PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 88

and that it has its maximum in the state of thermodynamic equilibrium

dS= 0, [isolated system, reversible process] (3.59)

From this we arrive at the following conditions of thermodynamic equilibrium for the ther-
modynamic functionsS,U,H,F, andG

function condition of extreme kind of extreme

entropy dS= 0 [U, V] maximum

entropy dS= 0 [H, p] maximum

internal energy dU= 0 [S, V] minimum

enthalpy dH= 0 [S, p] minimum

Helmholtz energy dF= 0 [T, V] minimum

Gibbs energy dG= 0 [T, p] minimum

The conditions of the functions extremes given in the table above are called theextensive
criteria of equilibrium, and they may be used to derive the so-calledintensive criteria[see
7.2.0.1].

Note:Note the connection between the equations in the above table and the Gibbs equa-

tions (3.33) through (3.36). It follows from equation (3.33), e.g., that at [S, V], dU= 0,

and at [U, V], dS= 0.

Example

Ascertain the change in the Helmholtz energy during reversible and irreversible processes at

constant volume and temperature.