Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

42 THE THERMODYNAMICS OF SIMPLE SYSTEMS

series of brilliant twentieth-century researches by Prigogine (Nobel Prize, 1977) and

coworkers. Here we shall restrict ourselves to uniform systems and processes that

are carried out very slowly so that thermodynamic variables change smoothly and do

not suffer the discontinuities and multiple-valued problems encountered in sudden

processes like explosions.

Each point on ap–Vgraph represents a thermodynamic state. Moving from one

thermodynamic state to another impelled by a change of one or more independent

variables is described as athermodynamic transition. Each transition fromV 1 toV 2

brought about by a change fromp 1 top 2 is represented by a curve on thep–Vgraph.

Real transitions can be carried out very slowly. When this is done, they can be made

to approach a limiting process of an infinitely slow transition that moves from one

state to another by infinitesimal steps, each of which is anequilibrium state. A finite

transition carried out in such a way as to approach an infinite sequence of equilibrium

states is called areversible transition.

All this talk about transitions through equilibrium states is, of course, self-

contradictory; if a state is at equilibrium, it isn’t transiting anywhere.^2 The reversible

process is an idealization which is taken seriously by otherwise skeptical scientists

because it brings the tremendous power of calculus to bear on thermodynamics. With

calculus and the concept of reversible transformations, we can build a majestic frame-

work that encompasses all classical thermodynamic change, including the change in

thermodynamic properties during chemical reactions. In addition to the utility of the

idealized reversible process, it is astonishing how nearly some real chemical systems

can be brought to true reversibility (see especially electrochemistry).

3.6 REVERSIBLE PROCESSES AND PATH INDEPENDENCE

One can determine the change of a thermodynamic state function if one knows the

initial and final states of the system. LetUiandUfbe the energy of a system in its

initial and final states. The change inUis

U=Uf−Ui

NeitherUfnorUiis known (classically) in an absolute sense, but this difficulty is

easily circumvented by definingUi≡0(orUf≡0) in some arbitrary state. Suppose

we define a potential energyUi≡0 in a coordinate system with thezaxis in the

direction of a field. Then we increasezby 1000 meters (lift the mass). This changes

the energy in the field. The unit acceleration in thegravitational fieldis very roughly

10 newtons (N); hence a mass of 1.0 kg increases inpotentialenergy by about

U=mgz=( 1. 0 )10(1000)= 10000 = 104 J=10 kJ

(^2) We ignore quantum fluctuations in classical thermodynamics.