What does the equation dw = -p_exdV represent?

The equation dw = -p_ex dV represents the work done during a process involving the expansion of a system against a constant external pressure. In this equation, dw refers to the infinitesimal amount of work done by the system, p_ex is the constant external pressure, and dV is the infinitesimal change in volume of the system.

When a system expands, it exerts pressure on its surroundings. If this pressure is constant, the work done during the expansion can be directly calculated using this relationship. The negative sign indicates that when the system does work on the surroundings (expand), it is losing energy, which is consistent with the convention that work done by the system is considered negative.

In thermodynamic terms, understanding the conditions under which work is done is crucial. For example, if the external pressure changes or if the process is not performed at a constant pressure, the equation would need to be altered to accurately describe that situation. This makes the specific representation of work against a constant external pressure particularly important in understanding various thermodynamic processes.