Modern Engineering Thermodynamics

124 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
4.8 POWER MODES OF ENERGY TRANSPORT
In thermodynamics, the time rate of change of a work mode, dW/dt, iscalledpower, and it represents the power
mode of an energy transport _W. Dividing each of the previous nine differential work mode equations by the time
differential dt produces an equation for the associated power mode. These results, summarized in Table 4.6, are
useful in calculating the power (i.e., work rates) in problems in which continuous rate processes occur. While
continuous rate processes can occur in both closed and open systems, they are more common in open systems.
4.9 WORK EFFICIENCY
Notice that, in all the work mode formulae given so far, no mention was made of the efficiency of the work transport
of energy. This is because all the mechanical and nonmechanical work mode formulae discussed earlier were developed
under the presumption of ideal circumstances, in which there were no friction losses or other inefficiencies
within the system. Under these conditions the work process could ideally be reversed at any time, and all the work
put into a system could be removed again simply by reversing the direction of the generalized force. Therefore, we
call all the mechanical and nonmechanical work (or power) mode formulae developed previously reversible work (or
power) formulae. Consequently—andthisisveryimportant—work or power calculations made with these formulae
do not agree with the measurement of actual work that occurs in a real system. In real systems that absorb work,
more actual work than that calculated from the previous formulae are required to produce the same effect on the system,
and in real work producing systems, less actual work is produced than calculated from the previous formulae.
In the real world, nothing is reversible. Not one of the work modes discussed earlier can actually be carried out
with 100% efficiency. Some are very close to being reversible (i.e., they have very high efficiencies) but none is
completely reversible. This lack of reversibility in the real world is due to a phenomenon of nature that we
describe with the second law of thermodynamics, which is discussed in detail in Chapter 7. Work modes with a
low degree of reversibility (i.e., high irreversibility) are those carried out with systems far from thermodynamic
equilibrium. Heat transfer, rapid chemical reactions (explosions), mechanical friction, and electrical resistance
are all common sources of irreversibility in engineering systems.
Engineers use the concept of a work transport energy conversion efficiency to describe the difference between
reversible and actual work. A general definition of the concept of an energy conversion efficiency is
Energy conversion efficiency = η E =
Desired energy result
Required energy input
(4.70)
Table 4.6 Power Modes of Energy Transport
Work Mode
Power Equation
Mechanical moving boundary
Mechanical rotating shaft
Mechanical elastic
Mechanical surface tension
ð WÞ _ moving
boundary
=p dV
dt
= p V
_
ð WÞ _ rotating
=T
dt
d = Tω
shaft
ð WÞ _ elastic
= −σV dε
dt
= −σV _ε
ð _ WÞ surface
tension
= −σ dA s dt
= −σ s A _
Electrical current
Electrical polarization
ð _ WÞ electrical
current
ð _ WÞ electrical
polarization
= − ϕi
= − E dP
= − E P
dt
_
Magnetic
ð WÞ _ magnetic
= − μ 0 Vð1 + χ m ÞH dH
dt
= − μ 0 Vð1 + χ m ÞH H _
Chemical ð WÞ _
chemical
= −∑μ
dm i i = −∑μ
dt
i
_m i
Mechanochemical
ð WÞ _
mechanochemical
= f dl = fl ⋅
dt