For which type of process is the equation dQ = TdS valid?

The equation (dQ = TdS) is valid specifically for reversible processes in thermodynamics. In this context, (dQ) represents the differential amount of heat added to the system, (T) is the absolute temperature of the system, and (dS) is the differential change in entropy.

In a reversible process, the system is always in equilibrium, which allows for the precise relationship between heat transfer and the change in entropy. This means that the heat exchange occurs slowly enough that the system can adjust to changes in state, maintaining thermodynamic equilibrium throughout the process. As a result, the heat added or removed can be defined accurately in relation to the entropy change.

In contrast, for irreversible processes, the relationship between heat and entropy is not as straightforward. Irreversibility often involves spontaneous processes and dissipation, leading to additional complexities where the equation (dQ = TdS) does not hold.

For isothermal and isobaric processes, while these conditions may occur within a reversible framework, they do not inherently imply the validity of the equation (dQ = TdS) without the additional condition of reversibility. Thus, the equation is most strictly applied in the context of reversible processes,