Physical Chemistry Third Edition

152 4 The Thermodynamics of Real Systems

4.1 Criteria for Spontaneous Processes

and for Equilibrium: The Gibbs and

Helmholtz Energies

In Chapters 2 and 3 we presented the fundamental principles of thermodynamics. In

this chapter we use these principles to construct thermodynamic tools with which to

analyze real systems. Learning to use these tools allows you to apply thermodynamics

in a useful way. Someone has facetiously said that the practice of thermodynamics is

like finding the right wrench with which to pound on the right screw.

Criteria for Spontaneous Processes in Closed Systems

The general criterion for spontaneous processes is that the entropy of the universe

must increase. We now express this criterion in terms of the properties of a closed

system that can exchange heat and work with its surroundings. We make the simplest

possible assumption about the surroundings: that the surroundings have a very large

thermal conductivity and a very large heat capacity so that all processes in the surround-

ings are reversible. Equation (3.2-27) asserts that under these conditions all processes

must obey

dS≥

dq

Tsurr



(dU−dw)

Tsurr

(4.1-1)

whereTsurris the temperature of the surroundings and where we have used the first

law to write the second equality. SinceTsurrmust be positive, we can multiply byTsurr

without changing the direction of the inequality, obtaining

dU−dw−TsurrdS≤ 0 (4.1-2)

We now consider several special cases.

The first case is that of anisolated system, which is a closed system that cannot

exchange either heat or work with its surroundings. In this casedq0 anddw0so

thatdU0 and

dS≥0 (isolated system) (4.1-3)

An isolated system is anadiabatic systemwith the additional requirement thatdw0,

so Eq. (4.1-3) is a special case of Eq. (3.2-22) for an adiabatic system.

The second case is thatdS0 anddw0,

dU≤0(Sconstant,dw0) (4.1-4)

This is a case that is not likely to be encountered in thermodynamics since there is no

convenient way to keep the entropy of a system constant while a process occurs.

The third case is that of anisothermal system(constant-temperature system). If

the system is maintained at the constant temperature of the surroundings (TTsurr),

Eq. (4.1-2) becomes

dU−TdS−dw≤0(TTsurrconstant) (4.1-5)