When is dS equal to zero during a process?

The change in entropy, denoted as dS, is equal to zero during cyclic processes and reversible processes due to the nature of these processes. In a cyclic process, a system returns to its original state after completing a series of changes, meaning that the net change in entropy for the system is zero, as there is no overall change in the system’s energy or state.

In reversible processes, which are idealized processes that can return to their initial state without any change in the surroundings, the total change in entropy of the system and surroundings also results in no net change. These processes are conducted quasi-statically, and thus, they maintain equilibrium at every stage, allowing for the entropy changes to balance out perfectly.

In contrast, exothermic reactions, irreversible processes, and adiabatic processes involve energy transformations or changes that typically result in an increase or decrease in entropy, depending on the specifics of the process. Therefore, the condition of dS being equal to zero is unique to cyclic and reversible actions. This understanding is crucial in thermodynamics, particularly in analyzing the efficiency and feasibility of reactions and processes.