What does the Clausius inequality imply about the change in entropy?

The Clausius inequality states that for any spontaneous process, the change in entropy (dS) is greater than or equal to the heat transfer (dq) divided by the temperature (T). This relationship can be articulated mathematically as dS ≥ dq / T.

This inequality accounts for the fact that entropy is a measure of energy dispersal in a system, and it emphasizes that whenever a process is irreversible, the entropy of the system will increase more than what is calculated by the heat transfer over temperature. In an irreversible process, some energy becomes unavailable for doing work, resulting in a net increase in entropy beyond just the ratio of heat exchanged to temperature.

When a process is reversible, the equality holds true, which is why the inequality form allows the inclusion of real-world processes that cannot be modeled as reversible. Therefore, the correct interpretation of the Clausius inequality reflects the second law of thermodynamics and underscores how entropy accounts for the irreversibility of natural processes.