By Daniel V. Schroeder

This article appears at thermodynamics and statistical mechanics. half I introduces suggestions of thermodynamics and statistical mechanics from a unified view. elements II and III discover additional functions of classical thermodynamics and statistical mechanics. all through, the emphasis is on real-world functions.

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**Example text**

Generalization of the notion of entropy We have introduced the concept of entropy with regard to the heat transfer or certain irreversible transformations do not lead to the creation of heat. Consider, for example, an irreversible athermic and isochoric reaction taking place in an isolated system. 1: dU TdS PdV Σμ dn i TdS dF As the system is isolated: dU 0 so dS In the same way that, at constant T and P, a chemical reaction is spontaneous only if ΔG < 0, similarly, at constant T and V, a spontaneous reaction is only possible if ΔF < 0.

Let us give a simple example of a system out of equilibrium but steady. Consider 2 reservoirs R1 and R2 at fixed temperatures T1 and T2 with T1 > T2. If the heat-transfer coefficient H is constant and the surface of contact A between the two reservoirs is constant, the heat flux from R1 to R2 is constant. HA T T const. The rate of increase of the entropy of the ensemble Σ of reservoirs R1 and R2 is also constant, because: A Logical Presentation of Thermodynamics 31 This state is steady because the heat flux is fixed, but it is not a state of equilibrium, because the system’s entropy increases.

1) The Helmholtz energy F is a potential Consider a system which exchanges heat with the outside, but not work or material, in a transformation which is not necessarily reversible. 3]: dU dF dU That is to say: dF 0 Thus, in these precise conditions: T const. V const. (no work exchanged) The negative variation of F stems from the positive variation of S. Thus, the Helmholtz energy F is a thermodynamic potential whose decrease yields a stable equilibrium characterized by the minimum of F: δF 0 and δ F 0 The stresses of constant temperature and volume could, a priori, exist in a thermostatic autoclave on condition that the volume of the dense phases (liquid and any solids) remain constant.