Thermodynamic systems, however, are not closed in general and being open to the environment proceed at constant temperature. For T = constant and a reversible case, (3.7.2) may be written as dW = -d(U - TS) = -dF (3.7.3)
where F (= U -TS) is called the 'Free energy', a term first introduced by Helmholtz. For this reason, F is also sometimes called the Helmholtz potential. (3.7.3) simply states that at constant temperature, the decrease of free energy gives the maximum external work obtainable from a reversible system. In the general case,
where the sign of equality refers to the reversible case.
Now, if the volume does not change and the system is isothermal-isometric, §W = 0, and
For such a system, therefore, the free energy available for doing external work has its minimum value. This value is 0 at equilibrium.
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