Chapter 3: The Second and Third Laws

The Second Law establishes that entropy, a measure of energy or matter dispersal, increases for any spontaneous change in an isolated system. Entropy is rigorously defined through reversible heat transfer as the quotient of heat absorbed and absolute temperature, and the Carnot cycle provides proof that entropy functions as a state variable depending only on initial and final conditions, not the path taken. The Boltzmann relationship connects entropy to molecular-level disorder by expressing it as the natural logarithm of the number of possible arrangements multiplied by Boltzmann's constant. To evaluate spontaneity more practically by considering only the system rather than the entire universe, two derived thermodynamic potentials are introduced: Helmholtz free energy, which predicts spontaneity at constant temperature and volume, and Gibbs free energy, which predicts spontaneity at constant temperature and pressure. The latter is particularly useful in chemistry since most reactions occur under these conditions. A significant result demonstrates that the decrease in Helmholtz energy equals the maximum useful work a system can perform at constant temperature. The chapter concludes by unifying the First and Second Laws through mathematical relationships called Maxwell relations, which reveal deep connections among pressure, temperature, volume, entropy, and other thermodynamic properties. These relations enable calculation of previously inaccessible quantities and facilitate derivation of how the Gibbs energy of ideal gases depends on pressure.