Overview of the fundamental principles and laws of thermodynamics, including concepts such as entropy, energy transfer, and equilibrium.
Introduction to Advanced Thermodynamics
Graduate‑level overview – concise, organized, and ready for study or presentation.
| Concept | Classical Definition | Advanced Extension |
|---|---|---|
| System & Surroundings | Closed, open, isolated | Control volume with moving boundaries; non‑equilibrium reservoirs |
| State Variables | (P, V, T, n) (intensive) and (U, H, S, G) (extensive) | Inclusion of internal variables (e.g., order parameters, defect densities) and non‑equilibrium potentials |
| Equation of State | Ideal gas, Van der Waals, etc. | Multi‑parameter equations (e.g., cubic‑plus‑association, SAFT) for complex fluids and mixtures |
| First Law | (\Delta U = Q - W) | Differential form with mass fluxes and chemical work: (\mathrm{d}U = \delta Q - \delta W + \sum_i \mu_i ,\mathrm{d}n_i) |
| Second Law | (\Delta S \ge 0) | Entropy production (\sigma = \dot S_{\text{gen}} \ge 0) expressed via flux‑force pairs (Onsager relations) |
| Potential | Natural Variables | Typical Use |
|---|---|---|
| Internal Energy (U(S,V,{n_i})) | (S, V, n_i) | Fundamental description; basis for Legendre transforms |
| Enthalpy (H(S,P,{n_i}) = U + PV) | (S, P, n_i) | Constant‑pressure processes, flow work |
| Helmholtz Free Energy (A(T,V,{n_i}) = U - TS) | (T, V, n_i) | Canonical ensemble, phase stability at fixed (T,V) |
| Gibbs Free Energy (G(T,P,{n_i}) = H - TS) | (T, P, n_i) | Isothermal‑isobaric systems, chemical equilibrium |
| Massieu–Planck Functions (\Phi = -A/kT) | (\beta = 1/kT) | Statistical‑mechanical link; convenient for Monte‑Carlo sampling |
| Exergy (Available Work) (B = U + P_0V - T_0S) | (P_0,T_0) (environment) | Efficiency analysis, irreversibility quantification |
Key point: Advanced thermodynamics often works with Legendre‑transformed potentials that match the constraints of the problem (e.g., open systems at constant temperature and pressure → Gibbs free energy).
[ \frac{\partial s}{\partial t} + \nabla!\cdot!\mathbf{J}_s = \sigma \qquad (\sigma \ge 0) ]