Physical Chemistry Third Edition

156 4 The Thermodynamics of Real Systems

Once a system has reached equilibrium, its state is independent of how that state

was reached. The Gibbs energy is at a minimum if processes at constantTandPare

considered. The Helmholtz energy is at a minimum if processes at constantTandVare

considered. If a simple closed system is at constantTandPbut not yet at equilibrium,

a spontaneous process could possibly increase the value ofA, but must decrease the

value ofG. If a simple closed system is at constantTandVbut is not yet at equilibrium,

a spontaneous process could possibly increase the value ofG, but must decrease the

value ofA.

Maximum Work

We now seek criteria for the maximum work that can be done on the surroundings by

a closed system. For a system at constant temperature, Eq. (4.1-5) is

dU−TdS−dwdA−dw≤0(Tconstant) (4.1-24)

This is the same as

dA≤dw (Tconstant) (4.1-25)

For a finite process at constant temperature

∆A≤w (Tconstant) (4.1-26)

At constant temperature, the Helmholtz energy of a system can be increased by doing

work on the system, but∆Acannot exceedw. Alternatively, the system can do work

on the surroundings by lowering its Helmholtz energy, but the work done on the sur-

roundings is limited by

dwsurr≤−dA (Tconstant) (4.1-27)

For a finite process at constant temperature

wsurr≤−∆A (Tconstant) (4.1-28)

A system that is not a simple system can exchange work with the surroundings in

different ways. We write

dw−P(transmitted)dV+dwnet (4.1-29)

The term−P(transmitted)dVrepresents the work that can be done on the system by

changing its volume. We now call this termcompression workorP–V work.The term

dwnetrepresents any work in addition to compression work that can be done on a non-

simple system. We call it thenet work. Two examples of net work are electrical work

and stress-strain work (stretching a spring or a rubber band). If the volume of a system

is constant,dwdwnetand we can write

wnet,surr≤−∆A (TandVconstant) (4.1-30)