Modern Engineering Thermodynamics

4.7 Nonmechanical Work Modes of Energy Transport 123
When the chemical potential is constant during the mass transfer from state 1 to state 2, Eq. (4.65) can be
integrated to give the chemical work of adding chemical species:
Chemical work of adding chemical species
ð 1 W 2 Þ chemica1
μ i = constant
= −∑ k
i=1
μ i ðm 2 − m 1 Þ i
(4.66)
Chemical work does not include the energy transports produced by chemical reactions, nor does it include the
energy transported across the system boundary with the mass transport itself. Mass flow energy transport is considered
later in this chapter, and the energy transports of chemical reactions are studied in detail in Chapter 9.
The chemical work presented here essentially deals only with those energy transports involved in the mixing or
separating of chemical species.
4.7.5 Mechanochemical Work
Mechanochemical work occurs whenever there is a direct energy conversion from chemical to mechanical energy.
Animal muscles are examples of mechanochemical systems. Small mechanochemical engines have also been
built using this work mode, and Figure 4.18 shows a small hydraulic pump driven by a mechanochemical contractile
fiber. The “fuel” used in mechanochemical engines is not “burned,” as in a standard heat engine. Often
it is merely diluted and a small amount of chemical work is simultaneously extracted.
Mechanochemical work is calculated as basic mechanical work. The generalized force is the intensive property
f, the force generated by or within the mechanochemical system, and the generalized displacement is the extensive
property l, the mechanical displacement of the system. Therefore,
ðdWÞ mechanochemical
= fdl (4.67)
Generally, the mechanochemical force f is not constant during the contraction-expansion cycle, so the total
mechanochemical work must be determined by a careful integration:
Mechanochemical work
ð 1 W 2 Þ mechanochemical =
Z 2
1
fdl
(4.68)
Note that, since the mechanochemical force comes from inside the system, a negative sign is not needed in Eqs. (4.67)
and (4.68).
A system may be exposed to only one of these work modes of energy transport,
or it may be exposed to several of them simultaneously. Since work is
an additive quantity, to get the total (or net) work of a system that has more
than one work mode present, we simply add all these work terms together:
Total differential work of all the work modes present
ðdWÞ total = pdV + T .dθ − σ dε − σ s dA
− ϕidt− EdP− μ 0 HdðVMÞ −∑ k
i =1
μ i dm i +fdl + ::: (4.69)
It is generally the engineer’s responsibility to determine the number and
type of work modes present in any problem statement or real world situation.
Often, the work modes of a problem are affected by how the system
boundaries are drawn (recall that boundary definition is a prerogative of the
problem solver). For example, if a system contains an electrical heater, then
electrical current work is done on the system. However, if the boundary is
drawn to exclude the heating element itself, then no electrical work occurs
and the energy transport becomes a heat transport from the surface of the
heating element into the system.
r 2 < r 1
Water
Collagen
B
strip
r 1 Coupling
belt
A
Concentrated LiBr solution
FIGURE 4.18
A simple mechanochemical Katchalsky engine.