The entropy change \(\Delta{S}\) in an isothermal expansion also depends on the temperature \(T\). For a given quantity of heat \(Q\), the increase in disorder is greater if the system is at a low temperature (so the molecules are moving slowly and are relatively well ordered to start with) than if the system is at a high temperature (so the molecules are moving rapidly in a relatively disordered state). We conclude that the entropy change \(\Delta{S}\) in this reversible isothermal process is inversely proportional to the Kelvin temperature \(T\).
Putting these ideas together, we define the entropy change \(\Delta{S}\) in a reversible isothermal process as