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

The size of the colored area (the saved work input) varies with the value

of the intermediate pressure Px, and it is of practical interest to determine

the conditions under which this area is maximized. The total work input for

a two-stage compressor is the sum of the work inputs for each stage of com-

pression, as determined from Eq. 7–57b:

(7–58)

The only variable in this equation is Px. The Pxvalue that minimizes the

total work is determined by differentiating this expression with respect to Px

and setting the resulting expression equal to zero. It yields

(7–59)

That is,to minimize compression work during two-stage compression, the

pressure ratio across each stage of the compressor must be the same. When

this condition is satisfied, the compression work at each stage becomes

identical, that is,wcomp I,inwcomp II,in.

Px 1 P 1 P 221 >^2 ¬or¬

Px

P 1



P 2

Px



nRT 1

n 1

ca

Px

P 1

b

1 n 1 2>n

 1 d

nRT 1

n 1

ca

P 2

Px

b

1 n 1 2>n

 1 d

wcomp,inwcomp I,in
wcomp II,in

368 | Thermodynamics

P

1

P 2

P 1

Isothermal

Px

Polytropic

Work saved

Intercooling

2

T

s

1

T 1

Intercooling

2

P 2

P 1

Px

v

FIGURE 7–46

P-vand T-sdiagrams for a two-stage

steady-flow compression process.

EXAMPLE 7–13 Work Input for Various Compression Processes

Air is compressed steadily by a reversible compressor from an inlet state of

100 kPa and 300 K to an exit pressure of 900 kPa. Determine the compressor

work per unit mass for (a) isentropic compression with k1.4, (b) polytropic

compression with n1.3, (c) isothermal compression, and (d) ideal two-

stage compression with intercooling with a polytropic exponent of 1.3.

Solution Air is compressed reversibly from a specified state to a specified

pressure. The compressor work is to be determined for the cases of

isentropic, polytropic, isothermal, and two-stage compression.