An inequality that relates the change in entropy dS in an irreversible process to the heat supplied to the system dQ and the thermodynamic temperature T, i.e. dS ≥ dQ/T. In the case of an irreversible adiabatic change, where dQ = 0, the Clausius inequality has the form dS > 0, which means that for this type of change the entropy of the system must increase. The inequality is named after Rudolf Julius Emmanuel Clausius. The Clausius inequality can be used to demonstrate that entropy increases in such processes as the free expansion of a gas and the cooling of an initially hot substance.