ABSTRACT
This is not a complete review of classical thermodynamics, containing only the fundamentals of the theory needed for the derivation of statistical mechanics. For example, the notion of temperature is accepted without elaborating on its origin. Two fundamental properties of a mechanical macroscopic system are not satisfied by a thermodynamic system due to the random nature of heat: (1) ignoring fiction, mechanical work, kinetic and potential energies can be converted to each other without a loss and (2) the dynamical state of a mechanical macroscopic system is deterministic These fundamental points constitute the basis for the development of thermodynamic and statistical mechanics theories. Presenting the notions of equilibrium, a reversible process, and an ideal gas, it is argued that the maximal mechanical work generated by an expanding vessel of ideal gas is by a reversible process. The first law is discussed together with a set of related equations, and the energy of an ideal gas in Joule’s experiment is shown to be, E = CVT + constant (CV – heat capacity). The entropy, S is defined and calculated for an ideal gas; the probabilistic nature of S (S ~ −lnP) is emphasized already in thermodynamics. The second law is stated and S is shown to be maximal in an isolated system at equilibrium. The third law is stated, and the various free energies are derived. It is shown that in an isothermal transformation from state a to state b the mechanical work, W, done on the surroundings is maximal for a reversible process, W ≤ A(a) −A(b) (A – the Helmholtz free energy). For a system at constant T that cannot do work, one obtains A(b) ≤ A(a), and thus at equilibrium, A = minimum(A[k*]) ([k*] is the optimal set of parameters for given T, V & N). The chapter ends with additional relations for the free energies (from Euler’s theorem) and the Gibbs-Duhem equation.
