This expression is the Clausius inequality. It will prove to be of great importance for
the discussion of the spontaneity of chemical reactions, as we shall see in Section 3.5.
• A brief illustration
Consider the transfer of energy as heat from one system—the hot source—at a temperature
Th to another system—the cold sink—at a temperature Tc (Fig. 3.10). When |dq|
leaves the hot source (so dqh < 0), the Clausius inequality implies that dS ≥ dqh/Th. When
|dq| enters the cold sink the Clausius inequality implies that dS ≥ dqc /Tc (with dqc > 0).
Overall, therefore