Second Law of Thermodynamics

The second law of thermodynamics is stated as the existence of an extensive function of state called the entropy that can only increase for an isolated system. Equilibrium is reached at maximum entropy. Reciprocal absolute temperature is defined as entropy change with energy. Entropy is additive for a composite system. Heat added to a chemically closed system increases entropy by an amount greater than the ratio of the heat to the absolute temperature for an irreversible process; entropy equals that ratio for a reversible process. We relate entropy to its historical roots including other postulates and the Carnot cycle for an ideal gas. The second law plus the first law establish a fundamental equation to calculate entropy changes as a function of state. Reversible and irreversible expansion of an ideal gas are illustrated. Enthalpy and entropy changes are calculated for an isobaric melting of ice. Entropy is related to quantum microstates of a system via probability of a macrostate.