Some Basic Relations of Equilibrium Thermodynamics

For later purposes we need a few further basic relations of equilibrium thermodynamics. Let us therefore restrict ourselves in this section to thermodynamic systems which are in external equilibrium with respect to a coupling to bath system as well as in internal equilibrium with respect to chemical reactions. 

23) we have already introduced the concept of reversible changes of the entropy due to idealized reversible exchanges of heat as infinitely slow processes with negligible irreversible entropy production. This concept is immediately extended to include reversible changes of the entropy which may likewise be caused by infinitely slow exchanges of volume V and chemical components N.. In the course of such processes, the system is not removed from equilibrium but is passing through a continuous series of equilibrium states. This means that in each state of such processes the system is characterized by its entropy S as a function of U, V and 

Let dS be the reversible change of entropy as caused by such idealized reversible changes dU, dV, dNp i = 1, 2,. .. of the macro-variables. dS may now be expressed as 

Equation (3.53) is known as Gibbs fundamental relation. Transforming (3.53) into 

25) we have already introduced the free energy F of a thermodynamic system as F = U - TS (for equilibrium T = T ). Taking the total differential of F we obtain by inserting dU from (3.54) 

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