Thermodynamics

State variables, the three laws, entropy, and the thermodynamic potentials.

Thermodynamics is the bookkeeping of energy, heat, and work in systems at equilibrium. From a handful of state variables and their equation of state, the first law accounts for energy, the heat capacities and the adiabatic exponent follow, the second and third laws introduce entropy and give time its direction, and the thermodynamic potentials package it all into the energy functions that select equilibrium.

• 3.1 State, equilibrium, and the equation of state — state variables, equilibrium, and the ideal-gas law $p = n k_B T$.
• 3.2 The first law — heat, work, internal energy, and the four standard processes.
• 3.3 Specific heats and the ratio γ — $c_v$, $c_p$, Mayer’s relation, and $\gamma$ from molecular structure.
• 3.4 Adiabatic processes and the speed of sound — $pV^\gamma = \text{const}$, the polytropic family, and $c^2 = \gamma RT/M$.
• 3.5 The second law and entropy — Carnot efficiency, entropy, $\Delta S \ge 0$, $S = k_B\ln W$, and the third law.
• 3.6 Enthalpy and the thermodynamic potentials — enthalpy, the Helmholtz and Gibbs free energies, natural variables, and Maxwell relations.