Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

That is, engine Ais converting 60 percent of the available work potential to
useful work. This ratio is only 43 percent for engine B.
The second-law efficiency can also be expressed as the ratio of the useful
work output and the maximum possible (reversible) work output:

(8–7)

This definition is more general since it can be applied to processes (in tur-
bines, piston–cylinder devices, etc.) as well as to cycles. Note that the second-
law efficiency cannot exceed 100 percent (Fig. 8–17).
We can also define a second-law efficiency for work-consuming noncyclic
(such as compressors) and cyclic (such as refrigerators) devices as the ratio
of the minimum (reversible) work input to the useful work input:

(8–8)

For cyclic devices such as refrigerators and heat pumps, it can also be
expressed in terms of the coefficients of performance as

(8–9)

Again, because of the way we defined the second-law efficiency, its value
cannot exceed 100 percent. In the above relations, the reversible work Wrev
should be determined by using the same initial and final states as in the
actual process.
The definitions above for the second-law efficiency do not apply to devices
that are not intended to produce or consume work. Therefore, we need a more
general definition. However, there is some disagreement on a general defini-
tion of the second-law efficiency, and thus a person may encounter different
definitions for the same device. The second-law efficiency is intended to serve
as a measure of approximation to reversible operation, and thus its value
should range from zero in the worst case (complete destruction of exergy) to
one in the best case (no destruction of exergy). With this in mind, we define
the second-law efficiency of a system during a process as (Fig. 8–18)

(8–10)

Therefore, when determining the second-law efficiency, the first thing we
need to do is determine how much exergy or work potential is consumed
during a process. In a reversible operation, we should be able to recover
entirely the exergy supplied during the process, and the irreversibility in this
case should be zero. The second-law efficiency is zero when we recover
none of the exergy supplied to the system. Note that the exergy can be sup-
plied or recovered at various amounts in various forms such as heat, work,
kinetic energy, potential energy, internal energy, and enthalpy. Sometimes
there are differing (though valid) opinions on what constitutes supplied
exergy, and this causes differing definitions for second-law efficiency. At all
times, however, the exergy recovered and the exergy destroyed (the irre-
versibility) must add up to the exergy supplied. Also, we need to define the
system precisely in order to identify correctly any interactions between the
system and its surroundings.

hII

Exergy recovered

Exergy supplied

 1 

Exergy destroyed

Exergy supplied

hII

COP

COPrev

¬¬ 1 refrigerators and heat pumps 2

hII

Wrev

Wu

¬¬ 1 work-consuming devices 2

hII

Wu

Wrev

¬¬ 1 work-producing devices 2

Chapter 8 | 433

ηΙΙ 100%

ηrev = 70%

ηth = 70%

Source

1000 K

Sink

300 K

FIGURE 8–17

Second-law efficiency of all reversible

devices is 100 percent.

Atmosphere

25 °C

Heat

Hot

water

80 °C

FIGURE 8–18

The second-law efficiency of naturally

occurring processes is zero if none of

the work potential is recovered.