Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.10 REVERSIBLE ANDIRREVERSIBLEPROCESSES: GENERALITIES 94

hdV=dti

w

bc

bc

compression

expansion

Figure 3.20 Adiabatic expansion work with internal friction for a fixed magnitude of

ÅV, as a function of the average rate of volume change. The open circles indicate the

reversible limits.

wexDwirrwrev. The excess work and frictional work are not equal, because the thermal
energy released by frictional work increases the gas pressure, makingwexless thanwfricfor
expansion and greater thanwfricfor compression. There seems to be no general method by
which the energy dissipated by internal friction can be evaluated, and it would be even more
difficult for an irreversible process with both work and heat.
Figure3.20shows the effect of the rate of change of the volume on the adiabatic work
for a fixed magnitude of the volume change. Note that the work of expansion and the work
of compression have opposite signs, and that it is only in the reversible limit that they have
the samemagnitude. The figure resembles Fig.3.17for electrical work of a galvanic cell
with the horizontal axis reversed, and is typical of irreversible work with partial energy
dissipation.

3.10 Reversible and Irreversible Processes: Generalities

This section summarizes some general characteristics of processes in closed systems. Some
of these statements will be needed to develop aspects of the second law in Chap. 4.

 Infinitesimal quantities of work during a process are calculated from an expression of

the form∂wD

P

iYidXi, whereXiis the work coordinate of kind of workiand

Yiis the conjugate work coefficient.

 The work coefficients and work coordinates ofreversiblework are state functions.

 Energy transferred across the boundary by work in a reversible process is fully recov-

ered as work of the opposite sign in the reverse reversible process. It follows from

the first law that heat is also fully recovered in the reverse process.

 When work occurs irreversibly at a finite rate, there is partial or complete dissipation

of energy. The dissipation results in a change that could also be accomplished with

positive heat, such as an increase of thermal energy within the system.

 Dissipative work is positive irreversible work with complete energy dissipation. The

work coordinate for this type of work is not a state function. Examples are stirring

work (Sec.3.7.1) and the work of electrical heating (Sec.3.8.2).