Modern Engineering Thermodynamics

13.5 Operating Efficiencies 459
For a Rankine cycle, the prime mover can be assumed to be insulated ( _Q pm = 0), then the prime mover power
output becomes
ð _W pm Þ Rankine = _m ðh 1 − h 2 Þ
and Eq. (7.5) gives the thermal efficiency of a Rankine cycle heat engine as
W
ðη T Þ Rankine = _ pm − j _W p j
= h 1 − h 2 − ðh 4 − h 3 Þ
ð13:3Þ
_Q boiler
h 1 − h 4
13.5 OPERATING EFFICIENCIES
Since no machine is really reversible, we need to develop a method of making accurate power consumption or
production calculations for real irreversible machines. This is usually done through the introduction of an
empirically determined performance measure, called an operating efficiency. Because of the manner in which this
type of technology evolved, several different types of efficiency measures are in common use today.
The physical meaning of an operating efficiency depends on where the system boundaries are drawn. If the system
under consideration consists of only the working fluid, then this efficiency represents the effect of the irreversibilities
that occur only within the working fluid. However, if the system under consideration consists of the entire workproducing
or work-absorbing machine (including the working fluid), then this efficiency represents the effect of the
irreversibilities within the working fluid as well as those within the machine itself (such as bearing friction). To be
effective, an operating efficiency should apply to a system consisting of the device plus the working fluid it contains.
13.5.1 Mechanical Efficiency
The first important measure of the performance of any device is the work transport energy efficiency η W ,which
is defined in Chapter 4 as the ratio of the actual work to the reversible work for a work-producing device:
ðη m Þ workproducing
device
= W actual
W reversible
=
_W actual
_W reversible
or the ratio of the reversible work to the actual work for a work-absorbing device:
ðη m Þ workabsorbing
device
= W reversible
W actual
= _ W reversible
_W actual
This efficiency compares the actual performance of a device with what would occur if the device were reversible
(but not adiabatic), and it is commonly known as the reversible efficiency of the device. However, in mechanical
devices, the source of the internal irreversibilities is primarily mechanical friction. Consequently, it is customary
to refer to the reversible efficiency of a mechanical device as simply the mechanical efficiency of the device and to
use the notation η m instead of η W . The mechanical efficiency of work-producing and work-absorbing devices is
defined mathematically in Table 13.2.
13.5.2 Isentropic Efficiency
Next, we define the isentropic efficiency η s as the ratio of the actual work to the isentropic work for a work-producing
device:
ðη s Þ workproducing
device
= W actual
W isentropic
=
_W actual
_W isentropic
or the ratio of the isentropic work to the actual work for a work-absorbing device:
ðη s Þ workabsorbing
actual
= W isentropic W
= _ isentropic
W actual _W
device
It is similar to the work transport energy efficiency η W , defined in Chapter 4, but whereas η W was based on
comparing the actual performance of the device with what would occur if the device were reversible, the