Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

3.10 REVERSIBLE ANDIRREVERSIBLEPROCESSES: GENERALITIES 95

 If a process is carried out adiabatically and has a reversible limit, the work for a given
initial equilibrium state and a given change in the work coordinate is least positive or
most negative in the reversible limit. The dependence of work on the rate of change
of the work coordinate is shown graphically for examples of dissipative work in Figs.
3.11(b) and3.15, and for examples of work with partial energy dissipation in Figs.
3.11(a),3.17, and3.20.
 The number of independent variables needed to describe equilibrium states of a
closed system is one greater than the number of independent work coordinates for
reversible work.^18 Thus, we could choose the independent variables to be each of the
work coordinates and in addition either the temperature or the internal energy.^19 The
number of independent variables needed to describe a nonequilibrium state is greater
(oftenmuchgreater) than this.
Table3.1lists general formulas for various kinds of work, including those that were
described in detail in Secs.3.4–3.8.

Table 3.1 Some kinds of work

Kind Formula Definitions

Linear mechanical work ∂wDFxsurdx FxsurDx-component of force exerted

by surroundings

dxDdisplacement inxdirection

Shaft work ∂wDbd# bDinternal torque at boundary

#Dangle of rotation

Expansion work ∂wDpbdV pbDaverage pressure at moving

boundary

Surface work of a flat surface ∂wD dAs Dsurface tension,AsDsurface area

Stretching or compression ∂wDFdl FDstress (positive for tension,

of a rod or spring negative for compression)

lDlength

Gravitational work ∂wDmgdh mDmass,hDheight

gDacceleration of free fall

Electrical work in a circuit ∂wDÅ ∂Qsys ÅDelectric potential difference

DRL

∂QsysDcharge entering system at right

Electric polarization ∂wDEdpEDelectric field strength

pDelectric dipole moment of system

Magnetization ∂wDBdmBDmagnetic flux density

mDmagnetic dipole moment of system

(^18) If the system has internal adiabatic partitions that allow different phases to have different temperatures in
equilibrium states, then the number of independent variables is equal to the number of work coordinates plus
the number of independent temperatures.
(^19) There may be exceptions to this statement in special cases. For example, along the triple line of a pure
substance the values ofVandT, or ofVandU, are not sufficient to determine the amounts in each of the three
possible phases.