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

Substituting this relation into the preceding equation and dividing each term

by T, we obtain

since

Also,Tis the absolute temperature, which is always positive. Thus,

or

Therefore, work-producing devices such as turbines (wis positive) deliver

more work, and work-consuming devices such as pumps and compressors

(wis negative) require less work when they operate reversibly (Fig. 7–44).

7–11 ■ MINIMIZING THE COMPRESSOR WORK

We have just shown that the work input to a compressor is minimized when

the compression process is executed in an internally reversible manner.

When the changes in kinetic and potential energies are negligible, the com-

pressor work is given by (Eq. 7–53)

(7–56)

Obviously one way of minimizing the compressor work is to approximate

an internally reversible process as much as possible by minimizing the irre-

versibilities such as friction, turbulence, and nonquasi-equilibrium compres-

sion. The extent to which this can be accomplished is limited by economic

considerations. A second (and more practical) way of reducing the compres-

sor work is to keep the specific volume of the gas as small as possible dur-

ing the compression process. This is done by maintaining the temperature of

the gas as low as possible during compression since the specific volume of a

gas is proportional to temperature. Therefore, reducing the work input to a

compressor requires that the gas be cooled as it is compressed.

To have a better understanding of the effect of cooling during the com-

pression process, we compare the work input requirements for three kinds

of processes: an isentropic process (involves no cooling), a polytropic

process(involves some cooling), and an isothermal process(involves maxi-

mum cooling). Assuming all three processes are executed between the same

pressure levels (P 1 and P 2 ) in an internally reversible manner and the gas

behaves as an ideal gas (PvRT) with constant specific heats, we see that

the compression work is determined by performing the integration in Eq.

7–56 for each case, with the following results:

wrev,in

2

1

v¬dP

wrevwact

0 wrev 0 wact

ds

dqact

T

dwrevdwact

T

ds

dqact

T

 0

366 | Thermodynamics

P 1 , T 1

TURBINE

P 2 , T 2

wrev > wact

FIGURE 7–44

A reversible turbine delivers more
work than an irreversible one if both
operate between the same end states.

SEE TUTORIAL CH. 7, SEC. 11 ON THE DVD.

INTERACTIVE

TUTORIAL