i). The negative sign in the work equation indicates that work is being done by the system on the surroundings. Thus, for a typical expansion process where the volume increases, the work done by the system is considered negative because the system is losing energy in the form of work.

This understanding leads to the conclusion that option B accurately reflects the proper relationship for work done in a constant external pressure scenario. The formula shows that as the system expands (with the final volume greater than the initial), the work done is indeed a negative value, consistent with the energy loss from the system.